mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -648,7 +648,7 @@ theorem exists_subset_affineIndependent_affineSpan_eq_top {s : Set P}
 
 variable (k V)
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 #print exists_affineIndependent /-
 theorem exists_affineIndependent (s : Set P) :
     ∃ (t : _) (_ : t ⊆ s), affineSpan k t = affineSpan k s ∧ AffineIndependent k (coe : t → P) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -87,8 +87,8 @@ theorem affineIndependent_iff_of_fintype [Fintype ι] (p : ι → P) :
   constructor
   · exact fun h w hw hs i => h Finset.univ w hw hs i (Finset.mem_univ _)
   · intro h s w hw hs i hi
-    rw [Finset.weightedVSub_indicator_subset _ _ (Finset.subset_univ s)] at hs 
-    rw [Finset.sum_indicator_subset _ (Finset.subset_univ s)] at hw 
+    rw [Finset.weightedVSub_indicator_subset _ _ (Finset.subset_univ s)] at hs
+    rw [Finset.sum_indicator_subset _ (Finset.subset_univ s)] at hw
     replace h := h ((↑s : Set ι).indicator w) hw hs i
     simpa [hi] using h
 #align affine_independent_iff_of_fintype affineIndependent_iff_of_fintype
@@ -136,17 +136,17 @@ theorem affineIndependent_iff_linearIndependent_vsub (p : ι → P) (i1 : ι) :
       exact hg
     exact h s2 f hf hs2 i (Finset.mem_insert_of_mem (Finset.mem_map.2 ⟨i, hi, rfl⟩))
   · intro h
-    rw [linearIndependent_iff'] at h 
+    rw [linearIndependent_iff'] at h
     intro s w hw hs i hi
     rw [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero s w p hw (p i1), ←
-      s.weighted_vsub_of_point_erase w p i1, Finset.weightedVSubOfPoint_apply] at hs 
+      s.weighted_vsub_of_point_erase w p i1, Finset.weightedVSubOfPoint_apply] at hs
     let f : ι → V := fun i => w i • (p i -ᵥ p i1)
     have hs2 : ∑ i in (s.erase i1).Subtype fun i => i ≠ i1, f i = 0 :=
       by
       rw [← hs]
       convert Finset.sum_subtype_of_mem f fun x => Finset.ne_of_mem_erase
     have h2 := h ((s.erase i1).Subtype fun i => i ≠ i1) (fun x => w x) hs2
-    simp_rw [Finset.mem_subtype] at h2 
+    simp_rw [Finset.mem_subtype] at h2
     have h2b : ∀ i ∈ s, i ≠ i1 → w i = 0 := fun i his hi =>
       h2 ⟨i, hi⟩ (Finset.mem_erase_of_ne_of_mem hi his)
     exact Finset.eq_zero_of_sum_eq_zero hw h2b i hi
@@ -219,15 +219,15 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
     ext i
     by_cases hi : i ∈ s1 ∪ s2
     · rw [← sub_eq_zero]
-      rw [Finset.sum_indicator_subset _ (Finset.subset_union_left s1 s2)] at hw1 
-      rw [Finset.sum_indicator_subset _ (Finset.subset_union_right s1 s2)] at hw2 
+      rw [Finset.sum_indicator_subset _ (Finset.subset_union_left s1 s2)] at hw1
+      rw [Finset.sum_indicator_subset _ (Finset.subset_union_right s1 s2)] at hw2
       have hws : ∑ i in s1 ∪ s2, (Set.indicator (↑s1) w1 - Set.indicator (↑s2) w2) i = 0 := by
         simp [hw1, hw2]
       rw [Finset.affineCombination_indicator_subset _ _ (Finset.subset_union_left s1 s2),
         Finset.affineCombination_indicator_subset _ _ (Finset.subset_union_right s1 s2), ←
-        @vsub_eq_zero_iff_eq V, Finset.affineCombination_vsub] at heq 
+        @vsub_eq_zero_iff_eq V, Finset.affineCombination_vsub] at heq
       exact ha (s1 ∪ s2) (Set.indicator (↑s1) w1 - Set.indicator (↑s2) w2) hws HEq i hi
-    · rw [← Finset.mem_coe, Finset.coe_union] at hi 
+    · rw [← Finset.mem_coe, Finset.coe_union] at hi
       simp [mt (Set.mem_union_left ↑s2) hi, mt (Set.mem_union_right ↑s1) hi]
   · intro ha s w hw hs i0 hi0
     let w1 : ι → k := Function.update (Function.const ι 0) i0 1
@@ -242,7 +242,7 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
       simp [w2, ← Finset.weightedVSub_vadd_affineCombination, hs, hw1s]
     replace ha := ha s s w2 w1 hw2 hw1 (hw1s.symm ▸ hw2s)
     have hws : w2 i0 - w1 i0 = 0 := by
-      rw [← Finset.mem_coe] at hi0 
+      rw [← Finset.mem_coe] at hi0
       rw [← Set.indicator_of_mem hi0 w2, ← Set.indicator_of_mem hi0 w1, ha, sub_self]
     simpa [w2] using hws
 #align affine_independent_iff_indicator_eq_of_affine_combination_eq affineIndependent_iff_indicator_eq_of_affineCombination_eq
@@ -264,11 +264,11 @@ theorem affineIndependent_iff_eq_of_fintype_affineCombination_eq [Fintype ι] (p
     simpa only [Set.indicator_univ, Finset.coe_univ] using h _ _ w1 w2 hw1 hw2 hweq
   · intro h s1 s2 w1 w2 hw1 hw2 hweq
     have hw1' : ∑ i, (s1 : Set ι).indicator w1 i = 1 := by
-      rwa [Finset.sum_indicator_subset _ (Finset.subset_univ s1)] at hw1 
+      rwa [Finset.sum_indicator_subset _ (Finset.subset_univ s1)] at hw1
     have hw2' : ∑ i, (s2 : Set ι).indicator w2 i = 1 := by
-      rwa [Finset.sum_indicator_subset _ (Finset.subset_univ s2)] at hw2 
+      rwa [Finset.sum_indicator_subset _ (Finset.subset_univ s2)] at hw2
     rw [Finset.affineCombination_indicator_subset w1 p (Finset.subset_univ s1),
-      Finset.affineCombination_indicator_subset w2 p (Finset.subset_univ s2)] at hweq 
+      Finset.affineCombination_indicator_subset w2 p (Finset.subset_univ s2)] at hweq
     exact h _ _ hw1' hw2' hweq
 #align affine_independent_iff_eq_of_fintype_affine_combination_eq affineIndependent_iff_eq_of_fintype_affineCombination_eq
 -/
@@ -306,7 +306,7 @@ protected theorem AffineIndependent.injective [Nontrivial k] {p : ι → P}
     (ha : AffineIndependent k p) : Function.Injective p :=
   by
   intro i j hij
-  rw [affineIndependent_iff_linearIndependent_vsub _ _ j] at ha 
+  rw [affineIndependent_iff_linearIndependent_vsub _ _ j] at ha
   by_contra hij'
   exact ha.ne_zero ⟨i, hij'⟩ (vsub_eq_zero_iff_eq.mpr hij)
 #align affine_independent.injective AffineIndependent.injective
@@ -409,7 +409,7 @@ theorem AffineIndependent.of_comp {p : ι → P} (f : P →ᵃ[k] P₂) (hai : A
   obtain ⟨i⟩ := h
   rw [affineIndependent_iff_linearIndependent_vsub k p i]
   simp_rw [affineIndependent_iff_linearIndependent_vsub k (f ∘ p) i, Function.comp_apply, ←
-    f.linear_map_vsub] at hai 
+    f.linear_map_vsub] at hai
   exact LinearIndependent.of_comp f.linear hai
 #align affine_independent.of_comp AffineIndependent.of_comp
 -/
@@ -422,7 +422,7 @@ theorem AffineIndependent.map' {p : ι → P} (hai : AffineIndependent k p) (f :
   by
   cases' isEmpty_or_nonempty ι with h h; · haveI := h; apply affineIndependent_of_subsingleton
   obtain ⟨i⟩ := h
-  rw [affineIndependent_iff_linearIndependent_vsub k p i] at hai 
+  rw [affineIndependent_iff_linearIndependent_vsub k p i] at hai
   simp_rw [affineIndependent_iff_linearIndependent_vsub k (f ∘ p) i, Function.comp_apply, ←
     f.linear_map_vsub]
   have hf' : f.linear.ker = ⊥ := by rwa [LinearMap.ker_eq_bot, f.linear_injective_iff]
@@ -467,16 +467,16 @@ theorem AffineIndependent.exists_mem_inter_of_exists_mem_inter_affineSpan [Nontr
     (ha : AffineIndependent k p) {s1 s2 : Set ι} {p0 : P} (hp0s1 : p0 ∈ affineSpan k (p '' s1))
     (hp0s2 : p0 ∈ affineSpan k (p '' s2)) : ∃ i : ι, i ∈ s1 ∩ s2 :=
   by
-  rw [Set.image_eq_range] at hp0s1 hp0s2 
+  rw [Set.image_eq_range] at hp0s1 hp0s2
   rw [mem_affineSpan_iff_eq_affineCombination, ←
-    Finset.eq_affineCombination_subset_iff_eq_affineCombination_subtype] at hp0s1 hp0s2 
+    Finset.eq_affineCombination_subset_iff_eq_affineCombination_subtype] at hp0s1 hp0s2
   rcases hp0s1 with ⟨fs1, hfs1, w1, hw1, hp0s1⟩
   rcases hp0s2 with ⟨fs2, hfs2, w2, hw2, hp0s2⟩
-  rw [affineIndependent_iff_indicator_eq_of_affineCombination_eq] at ha 
+  rw [affineIndependent_iff_indicator_eq_of_affineCombination_eq] at ha
   replace ha := ha fs1 fs2 w1 w2 hw1 hw2 (hp0s1 ▸ hp0s2)
   have hnz : ∑ i in fs1, w1 i ≠ 0 := hw1.symm ▸ one_ne_zero
   rcases Finset.exists_ne_zero_of_sum_ne_zero hnz with ⟨i, hifs1, hinz⟩
-  simp_rw [← Set.indicator_of_mem (Finset.mem_coe.2 hifs1) w1, ha] at hinz 
+  simp_rw [← Set.indicator_of_mem (Finset.mem_coe.2 hifs1) w1, ha] at hinz
   use i, hfs1 hifs1, hfs2 (Set.mem_of_indicator_ne_zero hinz)
 #align affine_independent.exists_mem_inter_of_exists_mem_inter_affine_span AffineIndependent.exists_mem_inter_of_exists_mem_inter_affineSpan
 -/
@@ -509,7 +509,7 @@ protected theorem AffineIndependent.mem_affineSpan_iff [Nontrivial k] {p : ι 
     have h :=
       AffineIndependent.exists_mem_inter_of_exists_mem_inter_affineSpan ha hs
         (mem_affineSpan k (Set.mem_image_of_mem _ (Set.mem_singleton _)))
-    rwa [← Set.nonempty_def, Set.inter_singleton_nonempty] at h 
+    rwa [← Set.nonempty_def, Set.inter_singleton_nonempty] at h
   · exact fun h => mem_affineSpan k (Set.mem_image_of_mem p h)
 #align affine_independent.mem_affine_span_iff AffineIndependent.mem_affineSpan_iff
 -/
@@ -529,11 +529,11 @@ theorem exists_nontrivial_relation_sum_zero_of_not_affine_ind {t : Finset V}
     (h : ¬AffineIndependent k (coe : t → V)) :
     ∃ f : V → k, ∑ e in t, f e • e = 0 ∧ ∑ e in t, f e = 0 ∧ ∃ x ∈ t, f x ≠ 0 := by
   classical
-  rw [affineIndependent_iff_of_fintype] at h 
-  simp only [exists_prop, Classical.not_forall] at h 
+  rw [affineIndependent_iff_of_fintype] at h
+  simp only [exists_prop, Classical.not_forall] at h
   obtain ⟨w, hw, hwt, i, hi⟩ := h
   simp only [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero _ w (coe : t → V) hw 0,
-    vsub_eq_sub, Finset.weightedVSubOfPoint_apply, sub_zero] at hwt 
+    vsub_eq_sub, Finset.weightedVSubOfPoint_apply, sub_zero] at hwt
   let f : ∀ x : V, x ∈ t → k := fun x hx => w ⟨x, hx⟩
   refine' ⟨fun x => if hx : x ∈ t then f x hx else (0 : k), _, _, by use i; simp [hi, f]⟩
   suffices (∑ e : V in t, dite (e ∈ t) (fun hx => f e hx • e) fun hx => 0) = 0 by convert this; ext;
@@ -567,7 +567,7 @@ theorem weightedVSub_mem_vectorSpan_pair {p : ι → P} (h : AffineIndependent k
   refine' ⟨fun h => _, fun h => _⟩
   · rcases h with ⟨r, hr⟩
     refine' ⟨r, fun i hi => _⟩
-    rw [s.affine_combination_vsub, ← s.weighted_vsub_const_smul, ← sub_eq_zero, ← map_sub] at hr 
+    rw [s.affine_combination_vsub, ← s.weighted_vsub_const_smul, ← sub_eq_zero, ← map_sub] at hr
     have hw' : ∑ j in s, (r • (w₁ - w₂) - w) j = 0 := by
       simp_rw [Pi.sub_apply, Pi.smul_apply, Pi.sub_apply, smul_sub, Finset.sum_sub_distrib, ←
         Finset.smul_sum, hw, hw₁, hw₂, sub_self]
@@ -577,7 +577,7 @@ theorem weightedVSub_mem_vectorSpan_pair {p : ι → P} (h : AffineIndependent k
   · rcases h with ⟨r, hr⟩
     refine' ⟨r, _⟩
     let w' i := r * (w₁ i - w₂ i)
-    change ∀ i ∈ s, w i = w' i at hr 
+    change ∀ i ∈ s, w i = w' i at hr
     rw [s.weighted_vsub_congr hr fun _ _ => rfl, s.affine_combination_vsub, ←
       s.weighted_vsub_const_smul]
     congr
@@ -624,21 +624,21 @@ theorem exists_subset_affineIndependent_affineSpan_eq_top {s : Set P}
     let hsv := Basis.ofVectorSpace k V
     have hsvi := hsv.linear_independent
     have hsvt := hsv.span_eq
-    rw [Basis.coe_ofVectorSpace] at hsvi hsvt 
+    rw [Basis.coe_ofVectorSpace] at hsvi hsvt
     have h0 : ∀ v : V, v ∈ Basis.ofVectorSpaceIndex _ _ → v ≠ 0 := by intro v hv;
       simpa using hsv.ne_zero ⟨v, hv⟩
-    rw [linearIndependent_set_iff_affineIndependent_vadd_union_singleton k h0 p₁] at hsvi 
+    rw [linearIndependent_set_iff_affineIndependent_vadd_union_singleton k h0 p₁] at hsvi
     exact
       ⟨{p₁} ∪ (fun v => v +ᵥ p₁) '' _, Set.empty_subset _, hsvi,
         affineSpan_singleton_union_vadd_eq_top_of_span_eq_top p₁ hsvt⟩
-  · rw [affineIndependent_set_iff_linearIndependent_vsub k hp₁] at h 
+  · rw [affineIndependent_set_iff_linearIndependent_vsub k hp₁] at h
     let bsv := Basis.extend h
     have hsvi := bsv.linear_independent
     have hsvt := bsv.span_eq
-    rw [Basis.coe_extend] at hsvi hsvt 
+    rw [Basis.coe_extend] at hsvi hsvt
     have hsv := h.subset_extend (Set.subset_univ _)
     have h0 : ∀ v : V, v ∈ h.extend _ → v ≠ 0 := by intro v hv; simpa using bsv.ne_zero ⟨v, hv⟩
-    rw [linearIndependent_set_iff_affineIndependent_vadd_union_singleton k h0 p₁] at hsvi 
+    rw [linearIndependent_set_iff_affineIndependent_vadd_union_singleton k h0 p₁] at hsvi
     refine' ⟨{p₁} ∪ (fun v => v +ᵥ p₁) '' h.extend (Set.subset_univ _), _, _⟩
     · refine' Set.Subset.trans _ (Set.union_subset_union_right _ (Set.image_subset _ hsv))
       simp [Set.image_image]
@@ -657,11 +657,11 @@ theorem exists_affineIndependent (s : Set P) :
   · exact ⟨∅, Set.empty_subset ∅, rfl, affineIndependent_of_subsingleton k _⟩
   obtain ⟨b, hb₁, hb₂, hb₃⟩ := exists_linearIndependent k ((Equiv.vaddConst p).symm '' s)
   have hb₀ : ∀ v : V, v ∈ b → v ≠ 0 := fun v hv => hb₃.ne_zero (⟨v, hv⟩ : b)
-  rw [linearIndependent_set_iff_affineIndependent_vadd_union_singleton k hb₀ p] at hb₃ 
+  rw [linearIndependent_set_iff_affineIndependent_vadd_union_singleton k hb₀ p] at hb₃
   refine' ⟨{p} ∪ Equiv.vaddConst p '' b, _, _, hb₃⟩
   · apply Set.union_subset (set.singleton_subset_iff.mpr hp)
     rwa [← (Equiv.vaddConst p).subset_symm_image b s]
-  · rw [Equiv.coe_vaddConst_symm, ← vectorSpan_eq_span_vsub_set_right k hp] at hb₂ 
+  · rw [Equiv.coe_vaddConst_symm, ← vectorSpan_eq_span_vsub_set_right k hp] at hb₂
     apply AffineSubspace.ext_of_direction_eq
     · have : Submodule.span k b = Submodule.span k (insert 0 b) := by simp
       simp only [direction_affineSpan, ← hb₂, Equiv.coe_vaddConst, Set.singleton_union,
@@ -717,15 +717,15 @@ theorem AffineIndependent.affineIndependent_of_not_mem_span {p : ι → P} {i :
     have hw' : ∑ x in s', w' x = 1 :=
       by
       simp_rw [w', Finset.sum_subtype_eq_sum_filter]
-      rw [← s.sum_filter_add_sum_filter_not (· ≠ i)] at hwm 
+      rw [← s.sum_filter_add_sum_filter_not (· ≠ i)] at hwm
       simp_rw [Classical.not_not, Finset.filter_eq', if_pos his.1, Finset.sum_singleton, ← wm, hwmi,
-        ← sub_eq_add_neg, sub_eq_zero] at hwm 
+        ← sub_eq_add_neg, sub_eq_zero] at hwm
       exact hwm
     rw [← s.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one hms his.1 hwmi, ←
       (Subtype.range_coe : _ = {x | x ≠ i}), ← Set.range_comp, ←
       s.affine_combination_subtype_eq_filter]
     exact affineCombination_mem_affineSpan hw' p'
-  · rw [not_and_or, Classical.not_not] at his 
+  · rw [not_and_or, Classical.not_not] at his
     let w' : { y // y ≠ i } → k := fun x => w x
     have hw' : ∑ x in s', w' x = 0 :=
       by
@@ -741,7 +741,7 @@ theorem AffineIndependent.affineIndependent_of_not_mem_span {p : ι → P} {i :
       exact hwx (his.neg_resolve_left hxs)
     intro j hj
     by_cases hji : j = i
-    · rw [hji] at hj 
+    · rw [hji] at hj
       exact hji.symm ▸ his.neg_resolve_left hj
     · exact ha s' w' hw' hs' ⟨j, hji⟩ (Finset.mem_subtype.2 hj)
 #align affine_independent.affine_independent_of_not_mem_span AffineIndependent.affineIndependent_of_not_mem_span
@@ -822,9 +822,9 @@ theorem sign_eq_of_affineCombination_mem_affineSpan_pair {p : ι → P} (h : Aff
     (hij : SignType.sign (w₂ i) = SignType.sign (w₂ j)) :
     SignType.sign (w i) = SignType.sign (w j) :=
   by
-  rw [affineCombination_mem_affineSpan_pair h hw hw₁ hw₂] at hs 
+  rw [affineCombination_mem_affineSpan_pair h hw hw₁ hw₂] at hs
   rcases hs with ⟨r, hr⟩
-  dsimp only at hr 
+  dsimp only at hr
   rw [hr i hi, hr j hj, hi0, hj0, add_zero, add_zero, sub_zero, sub_zero, sign_mul, sign_mul, hij]
 #align sign_eq_of_affine_combination_mem_affine_span_pair sign_eq_of_affineCombination_mem_affineSpan_pair
 -/
@@ -842,7 +842,7 @@ theorem sign_eq_of_affineCombination_mem_affineSpan_single_lineMap {p : ι → P
     SignType.sign (w i₂) = SignType.sign (w i₃) := by
   classical
   rw [← s.affine_combination_affine_combination_single_weights k p h₁, ←
-    s.affine_combination_affine_combination_line_map_weights p h₂ h₃ c] at hs 
+    s.affine_combination_affine_combination_line_map_weights p h₂ h₃ c] at hs
   refine'
     sign_eq_of_affineCombination_mem_affineSpan_pair h hw
       (s.sum_affine_combination_single_weights k h₁)
@@ -1058,16 +1058,16 @@ theorem centroid_eq_iff [CharZero k] {n : ℕ} (s : Simplex k P n) {fs₁ fs₂
   by
   refine' ⟨fun h => _, congr_arg _⟩
   rw [Finset.centroid_eq_affineCombination_fintype, Finset.centroid_eq_affineCombination_fintype] at
-    h 
+    h
   have ha :=
     (affineIndependent_iff_indicator_eq_of_affineCombination_eq k s.points).1 s.independent _ _ _ _
       (fs₁.sum_centroid_weights_indicator_eq_one_of_card_eq_add_one k h₁)
       (fs₂.sum_centroid_weights_indicator_eq_one_of_card_eq_add_one k h₂) h
   simp_rw [Finset.coe_univ, Set.indicator_univ, Function.funext_iff,
-    Finset.centroidWeightsIndicator_def, Finset.centroidWeights, h₁, h₂] at ha 
+    Finset.centroidWeightsIndicator_def, Finset.centroidWeights, h₁, h₂] at ha
   ext i
   specialize ha i
-  have key : ∀ n : ℕ, (n : k) + 1 ≠ 0 := fun n h => by norm_cast at h 
+  have key : ∀ n : ℕ, (n : k) + 1 ≠ 0 := fun n h => by norm_cast at h
   -- we should be able to golf this to `refine ⟨λ hi, decidable.by_contradiction (λ hni, _), ...⟩`,
       -- but for some unknown reason it doesn't work.
       constructor <;>
@@ -1098,7 +1098,7 @@ theorem centroid_eq_of_range_eq {n : ℕ} {s₁ s₂ : Simplex k P n}
     (h : Set.range s₁.points = Set.range s₂.points) :
     Finset.univ.centroid k s₁.points = Finset.univ.centroid k s₂.points :=
   by
-  rw [← Set.image_univ, ← Set.image_univ, ← Finset.coe_univ] at h 
+  rw [← Set.image_univ, ← Set.image_univ, ← Finset.coe_univ] at h
   exact
     finset.univ.centroid_eq_of_inj_on_of_image_eq k _
       (fun _ _ _ _ he => AffineIndependent.injective s₁.independent he)

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -100,6 +100,56 @@ from a base point in that family are linearly independent. -/
 theorem affineIndependent_iff_linearIndependent_vsub (p : ι → P) (i1 : ι) :
     AffineIndependent k p ↔ LinearIndependent k fun i : { x // x ≠ i1 } => (p i -ᵥ p i1 : V) := by
   classical
+  constructor
+  · intro h
+    rw [linearIndependent_iff']
+    intro s g hg i hi
+    set f : ι → k := fun x => if hx : x = i1 then -∑ y in s, g y else g ⟨x, hx⟩ with hfdef
+    let s2 : Finset ι := insert i1 (s.map (embedding.subtype _))
+    have hfg : ∀ x : { x // x ≠ i1 }, g x = f x :=
+      by
+      intro x
+      rw [hfdef]
+      dsimp only
+      erw [dif_neg x.property, Subtype.coe_eta]
+    rw [hfg]
+    have hf : ∑ ι in s2, f ι = 0 :=
+      by
+      rw [Finset.sum_insert
+          (Finset.not_mem_map_subtype_of_not_property s (Classical.not_not.2 rfl)),
+        Finset.sum_subtype_map_embedding fun x hx => (hfg x).symm]
+      rw [hfdef]
+      dsimp only
+      rw [dif_pos rfl]
+      exact neg_add_self _
+    have hs2 : s2.weighted_vsub p f = (0 : V) :=
+      by
+      set f2 : ι → V := fun x => f x • (p x -ᵥ p i1) with hf2def
+      set g2 : { x // x ≠ i1 } → V := fun x => g x • (p x -ᵥ p i1) with hg2def
+      have hf2g2 : ∀ x : { x // x ≠ i1 }, f2 x = g2 x :=
+        by
+        simp_rw [hf2def, hg2def, hfg]
+        exact fun x => rfl
+      rw [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero s2 f p hf (p i1),
+        Finset.weightedVSubOfPoint_insert, Finset.weightedVSubOfPoint_apply,
+        Finset.sum_subtype_map_embedding fun x hx => hf2g2 x]
+      exact hg
+    exact h s2 f hf hs2 i (Finset.mem_insert_of_mem (Finset.mem_map.2 ⟨i, hi, rfl⟩))
+  · intro h
+    rw [linearIndependent_iff'] at h 
+    intro s w hw hs i hi
+    rw [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero s w p hw (p i1), ←
+      s.weighted_vsub_of_point_erase w p i1, Finset.weightedVSubOfPoint_apply] at hs 
+    let f : ι → V := fun i => w i • (p i -ᵥ p i1)
+    have hs2 : ∑ i in (s.erase i1).Subtype fun i => i ≠ i1, f i = 0 :=
+      by
+      rw [← hs]
+      convert Finset.sum_subtype_of_mem f fun x => Finset.ne_of_mem_erase
+    have h2 := h ((s.erase i1).Subtype fun i => i ≠ i1) (fun x => w x) hs2
+    simp_rw [Finset.mem_subtype] at h2 
+    have h2b : ∀ i ∈ s, i ≠ i1 → w i = 0 := fun i his hi =>
+      h2 ⟨i, hi⟩ (Finset.mem_erase_of_ne_of_mem hi his)
+    exact Finset.eq_zero_of_sum_eq_zero hw h2b i hi
 #align affine_independent_iff_linear_independent_vsub affineIndependent_iff_linearIndependent_vsub
 -/
 
@@ -162,7 +212,39 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
           ∑ i in s2, w2 i = 1 →
             s1.affineCombination k p w1 = s2.affineCombination k p w2 →
               Set.indicator (↑s1) w1 = Set.indicator (↑s2) w2 :=
-  by classical
+  by
+  classical
+  constructor
+  · intro ha s1 s2 w1 w2 hw1 hw2 heq
+    ext i
+    by_cases hi : i ∈ s1 ∪ s2
+    · rw [← sub_eq_zero]
+      rw [Finset.sum_indicator_subset _ (Finset.subset_union_left s1 s2)] at hw1 
+      rw [Finset.sum_indicator_subset _ (Finset.subset_union_right s1 s2)] at hw2 
+      have hws : ∑ i in s1 ∪ s2, (Set.indicator (↑s1) w1 - Set.indicator (↑s2) w2) i = 0 := by
+        simp [hw1, hw2]
+      rw [Finset.affineCombination_indicator_subset _ _ (Finset.subset_union_left s1 s2),
+        Finset.affineCombination_indicator_subset _ _ (Finset.subset_union_right s1 s2), ←
+        @vsub_eq_zero_iff_eq V, Finset.affineCombination_vsub] at heq 
+      exact ha (s1 ∪ s2) (Set.indicator (↑s1) w1 - Set.indicator (↑s2) w2) hws HEq i hi
+    · rw [← Finset.mem_coe, Finset.coe_union] at hi 
+      simp [mt (Set.mem_union_left ↑s2) hi, mt (Set.mem_union_right ↑s1) hi]
+  · intro ha s w hw hs i0 hi0
+    let w1 : ι → k := Function.update (Function.const ι 0) i0 1
+    have hw1 : ∑ i in s, w1 i = 1 := by
+      rw [Finset.sum_update_of_mem hi0, Finset.sum_const_zero, add_zero]
+    have hw1s : s.affine_combination k p w1 = p i0 :=
+      s.affine_combination_of_eq_one_of_eq_zero w1 p hi0 (Function.update_same _ _ _) fun _ _ hne =>
+        Function.update_noteq hne _ _
+    let w2 := w + w1
+    have hw2 : ∑ i in s, w2 i = 1 := by simp [w2, Finset.sum_add_distrib, hw, hw1]
+    have hw2s : s.affine_combination k p w2 = p i0 := by
+      simp [w2, ← Finset.weightedVSub_vadd_affineCombination, hs, hw1s]
+    replace ha := ha s s w2 w1 hw2 hw1 (hw1s.symm ▸ hw2s)
+    have hws : w2 i0 - w1 i0 = 0 := by
+      rw [← Finset.mem_coe] at hi0 
+      rw [← Set.indicator_of_mem hi0 w2, ← Set.indicator_of_mem hi0 w1, ha, sub_self]
+    simpa [w2] using hws
 #align affine_independent_iff_indicator_eq_of_affine_combination_eq affineIndependent_iff_indicator_eq_of_affineCombination_eq
 -/
 
@@ -235,7 +317,25 @@ protected theorem AffineIndependent.injective [Nontrivial k] {p : ι → P}
 composition of an embedding into index type with the original
 family. -/
 theorem AffineIndependent.comp_embedding {ι2 : Type _} (f : ι2 ↪ ι) {p : ι → P}
-    (ha : AffineIndependent k p) : AffineIndependent k (p ∘ f) := by classical
+    (ha : AffineIndependent k p) : AffineIndependent k (p ∘ f) := by
+  classical
+  intro fs w hw hs i0 hi0
+  let fs' := fs.map f
+  let w' i := if h : ∃ i2, f i2 = i then w h.some else 0
+  have hw' : ∀ i2 : ι2, w' (f i2) = w i2 := by
+    intro i2
+    have h : ∃ i : ι2, f i = f i2 := ⟨i2, rfl⟩
+    have hs : h.some = i2 := f.injective h.some_spec
+    simp_rw [w', dif_pos h, hs]
+  have hw's : ∑ i in fs', w' i = 0 := by
+    rw [← hw, Finset.sum_map]
+    simp [hw']
+  have hs' : fs'.weighted_vsub p w' = (0 : V) :=
+    by
+    rw [← hs, Finset.weightedVSub_map]
+    congr with i
+    simp [hw']
+  rw [← ha fs' w' hw's hs' (f i0) ((Finset.mem_map' _).2 hi0), hw']
 #align affine_independent.comp_embedding AffineIndependent.comp_embedding
 -/
 
@@ -427,7 +527,19 @@ theorem AffineIndependent.not_mem_affineSpan_diff [Nontrivial k] {p : ι → P}
 #print exists_nontrivial_relation_sum_zero_of_not_affine_ind /-
 theorem exists_nontrivial_relation_sum_zero_of_not_affine_ind {t : Finset V}
     (h : ¬AffineIndependent k (coe : t → V)) :
-    ∃ f : V → k, ∑ e in t, f e • e = 0 ∧ ∑ e in t, f e = 0 ∧ ∃ x ∈ t, f x ≠ 0 := by classical
+    ∃ f : V → k, ∑ e in t, f e • e = 0 ∧ ∑ e in t, f e = 0 ∧ ∃ x ∈ t, f x ≠ 0 := by
+  classical
+  rw [affineIndependent_iff_of_fintype] at h 
+  simp only [exists_prop, Classical.not_forall] at h 
+  obtain ⟨w, hw, hwt, i, hi⟩ := h
+  simp only [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero _ w (coe : t → V) hw 0,
+    vsub_eq_sub, Finset.weightedVSubOfPoint_apply, sub_zero] at hwt 
+  let f : ∀ x : V, x ∈ t → k := fun x hx => w ⟨x, hx⟩
+  refine' ⟨fun x => if hx : x ∈ t then f x hx else (0 : k), _, _, by use i; simp [hi, f]⟩
+  suffices (∑ e : V in t, dite (e ∈ t) (fun hx => f e hx • e) fun hx => 0) = 0 by convert this; ext;
+    by_cases hx : x ∈ t <;> simp [hx]
+  all_goals
+    simp only [Finset.sum_dite_of_true fun x h => h, Subtype.val_eq_coe, Finset.mk_coe, f, hwt, hw]
 #align exists_nontrivial_relation_sum_zero_of_not_affine_ind exists_nontrivial_relation_sum_zero_of_not_affine_ind
 -/
 
@@ -590,7 +702,48 @@ variable {k V P}
 the affine span of that family, the family is affinely independent. -/
 theorem AffineIndependent.affineIndependent_of_not_mem_span {p : ι → P} {i : ι}
     (ha : AffineIndependent k fun x : { y // y ≠ i } => p x)
-    (hi : p i ∉ affineSpan k (p '' {x | x ≠ i})) : AffineIndependent k p := by classical
+    (hi : p i ∉ affineSpan k (p '' {x | x ≠ i})) : AffineIndependent k p := by
+  classical
+  intro s w hw hs
+  let s' : Finset { y // y ≠ i } := s.subtype (· ≠ i)
+  let p' : { y // y ≠ i } → P := fun x => p x
+  by_cases his : i ∈ s ∧ w i ≠ 0
+  · refine' False.elim (hi _)
+    let wm : ι → k := -(w i)⁻¹ • w
+    have hms : s.weighted_vsub p wm = (0 : V) := by simp [wm, hs]
+    have hwm : ∑ i in s, wm i = 0 := by simp [wm, ← Finset.mul_sum, hw]
+    have hwmi : wm i = -1 := by simp [wm, his.2]
+    let w' : { y // y ≠ i } → k := fun x => wm x
+    have hw' : ∑ x in s', w' x = 1 :=
+      by
+      simp_rw [w', Finset.sum_subtype_eq_sum_filter]
+      rw [← s.sum_filter_add_sum_filter_not (· ≠ i)] at hwm 
+      simp_rw [Classical.not_not, Finset.filter_eq', if_pos his.1, Finset.sum_singleton, ← wm, hwmi,
+        ← sub_eq_add_neg, sub_eq_zero] at hwm 
+      exact hwm
+    rw [← s.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one hms his.1 hwmi, ←
+      (Subtype.range_coe : _ = {x | x ≠ i}), ← Set.range_comp, ←
+      s.affine_combination_subtype_eq_filter]
+    exact affineCombination_mem_affineSpan hw' p'
+  · rw [not_and_or, Classical.not_not] at his 
+    let w' : { y // y ≠ i } → k := fun x => w x
+    have hw' : ∑ x in s', w' x = 0 :=
+      by
+      simp_rw [Finset.sum_subtype_eq_sum_filter]
+      rw [Finset.sum_filter_of_ne, hw]
+      rintro x hxs hwx rfl
+      exact hwx (his.neg_resolve_left hxs)
+    have hs' : s'.weighted_vsub p' w' = (0 : V) :=
+      by
+      simp_rw [Finset.weightedVSub_subtype_eq_filter]
+      rw [Finset.weightedVSub_filter_of_ne, hs]
+      rintro x hxs hwx rfl
+      exact hwx (his.neg_resolve_left hxs)
+    intro j hj
+    by_cases hji : j = i
+    · rw [hji] at hj 
+      exact hji.symm ▸ his.neg_resolve_left hj
+    · exact ha s' w' hw' hs' ⟨j, hji⟩ (Finset.mem_subtype.2 hj)
 #align affine_independent.affine_independent_of_not_mem_span AffineIndependent.affineIndependent_of_not_mem_span
 -/
 
@@ -686,7 +839,19 @@ theorem sign_eq_of_affineCombination_mem_affineSpan_single_lineMap {p : ι → P
     (h₁ : i₁ ∈ s) (h₂ : i₂ ∈ s) (h₃ : i₃ ∈ s) (h₁₂ : i₁ ≠ i₂) (h₁₃ : i₁ ≠ i₃) (h₂₃ : i₂ ≠ i₃)
     {c : k} (hc0 : 0 < c) (hc1 : c < 1)
     (hs : s.affineCombination k p w ∈ line[k, p i₁, AffineMap.lineMap (p i₂) (p i₃) c]) :
-    SignType.sign (w i₂) = SignType.sign (w i₃) := by classical
+    SignType.sign (w i₂) = SignType.sign (w i₃) := by
+  classical
+  rw [← s.affine_combination_affine_combination_single_weights k p h₁, ←
+    s.affine_combination_affine_combination_line_map_weights p h₂ h₃ c] at hs 
+  refine'
+    sign_eq_of_affineCombination_mem_affineSpan_pair h hw
+      (s.sum_affine_combination_single_weights k h₁)
+      (s.sum_affine_combination_line_map_weights h₂ h₃ c) hs h₂ h₃
+      (Finset.affineCombinationSingleWeights_apply_of_ne k h₁₂.symm)
+      (Finset.affineCombinationSingleWeights_apply_of_ne k h₁₃.symm) _
+  rw [Finset.affineCombinationLineMapWeights_apply_left h₂₃,
+    Finset.affineCombinationLineMapWeights_apply_right h₂₃]
+  simp [hc0, sub_pos.2 hc1]
 #align sign_eq_of_affine_combination_mem_affine_span_single_line_map sign_eq_of_affineCombination_mem_affineSpan_single_lineMap
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -100,56 +100,6 @@ from a base point in that family are linearly independent. -/
 theorem affineIndependent_iff_linearIndependent_vsub (p : ι → P) (i1 : ι) :
     AffineIndependent k p ↔ LinearIndependent k fun i : { x // x ≠ i1 } => (p i -ᵥ p i1 : V) := by
   classical
-  constructor
-  · intro h
-    rw [linearIndependent_iff']
-    intro s g hg i hi
-    set f : ι → k := fun x => if hx : x = i1 then -∑ y in s, g y else g ⟨x, hx⟩ with hfdef
-    let s2 : Finset ι := insert i1 (s.map (embedding.subtype _))
-    have hfg : ∀ x : { x // x ≠ i1 }, g x = f x :=
-      by
-      intro x
-      rw [hfdef]
-      dsimp only
-      erw [dif_neg x.property, Subtype.coe_eta]
-    rw [hfg]
-    have hf : ∑ ι in s2, f ι = 0 :=
-      by
-      rw [Finset.sum_insert
-          (Finset.not_mem_map_subtype_of_not_property s (Classical.not_not.2 rfl)),
-        Finset.sum_subtype_map_embedding fun x hx => (hfg x).symm]
-      rw [hfdef]
-      dsimp only
-      rw [dif_pos rfl]
-      exact neg_add_self _
-    have hs2 : s2.weighted_vsub p f = (0 : V) :=
-      by
-      set f2 : ι → V := fun x => f x • (p x -ᵥ p i1) with hf2def
-      set g2 : { x // x ≠ i1 } → V := fun x => g x • (p x -ᵥ p i1) with hg2def
-      have hf2g2 : ∀ x : { x // x ≠ i1 }, f2 x = g2 x :=
-        by
-        simp_rw [hf2def, hg2def, hfg]
-        exact fun x => rfl
-      rw [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero s2 f p hf (p i1),
-        Finset.weightedVSubOfPoint_insert, Finset.weightedVSubOfPoint_apply,
-        Finset.sum_subtype_map_embedding fun x hx => hf2g2 x]
-      exact hg
-    exact h s2 f hf hs2 i (Finset.mem_insert_of_mem (Finset.mem_map.2 ⟨i, hi, rfl⟩))
-  · intro h
-    rw [linearIndependent_iff'] at h 
-    intro s w hw hs i hi
-    rw [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero s w p hw (p i1), ←
-      s.weighted_vsub_of_point_erase w p i1, Finset.weightedVSubOfPoint_apply] at hs 
-    let f : ι → V := fun i => w i • (p i -ᵥ p i1)
-    have hs2 : ∑ i in (s.erase i1).Subtype fun i => i ≠ i1, f i = 0 :=
-      by
-      rw [← hs]
-      convert Finset.sum_subtype_of_mem f fun x => Finset.ne_of_mem_erase
-    have h2 := h ((s.erase i1).Subtype fun i => i ≠ i1) (fun x => w x) hs2
-    simp_rw [Finset.mem_subtype] at h2 
-    have h2b : ∀ i ∈ s, i ≠ i1 → w i = 0 := fun i his hi =>
-      h2 ⟨i, hi⟩ (Finset.mem_erase_of_ne_of_mem hi his)
-    exact Finset.eq_zero_of_sum_eq_zero hw h2b i hi
 #align affine_independent_iff_linear_independent_vsub affineIndependent_iff_linearIndependent_vsub
 -/
 
@@ -212,39 +162,7 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
           ∑ i in s2, w2 i = 1 →
             s1.affineCombination k p w1 = s2.affineCombination k p w2 →
               Set.indicator (↑s1) w1 = Set.indicator (↑s2) w2 :=
-  by
-  classical
-  constructor
-  · intro ha s1 s2 w1 w2 hw1 hw2 heq
-    ext i
-    by_cases hi : i ∈ s1 ∪ s2
-    · rw [← sub_eq_zero]
-      rw [Finset.sum_indicator_subset _ (Finset.subset_union_left s1 s2)] at hw1 
-      rw [Finset.sum_indicator_subset _ (Finset.subset_union_right s1 s2)] at hw2 
-      have hws : ∑ i in s1 ∪ s2, (Set.indicator (↑s1) w1 - Set.indicator (↑s2) w2) i = 0 := by
-        simp [hw1, hw2]
-      rw [Finset.affineCombination_indicator_subset _ _ (Finset.subset_union_left s1 s2),
-        Finset.affineCombination_indicator_subset _ _ (Finset.subset_union_right s1 s2), ←
-        @vsub_eq_zero_iff_eq V, Finset.affineCombination_vsub] at heq 
-      exact ha (s1 ∪ s2) (Set.indicator (↑s1) w1 - Set.indicator (↑s2) w2) hws HEq i hi
-    · rw [← Finset.mem_coe, Finset.coe_union] at hi 
-      simp [mt (Set.mem_union_left ↑s2) hi, mt (Set.mem_union_right ↑s1) hi]
-  · intro ha s w hw hs i0 hi0
-    let w1 : ι → k := Function.update (Function.const ι 0) i0 1
-    have hw1 : ∑ i in s, w1 i = 1 := by
-      rw [Finset.sum_update_of_mem hi0, Finset.sum_const_zero, add_zero]
-    have hw1s : s.affine_combination k p w1 = p i0 :=
-      s.affine_combination_of_eq_one_of_eq_zero w1 p hi0 (Function.update_same _ _ _) fun _ _ hne =>
-        Function.update_noteq hne _ _
-    let w2 := w + w1
-    have hw2 : ∑ i in s, w2 i = 1 := by simp [w2, Finset.sum_add_distrib, hw, hw1]
-    have hw2s : s.affine_combination k p w2 = p i0 := by
-      simp [w2, ← Finset.weightedVSub_vadd_affineCombination, hs, hw1s]
-    replace ha := ha s s w2 w1 hw2 hw1 (hw1s.symm ▸ hw2s)
-    have hws : w2 i0 - w1 i0 = 0 := by
-      rw [← Finset.mem_coe] at hi0 
-      rw [← Set.indicator_of_mem hi0 w2, ← Set.indicator_of_mem hi0 w1, ha, sub_self]
-    simpa [w2] using hws
+  by classical
 #align affine_independent_iff_indicator_eq_of_affine_combination_eq affineIndependent_iff_indicator_eq_of_affineCombination_eq
 -/
 
@@ -317,25 +235,7 @@ protected theorem AffineIndependent.injective [Nontrivial k] {p : ι → P}
 composition of an embedding into index type with the original
 family. -/
 theorem AffineIndependent.comp_embedding {ι2 : Type _} (f : ι2 ↪ ι) {p : ι → P}
-    (ha : AffineIndependent k p) : AffineIndependent k (p ∘ f) := by
-  classical
-  intro fs w hw hs i0 hi0
-  let fs' := fs.map f
-  let w' i := if h : ∃ i2, f i2 = i then w h.some else 0
-  have hw' : ∀ i2 : ι2, w' (f i2) = w i2 := by
-    intro i2
-    have h : ∃ i : ι2, f i = f i2 := ⟨i2, rfl⟩
-    have hs : h.some = i2 := f.injective h.some_spec
-    simp_rw [w', dif_pos h, hs]
-  have hw's : ∑ i in fs', w' i = 0 := by
-    rw [← hw, Finset.sum_map]
-    simp [hw']
-  have hs' : fs'.weighted_vsub p w' = (0 : V) :=
-    by
-    rw [← hs, Finset.weightedVSub_map]
-    congr with i
-    simp [hw']
-  rw [← ha fs' w' hw's hs' (f i0) ((Finset.mem_map' _).2 hi0), hw']
+    (ha : AffineIndependent k p) : AffineIndependent k (p ∘ f) := by classical
 #align affine_independent.comp_embedding AffineIndependent.comp_embedding
 -/
 
@@ -527,19 +427,7 @@ theorem AffineIndependent.not_mem_affineSpan_diff [Nontrivial k] {p : ι → P}
 #print exists_nontrivial_relation_sum_zero_of_not_affine_ind /-
 theorem exists_nontrivial_relation_sum_zero_of_not_affine_ind {t : Finset V}
     (h : ¬AffineIndependent k (coe : t → V)) :
-    ∃ f : V → k, ∑ e in t, f e • e = 0 ∧ ∑ e in t, f e = 0 ∧ ∃ x ∈ t, f x ≠ 0 := by
-  classical
-  rw [affineIndependent_iff_of_fintype] at h 
-  simp only [exists_prop, Classical.not_forall] at h 
-  obtain ⟨w, hw, hwt, i, hi⟩ := h
-  simp only [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero _ w (coe : t → V) hw 0,
-    vsub_eq_sub, Finset.weightedVSubOfPoint_apply, sub_zero] at hwt 
-  let f : ∀ x : V, x ∈ t → k := fun x hx => w ⟨x, hx⟩
-  refine' ⟨fun x => if hx : x ∈ t then f x hx else (0 : k), _, _, by use i; simp [hi, f]⟩
-  suffices (∑ e : V in t, dite (e ∈ t) (fun hx => f e hx • e) fun hx => 0) = 0 by convert this; ext;
-    by_cases hx : x ∈ t <;> simp [hx]
-  all_goals
-    simp only [Finset.sum_dite_of_true fun x h => h, Subtype.val_eq_coe, Finset.mk_coe, f, hwt, hw]
+    ∃ f : V → k, ∑ e in t, f e • e = 0 ∧ ∑ e in t, f e = 0 ∧ ∃ x ∈ t, f x ≠ 0 := by classical
 #align exists_nontrivial_relation_sum_zero_of_not_affine_ind exists_nontrivial_relation_sum_zero_of_not_affine_ind
 -/
 
@@ -702,48 +590,7 @@ variable {k V P}
 the affine span of that family, the family is affinely independent. -/
 theorem AffineIndependent.affineIndependent_of_not_mem_span {p : ι → P} {i : ι}
     (ha : AffineIndependent k fun x : { y // y ≠ i } => p x)
-    (hi : p i ∉ affineSpan k (p '' {x | x ≠ i})) : AffineIndependent k p := by
-  classical
-  intro s w hw hs
-  let s' : Finset { y // y ≠ i } := s.subtype (· ≠ i)
-  let p' : { y // y ≠ i } → P := fun x => p x
-  by_cases his : i ∈ s ∧ w i ≠ 0
-  · refine' False.elim (hi _)
-    let wm : ι → k := -(w i)⁻¹ • w
-    have hms : s.weighted_vsub p wm = (0 : V) := by simp [wm, hs]
-    have hwm : ∑ i in s, wm i = 0 := by simp [wm, ← Finset.mul_sum, hw]
-    have hwmi : wm i = -1 := by simp [wm, his.2]
-    let w' : { y // y ≠ i } → k := fun x => wm x
-    have hw' : ∑ x in s', w' x = 1 :=
-      by
-      simp_rw [w', Finset.sum_subtype_eq_sum_filter]
-      rw [← s.sum_filter_add_sum_filter_not (· ≠ i)] at hwm 
-      simp_rw [Classical.not_not, Finset.filter_eq', if_pos his.1, Finset.sum_singleton, ← wm, hwmi,
-        ← sub_eq_add_neg, sub_eq_zero] at hwm 
-      exact hwm
-    rw [← s.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one hms his.1 hwmi, ←
-      (Subtype.range_coe : _ = {x | x ≠ i}), ← Set.range_comp, ←
-      s.affine_combination_subtype_eq_filter]
-    exact affineCombination_mem_affineSpan hw' p'
-  · rw [not_and_or, Classical.not_not] at his 
-    let w' : { y // y ≠ i } → k := fun x => w x
-    have hw' : ∑ x in s', w' x = 0 :=
-      by
-      simp_rw [Finset.sum_subtype_eq_sum_filter]
-      rw [Finset.sum_filter_of_ne, hw]
-      rintro x hxs hwx rfl
-      exact hwx (his.neg_resolve_left hxs)
-    have hs' : s'.weighted_vsub p' w' = (0 : V) :=
-      by
-      simp_rw [Finset.weightedVSub_subtype_eq_filter]
-      rw [Finset.weightedVSub_filter_of_ne, hs]
-      rintro x hxs hwx rfl
-      exact hwx (his.neg_resolve_left hxs)
-    intro j hj
-    by_cases hji : j = i
-    · rw [hji] at hj 
-      exact hji.symm ▸ his.neg_resolve_left hj
-    · exact ha s' w' hw' hs' ⟨j, hji⟩ (Finset.mem_subtype.2 hj)
+    (hi : p i ∉ affineSpan k (p '' {x | x ≠ i})) : AffineIndependent k p := by classical
 #align affine_independent.affine_independent_of_not_mem_span AffineIndependent.affineIndependent_of_not_mem_span
 -/
 
@@ -839,19 +686,7 @@ theorem sign_eq_of_affineCombination_mem_affineSpan_single_lineMap {p : ι → P
     (h₁ : i₁ ∈ s) (h₂ : i₂ ∈ s) (h₃ : i₃ ∈ s) (h₁₂ : i₁ ≠ i₂) (h₁₃ : i₁ ≠ i₃) (h₂₃ : i₂ ≠ i₃)
     {c : k} (hc0 : 0 < c) (hc1 : c < 1)
     (hs : s.affineCombination k p w ∈ line[k, p i₁, AffineMap.lineMap (p i₂) (p i₃) c]) :
-    SignType.sign (w i₂) = SignType.sign (w i₃) := by
-  classical
-  rw [← s.affine_combination_affine_combination_single_weights k p h₁, ←
-    s.affine_combination_affine_combination_line_map_weights p h₂ h₃ c] at hs 
-  refine'
-    sign_eq_of_affineCombination_mem_affineSpan_pair h hw
-      (s.sum_affine_combination_single_weights k h₁)
-      (s.sum_affine_combination_line_map_weights h₂ h₃ c) hs h₂ h₃
-      (Finset.affineCombinationSingleWeights_apply_of_ne k h₁₂.symm)
-      (Finset.affineCombinationSingleWeights_apply_of_ne k h₁₃.symm) _
-  rw [Finset.affineCombinationLineMapWeights_apply_left h₂₃,
-    Finset.affineCombinationLineMapWeights_apply_right h₂₃]
-  simp [hc0, sub_pos.2 hc1]
+    SignType.sign (w i₂) = SignType.sign (w i₃) := by classical
 #align sign_eq_of_affine_combination_mem_affine_span_single_line_map sign_eq_of_affineCombination_mem_affineSpan_single_lineMap
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -660,7 +660,7 @@ theorem exists_affineIndependent (s : Set P) :
   rw [linearIndependent_set_iff_affineIndependent_vadd_union_singleton k hb₀ p] at hb₃ 
   refine' ⟨{p} ∪ Equiv.vaddConst p '' b, _, _, hb₃⟩
   · apply Set.union_subset (set.singleton_subset_iff.mpr hp)
-    rwa [← (Equiv.vaddConst p).subset_image' b s]
+    rwa [← (Equiv.vaddConst p).subset_symm_image b s]
   · rw [Equiv.coe_vaddConst_symm, ← vectorSpan_eq_span_vsub_set_right k hp] at hb₂ 
     apply AffineSubspace.ext_of_direction_eq
     · have : Submodule.span k b = Submodule.span k (insert 0 b) := by simp

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -88,7 +88,7 @@ theorem affineIndependent_iff_of_fintype [Fintype ι] (p : ι → P) :
   · exact fun h w hw hs i => h Finset.univ w hw hs i (Finset.mem_univ _)
   · intro h s w hw hs i hi
     rw [Finset.weightedVSub_indicator_subset _ _ (Finset.subset_univ s)] at hs 
-    rw [Set.sum_indicator_subset _ (Finset.subset_univ s)] at hw 
+    rw [Finset.sum_indicator_subset _ (Finset.subset_univ s)] at hw 
     replace h := h ((↑s : Set ι).indicator w) hw hs i
     simpa [hi] using h
 #align affine_independent_iff_of_fintype affineIndependent_iff_of_fintype
@@ -219,8 +219,8 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
     ext i
     by_cases hi : i ∈ s1 ∪ s2
     · rw [← sub_eq_zero]
-      rw [Set.sum_indicator_subset _ (Finset.subset_union_left s1 s2)] at hw1 
-      rw [Set.sum_indicator_subset _ (Finset.subset_union_right s1 s2)] at hw2 
+      rw [Finset.sum_indicator_subset _ (Finset.subset_union_left s1 s2)] at hw1 
+      rw [Finset.sum_indicator_subset _ (Finset.subset_union_right s1 s2)] at hw2 
       have hws : ∑ i in s1 ∪ s2, (Set.indicator (↑s1) w1 - Set.indicator (↑s2) w2) i = 0 := by
         simp [hw1, hw2]
       rw [Finset.affineCombination_indicator_subset _ _ (Finset.subset_union_left s1 s2),
@@ -264,9 +264,9 @@ theorem affineIndependent_iff_eq_of_fintype_affineCombination_eq [Fintype ι] (p
     simpa only [Set.indicator_univ, Finset.coe_univ] using h _ _ w1 w2 hw1 hw2 hweq
   · intro h s1 s2 w1 w2 hw1 hw2 hweq
     have hw1' : ∑ i, (s1 : Set ι).indicator w1 i = 1 := by
-      rwa [Set.sum_indicator_subset _ (Finset.subset_univ s1)] at hw1 
+      rwa [Finset.sum_indicator_subset _ (Finset.subset_univ s1)] at hw1 
     have hw2' : ∑ i, (s2 : Set ι).indicator w2 i = 1 := by
-      rwa [Set.sum_indicator_subset _ (Finset.subset_univ s2)] at hw2 
+      rwa [Finset.sum_indicator_subset _ (Finset.subset_univ s2)] at hw2 
     rw [Finset.affineCombination_indicator_subset w1 p (Finset.subset_univ s1),
       Finset.affineCombination_indicator_subset w2 p (Finset.subset_univ s2)] at hweq 
     exact h _ _ hw1' hw2' hweq

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

@@ -530,7 +530,7 @@ theorem exists_nontrivial_relation_sum_zero_of_not_affine_ind {t : Finset V}
     ∃ f : V → k, ∑ e in t, f e • e = 0 ∧ ∑ e in t, f e = 0 ∧ ∃ x ∈ t, f x ≠ 0 := by
   classical
   rw [affineIndependent_iff_of_fintype] at h 
-  simp only [exists_prop, not_forall] at h 
+  simp only [exists_prop, Classical.not_forall] at h 
   obtain ⟨w, hw, hwt, i, hi⟩ := h
   simp only [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero _ w (coe : t → V) hw 0,
     vsub_eq_sub, Finset.weightedVSubOfPoint_apply, sub_zero] at hwt 

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,12 +3,12 @@ Copyright (c) 2020 Joseph Myers. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
 -/
-import Mathbin.Data.Finset.Sort
-import Mathbin.Data.Fin.VecNotation
-import Mathbin.Data.Sign
-import Mathbin.LinearAlgebra.AffineSpace.Combination
-import Mathbin.LinearAlgebra.AffineSpace.AffineEquiv
-import Mathbin.LinearAlgebra.Basis
+import Data.Finset.Sort
+import Data.Fin.VecNotation
+import Data.Sign
+import LinearAlgebra.AffineSpace.Combination
+import LinearAlgebra.AffineSpace.AffineEquiv
+import LinearAlgebra.Basis
 
 #align_import linear_algebra.affine_space.independent from "leanprover-community/mathlib"@"4f81bc21e32048db7344b7867946e992cf5f68cc"
 
@@ -648,7 +648,7 @@ theorem exists_subset_affineIndependent_affineSpan_eq_top {s : Set P}
 
 variable (k V)
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 #print exists_affineIndependent /-
 theorem exists_affineIndependent (s : Set P) :
     ∃ (t : _) (_ : t ⊆ s), affineSpan k t = affineSpan k s ∧ AffineIndependent k (coe : t → P) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Joseph Myers. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
-
-! This file was ported from Lean 3 source module linear_algebra.affine_space.independent
-! leanprover-community/mathlib commit 4f81bc21e32048db7344b7867946e992cf5f68cc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Finset.Sort
 import Mathbin.Data.Fin.VecNotation
@@ -15,6 +10,8 @@ import Mathbin.LinearAlgebra.AffineSpace.Combination
 import Mathbin.LinearAlgebra.AffineSpace.AffineEquiv
 import Mathbin.LinearAlgebra.Basis
 
+#align_import linear_algebra.affine_space.independent from "leanprover-community/mathlib"@"4f81bc21e32048db7344b7867946e992cf5f68cc"
+
 /-!
 # Affine independence
 
@@ -651,7 +648,7 @@ theorem exists_subset_affineIndependent_affineSpan_eq_top {s : Set P}
 
 variable (k V)
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 #print exists_affineIndependent /-
 theorem exists_affineIndependent (s : Set P) :
     ∃ (t : _) (_ : t ⊆ s), affineSpan k t = affineSpan k s ∧ AffineIndependent k (coe : t → P) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -53,8 +53,6 @@ variable (k : Type _) {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Modul
 
 variable [affine_space V P] {ι : Type _}
 
-include V
-
 #print AffineIndependent /-
 /-- An indexed family is said to be affinely independent if no
 nontrivial weighted subtractions (where the sum of weights is 0) are
@@ -64,6 +62,7 @@ def AffineIndependent (p : ι → P) : Prop :=
 #align affine_independent AffineIndependent
 -/
 
+#print affineIndependent_def /-
 /-- The definition of `affine_independent`. -/
 theorem affineIndependent_def (p : ι → P) :
     AffineIndependent k p ↔
@@ -71,12 +70,16 @@ theorem affineIndependent_def (p : ι → P) :
         ∑ i in s, w i = 0 → s.weightedVSub p w = (0 : V) → ∀ i ∈ s, w i = 0 :=
   Iff.rfl
 #align affine_independent_def affineIndependent_def
+-/
 
+#print affineIndependent_of_subsingleton /-
 /-- A family with at most one point is affinely independent. -/
 theorem affineIndependent_of_subsingleton [Subsingleton ι] (p : ι → P) : AffineIndependent k p :=
   fun s w h hs i hi => Fintype.eq_of_subsingleton_of_sum_eq h i hi
 #align affine_independent_of_subsingleton affineIndependent_of_subsingleton
+-/
 
+#print affineIndependent_iff_of_fintype /-
 /-- A family indexed by a `fintype` is affinely independent if and
 only if no nontrivial weighted subtractions over `finset.univ` (where
 the sum of the weights is 0) are 0. -/
@@ -92,7 +95,9 @@ theorem affineIndependent_iff_of_fintype [Fintype ι] (p : ι → P) :
     replace h := h ((↑s : Set ι).indicator w) hw hs i
     simpa [hi] using h
 #align affine_independent_iff_of_fintype affineIndependent_iff_of_fintype
+-/
 
+#print affineIndependent_iff_linearIndependent_vsub /-
 /-- A family is affinely independent if and only if the differences
 from a base point in that family are linearly independent. -/
 theorem affineIndependent_iff_linearIndependent_vsub (p : ι → P) (i1 : ι) :
@@ -149,7 +154,9 @@ theorem affineIndependent_iff_linearIndependent_vsub (p : ι → P) (i1 : ι) :
       h2 ⟨i, hi⟩ (Finset.mem_erase_of_ne_of_mem hi his)
     exact Finset.eq_zero_of_sum_eq_zero hw h2b i hi
 #align affine_independent_iff_linear_independent_vsub affineIndependent_iff_linearIndependent_vsub
+-/
 
+#print affineIndependent_set_iff_linearIndependent_vsub /-
 /-- A set is affinely independent if and only if the differences from
 a base point in that set are linearly independent. -/
 theorem affineIndependent_set_iff_linearIndependent_vsub {s : Set P} {p₁ : P} (hp₁ : p₁ ∈ s) :
@@ -175,7 +182,9 @@ theorem affineIndependent_set_iff_linearIndependent_vsub {s : Set P} {p₁ : P}
     convert
       h.comp f fun x1 x2 hx => Subtype.ext (Subtype.ext (vsub_left_cancel (Subtype.ext_iff.1 hx)))
 #align affine_independent_set_iff_linear_independent_vsub affineIndependent_set_iff_linearIndependent_vsub
+-/
 
+#print linearIndependent_set_iff_affineIndependent_vadd_union_singleton /-
 /-- A set of nonzero vectors is linearly independent if and only if,
 given a point `p₁`, the vectors added to `p₁` and `p₁` itself are
 affinely independent. -/
@@ -193,7 +202,9 @@ theorem linearIndependent_set_iff_affineIndependent_vadd_union_singleton {s : Se
     exact Set.diff_singleton_eq_self fun h => hs 0 h rfl
   rw [h]
 #align linear_independent_set_iff_affine_independent_vadd_union_singleton linearIndependent_set_iff_affineIndependent_vadd_union_singleton
+-/
 
+#print affineIndependent_iff_indicator_eq_of_affineCombination_eq /-
 /-- A family is affinely independent if and only if any affine
 combinations (with sum of weights 1) that evaluate to the same point
 have equal `set.indicator`. -/
@@ -238,7 +249,9 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
       rw [← Set.indicator_of_mem hi0 w2, ← Set.indicator_of_mem hi0 w1, ha, sub_self]
     simpa [w2] using hws
 #align affine_independent_iff_indicator_eq_of_affine_combination_eq affineIndependent_iff_indicator_eq_of_affineCombination_eq
+-/
 
+#print affineIndependent_iff_eq_of_fintype_affineCombination_eq /-
 /-- A finite family is affinely independent if and only if any affine
 combinations (with sum of weights 1) that evaluate to the same point are equal. -/
 theorem affineIndependent_iff_eq_of_fintype_affineCombination_eq [Fintype ι] (p : ι → P) :
@@ -261,9 +274,11 @@ theorem affineIndependent_iff_eq_of_fintype_affineCombination_eq [Fintype ι] (p
       Finset.affineCombination_indicator_subset w2 p (Finset.subset_univ s2)] at hweq 
     exact h _ _ hw1' hw2' hweq
 #align affine_independent_iff_eq_of_fintype_affine_combination_eq affineIndependent_iff_eq_of_fintype_affineCombination_eq
+-/
 
 variable {k}
 
+#print AffineIndependent.units_lineMap /-
 /-- If we single out one member of an affine-independent family of points and affinely transport
 all others along the line joining them to this member, the resulting new family of points is affine-
 independent.
@@ -276,14 +291,18 @@ theorem AffineIndependent.units_lineMap {p : ι → P} (hp : AffineIndependent k
   simp only [AffineMap.lineMap_vsub_left, AffineMap.coe_const, AffineMap.lineMap_same]
   exact hp.units_smul fun i => w i
 #align affine_independent.units_line_map AffineIndependent.units_lineMap
+-/
 
+#print AffineIndependent.indicator_eq_of_affineCombination_eq /-
 theorem AffineIndependent.indicator_eq_of_affineCombination_eq {p : ι → P}
     (ha : AffineIndependent k p) (s₁ s₂ : Finset ι) (w₁ w₂ : ι → k) (hw₁ : ∑ i in s₁, w₁ i = 1)
     (hw₂ : ∑ i in s₂, w₂ i = 1) (h : s₁.affineCombination k p w₁ = s₂.affineCombination k p w₂) :
     Set.indicator (↑s₁) w₁ = Set.indicator (↑s₂) w₂ :=
   (affineIndependent_iff_indicator_eq_of_affineCombination_eq k p).1 ha s₁ s₂ w₁ w₂ hw₁ hw₂ h
 #align affine_independent.indicator_eq_of_affine_combination_eq AffineIndependent.indicator_eq_of_affineCombination_eq
+-/
 
+#print AffineIndependent.injective /-
 /-- An affinely independent family is injective, if the underlying
 ring is nontrivial. -/
 protected theorem AffineIndependent.injective [Nontrivial k] {p : ι → P}
@@ -294,7 +313,9 @@ protected theorem AffineIndependent.injective [Nontrivial k] {p : ι → P}
   by_contra hij'
   exact ha.ne_zero ⟨i, hij'⟩ (vsub_eq_zero_iff_eq.mpr hij)
 #align affine_independent.injective AffineIndependent.injective
+-/
 
+#print AffineIndependent.comp_embedding /-
 /-- If a family is affinely independent, so is any subfamily given by
 composition of an embedding into index type with the original
 family. -/
@@ -319,14 +340,18 @@ theorem AffineIndependent.comp_embedding {ι2 : Type _} (f : ι2 ↪ ι) {p : ι
     simp [hw']
   rw [← ha fs' w' hw's hs' (f i0) ((Finset.mem_map' _).2 hi0), hw']
 #align affine_independent.comp_embedding AffineIndependent.comp_embedding
+-/
 
+#print AffineIndependent.subtype /-
 /-- If a family is affinely independent, so is any subfamily indexed
 by a subtype of the index type. -/
 protected theorem AffineIndependent.subtype {p : ι → P} (ha : AffineIndependent k p) (s : Set ι) :
     AffineIndependent k fun i : s => p i :=
   ha.comp_embedding (Embedding.subtype _)
 #align affine_independent.subtype AffineIndependent.subtype
+-/
 
+#print AffineIndependent.range /-
 /-- If an indexed family of points is affinely independent, so is the
 corresponding set of points. -/
 protected theorem AffineIndependent.range {p : ι → P} (ha : AffineIndependent k p) :
@@ -339,7 +364,9 @@ protected theorem AffineIndependent.range {p : ι → P} (ha : AffineIndependent
   ext
   simp [hf]
 #align affine_independent.range AffineIndependent.range
+-/
 
+#print affineIndependent_equiv /-
 theorem affineIndependent_equiv {ι' : Type _} (e : ι ≃ ι') {p : ι' → P} :
     AffineIndependent k (p ∘ e) ↔ AffineIndependent k p :=
   by
@@ -349,14 +376,18 @@ theorem affineIndependent_equiv {ι' : Type _} (e : ι ≃ ι') {p : ι' → P}
   rw [this]
   exact h.comp_embedding e.symm.to_embedding
 #align affine_independent_equiv affineIndependent_equiv
+-/
 
+#print AffineIndependent.mono /-
 /-- If a set of points is affinely independent, so is any subset. -/
 protected theorem AffineIndependent.mono {s t : Set P}
     (ha : AffineIndependent k (fun x => x : t → P)) (hs : s ⊆ t) :
     AffineIndependent k (fun x => x : s → P) :=
   ha.comp_embedding (s.embeddingOfSubset t hs)
 #align affine_independent.mono AffineIndependent.mono
+-/
 
+#print AffineIndependent.of_set_of_injective /-
 /-- If the range of an injective indexed family of points is affinely
 independent, so is that family. -/
 theorem AffineIndependent.of_set_of_injective {p : ι → P}
@@ -366,13 +397,13 @@ theorem AffineIndependent.of_set_of_injective {p : ι → P}
     (⟨fun i => ⟨p i, Set.mem_range_self _⟩, fun x y h => hi (Subtype.mk_eq_mk.1 h)⟩ :
       ι ↪ Set.range p)
 #align affine_independent.of_set_of_injective AffineIndependent.of_set_of_injective
+-/
 
 section Composition
 
 variable {V₂ P₂ : Type _} [AddCommGroup V₂] [Module k V₂] [affine_space V₂ P₂]
 
-include V₂
-
+#print AffineIndependent.of_comp /-
 /-- If the image of a family of points in affine space under an affine transformation is affine-
 independent, then the original family of points is also affine-independent. -/
 theorem AffineIndependent.of_comp {p : ι → P} (f : P →ᵃ[k] P₂) (hai : AffineIndependent k (f ∘ p)) :
@@ -384,7 +415,9 @@ theorem AffineIndependent.of_comp {p : ι → P} (f : P →ᵃ[k] P₂) (hai : A
     f.linear_map_vsub] at hai 
   exact LinearIndependent.of_comp f.linear hai
 #align affine_independent.of_comp AffineIndependent.of_comp
+-/
 
+#print AffineIndependent.map' /-
 /-- The image of a family of points in affine space, under an injective affine transformation, is
 affine-independent. -/
 theorem AffineIndependent.map' {p : ι → P} (hai : AffineIndependent k p) (f : P →ᵃ[k] P₂)
@@ -398,19 +431,25 @@ theorem AffineIndependent.map' {p : ι → P} (hai : AffineIndependent k p) (f :
   have hf' : f.linear.ker = ⊥ := by rwa [LinearMap.ker_eq_bot, f.linear_injective_iff]
   exact LinearIndependent.map' hai f.linear hf'
 #align affine_independent.map' AffineIndependent.map'
+-/
 
+#print AffineMap.affineIndependent_iff /-
 /-- Injective affine maps preserve affine independence. -/
 theorem AffineMap.affineIndependent_iff {p : ι → P} (f : P →ᵃ[k] P₂) (hf : Function.Injective f) :
     AffineIndependent k (f ∘ p) ↔ AffineIndependent k p :=
   ⟨AffineIndependent.of_comp f, fun hai => AffineIndependent.map' hai f hf⟩
 #align affine_map.affine_independent_iff AffineMap.affineIndependent_iff
+-/
 
+#print AffineEquiv.affineIndependent_iff /-
 /-- Affine equivalences preserve affine independence of families of points. -/
 theorem AffineEquiv.affineIndependent_iff {p : ι → P} (e : P ≃ᵃ[k] P₂) :
     AffineIndependent k (e ∘ p) ↔ AffineIndependent k p :=
   e.toAffineMap.affineIndependent_iff e.toEquiv.Injective
 #align affine_equiv.affine_independent_iff AffineEquiv.affineIndependent_iff
+-/
 
+#print AffineEquiv.affineIndependent_set_of_eq_iff /-
 /-- Affine equivalences preserve affine independence of subsets. -/
 theorem AffineEquiv.affineIndependent_set_of_eq_iff {s : Set P} (e : P ≃ᵃ[k] P₂) :
     AffineIndependent k (coe : e '' s → P₂) ↔ AffineIndependent k (coe : s → P) :=
@@ -418,9 +457,11 @@ theorem AffineEquiv.affineIndependent_set_of_eq_iff {s : Set P} (e : P ≃ᵃ[k]
   have : e ∘ (coe : s → P) = (coe : e '' s → P₂) ∘ (e : P ≃ P₂).image s := rfl
   rw [← e.affine_independent_iff, this, affineIndependent_equiv]
 #align affine_equiv.affine_independent_set_of_eq_iff AffineEquiv.affineIndependent_set_of_eq_iff
+-/
 
 end Composition
 
+#print AffineIndependent.exists_mem_inter_of_exists_mem_inter_affineSpan /-
 /-- If a family is affinely independent, and the spans of points
 indexed by two subsets of the index type have a point in common, those
 subsets of the index type have an element in common, if the underlying
@@ -441,7 +482,9 @@ theorem AffineIndependent.exists_mem_inter_of_exists_mem_inter_affineSpan [Nontr
   simp_rw [← Set.indicator_of_mem (Finset.mem_coe.2 hifs1) w1, ha] at hinz 
   use i, hfs1 hifs1, hfs2 (Set.mem_of_indicator_ne_zero hinz)
 #align affine_independent.exists_mem_inter_of_exists_mem_inter_affine_span AffineIndependent.exists_mem_inter_of_exists_mem_inter_affineSpan
+-/
 
+#print AffineIndependent.affineSpan_disjoint_of_disjoint /-
 /-- If a family is affinely independent, the spans of points indexed
 by disjoint subsets of the index type are disjoint, if the underlying
 ring is nontrivial. -/
@@ -453,7 +496,9 @@ theorem AffineIndependent.affineSpan_disjoint_of_disjoint [Nontrivial k] {p : ι
   cases' ha.exists_mem_inter_of_exists_mem_inter_affine_span hp0s1 hp0s2 with i hi
   exact Set.disjoint_iff.1 hd hi
 #align affine_independent.affine_span_disjoint_of_disjoint AffineIndependent.affineSpan_disjoint_of_disjoint
+-/
 
+#print AffineIndependent.mem_affineSpan_iff /-
 /-- If a family is affinely independent, a point in the family is in
 the span of some of the points given by a subset of the index type if
 and only if that point's index is in the subset, if the underlying
@@ -470,7 +515,9 @@ protected theorem AffineIndependent.mem_affineSpan_iff [Nontrivial k] {p : ι 
     rwa [← Set.nonempty_def, Set.inter_singleton_nonempty] at h 
   · exact fun h => mem_affineSpan k (Set.mem_image_of_mem p h)
 #align affine_independent.mem_affine_span_iff AffineIndependent.mem_affineSpan_iff
+-/
 
+#print AffineIndependent.not_mem_affineSpan_diff /-
 /-- If a family is affinely independent, a point in the family is not
 in the affine span of the other points, if the underlying ring is
 nontrivial. -/
@@ -478,7 +525,9 @@ theorem AffineIndependent.not_mem_affineSpan_diff [Nontrivial k] {p : ι → P}
     (ha : AffineIndependent k p) (i : ι) (s : Set ι) : p i ∉ affineSpan k (p '' (s \ {i})) := by
   simp [ha]
 #align affine_independent.not_mem_affine_span_diff AffineIndependent.not_mem_affineSpan_diff
+-/
 
+#print exists_nontrivial_relation_sum_zero_of_not_affine_ind /-
 theorem exists_nontrivial_relation_sum_zero_of_not_affine_ind {t : Finset V}
     (h : ¬AffineIndependent k (coe : t → V)) :
     ∃ f : V → k, ∑ e in t, f e • e = 0 ∧ ∑ e in t, f e = 0 ∧ ∃ x ∈ t, f x ≠ 0 := by
@@ -495,7 +544,9 @@ theorem exists_nontrivial_relation_sum_zero_of_not_affine_ind {t : Finset V}
   all_goals
     simp only [Finset.sum_dite_of_true fun x h => h, Subtype.val_eq_coe, Finset.mk_coe, f, hwt, hw]
 #align exists_nontrivial_relation_sum_zero_of_not_affine_ind exists_nontrivial_relation_sum_zero_of_not_affine_ind
+-/
 
+#print affineIndependent_iff /-
 /-- Viewing a module as an affine space modelled on itself, we can characterise affine independence
 in terms of linear combinations. -/
 theorem affineIndependent_iff {ι} {p : ι → V} :
@@ -503,7 +554,9 @@ theorem affineIndependent_iff {ι} {p : ι → V} :
       ∀ (s : Finset ι) (w : ι → k), s.Sum w = 0 → ∑ e in s, w e • p e = 0 → ∀ e ∈ s, w e = 0 :=
   forall₃_congr fun s w hw => by simp [s.weighted_vsub_eq_linear_combination hw]
 #align affine_independent_iff affineIndependent_iff
+-/
 
+#print weightedVSub_mem_vectorSpan_pair /-
 /-- Given an affinely independent family of points, a weighted subtraction lies in the
 `vector_span` of two points given as affine combinations if and only if it is a weighted
 subtraction with weights a multiple of the difference between the weights of the two points. -/
@@ -532,7 +585,9 @@ theorem weightedVSub_mem_vectorSpan_pair {p : ι → P} (h : AffineIndependent k
       s.weighted_vsub_const_smul]
     congr
 #align weighted_vsub_mem_vector_span_pair weightedVSub_mem_vectorSpan_pair
+-/
 
+#print affineCombination_mem_affineSpan_pair /-
 /-- Given an affinely independent family of points, an affine combination lies in the
 span of two points given as affine combinations if and only if it is an affine combination
 with weights those of one point plus a multiple of the difference between the weights of the
@@ -550,6 +605,7 @@ theorem affineCombination_mem_affineSpan_pair {p : ι → P} (h : AffineIndepend
   · simp only [Pi.sub_apply, sub_eq_iff_eq_add]
   · simp_rw [Pi.sub_apply, Finset.sum_sub_distrib, hw, hw₁, sub_self]
 #align affine_combination_mem_affine_span_pair affineCombination_mem_affineSpan_pair
+-/
 
 end AffineIndependent
 
@@ -559,8 +615,7 @@ variable {k : Type _} {V : Type _} {P : Type _} [DivisionRing k] [AddCommGroup V
 
 variable [affine_space V P] {ι : Type _}
 
-include V
-
+#print exists_subset_affineIndependent_affineSpan_eq_top /-
 /-- An affinely independent set of points can be extended to such a
 set that spans the whole space. -/
 theorem exists_subset_affineIndependent_affineSpan_eq_top {s : Set P}
@@ -592,10 +647,12 @@ theorem exists_subset_affineIndependent_affineSpan_eq_top {s : Set P}
       simp [Set.image_image]
     · use hsvi, affineSpan_singleton_union_vadd_eq_top_of_span_eq_top p₁ hsvt
 #align exists_subset_affine_independent_affine_span_eq_top exists_subset_affineIndependent_affineSpan_eq_top
+-/
 
 variable (k V)
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+#print exists_affineIndependent /-
 theorem exists_affineIndependent (s : Set P) :
     ∃ (t : _) (_ : t ⊆ s), affineSpan k t = affineSpan k s ∧ AffineIndependent k (coe : t → P) :=
   by
@@ -620,9 +677,11 @@ theorem exists_affineIndependent (s : Set P) :
       simp only [Equiv.coe_vaddConst, Set.singleton_union, Set.mem_inter_iff, coe_affineSpan]
       exact ⟨mem_spanPoints k _ _ (Set.mem_insert p _), mem_spanPoints k _ _ hp⟩
 #align exists_affine_independent exists_affineIndependent
+-/
 
 variable (k) {V P}
 
+#print affineIndependent_of_ne /-
 /-- Two different points are affinely independent. -/
 theorem affineIndependent_of_ne {p₁ p₂ : P} (h : p₁ ≠ p₂) : AffineIndependent k ![p₁, p₂] :=
   by
@@ -637,9 +696,11 @@ theorem affineIndependent_of_ne {p₁ p₂ : P} (h : p₁ ≠ p₂) : AffineInde
   have hz : (![p₁, p₂] ↑default -ᵥ ![p₁, p₂] 0 : V) ≠ 0 := by rw [he' default]; simpa using h.symm
   exact linearIndependent_unique _ hz
 #align affine_independent_of_ne affineIndependent_of_ne
+-/
 
 variable {k V P}
 
+#print AffineIndependent.affineIndependent_of_not_mem_span /-
 /-- If all but one point of a family are affinely independent, and that point does not lie in
 the affine span of that family, the family is affinely independent. -/
 theorem AffineIndependent.affineIndependent_of_not_mem_span {p : ι → P} {i : ι}
@@ -687,7 +748,9 @@ theorem AffineIndependent.affineIndependent_of_not_mem_span {p : ι → P} {i :
       exact hji.symm ▸ his.neg_resolve_left hj
     · exact ha s' w' hw' hs' ⟨j, hji⟩ (Finset.mem_subtype.2 hj)
 #align affine_independent.affine_independent_of_not_mem_span AffineIndependent.affineIndependent_of_not_mem_span
+-/
 
+#print affineIndependent_of_ne_of_mem_of_mem_of_not_mem /-
 /-- If distinct points `p₁` and `p₂` lie in `s` but `p₃` does not, the three points are affinely
 independent. -/
 theorem affineIndependent_of_ne_of_mem_of_mem_of_not_mem {s : AffineSubspace k P} {p₁ p₂ p₃ : P}
@@ -707,7 +770,9 @@ theorem affineIndependent_of_ne_of_mem_of_mem_of_not_mem {s : AffineSubspace k P
   intro x
   fin_cases x <;> simp [hp₁, hp₂]
 #align affine_independent_of_ne_of_mem_of_mem_of_not_mem affineIndependent_of_ne_of_mem_of_mem_of_not_mem
+-/
 
+#print affineIndependent_of_ne_of_mem_of_not_mem_of_mem /-
 /-- If distinct points `p₁` and `p₃` lie in `s` but `p₂` does not, the three points are affinely
 independent. -/
 theorem affineIndependent_of_ne_of_mem_of_not_mem_of_mem {s : AffineSubspace k P} {p₁ p₂ p₃ : P}
@@ -719,7 +784,9 @@ theorem affineIndependent_of_ne_of_mem_of_not_mem_of_mem {s : AffineSubspace k P
   ext x
   fin_cases x <;> rfl
 #align affine_independent_of_ne_of_mem_of_not_mem_of_mem affineIndependent_of_ne_of_mem_of_not_mem_of_mem
+-/
 
+#print affineIndependent_of_ne_of_not_mem_of_mem_of_mem /-
 /-- If distinct points `p₂` and `p₃` lie in `s` but `p₁` does not, the three points are affinely
 independent. -/
 theorem affineIndependent_of_ne_of_not_mem_of_mem_of_mem {s : AffineSubspace k P} {p₁ p₂ p₃ : P}
@@ -731,6 +798,7 @@ theorem affineIndependent_of_ne_of_not_mem_of_mem_of_mem {s : AffineSubspace k P
   ext x
   fin_cases x <;> rfl
 #align affine_independent_of_ne_of_not_mem_of_mem_of_mem affineIndependent_of_ne_of_not_mem_of_mem_of_mem
+-/
 
 end DivisionRing
 
@@ -740,10 +808,9 @@ variable {k : Type _} {V : Type _} {P : Type _} [LinearOrderedRing k] [AddCommGr
 
 variable [Module k V] [affine_space V P] {ι : Type _}
 
-include V
-
 attribute [local instance] LinearOrderedRing.decidableLt
 
+#print sign_eq_of_affineCombination_mem_affineSpan_pair /-
 /-- Given an affinely independent family of points, suppose that an affine combination lies in
 the span of two points given as affine combinations, and suppose that, for two indices, the
 coefficients in the first point in the span are zero and those in the second point in the span
@@ -763,7 +830,9 @@ theorem sign_eq_of_affineCombination_mem_affineSpan_pair {p : ι → P} (h : Aff
   dsimp only at hr 
   rw [hr i hi, hr j hj, hi0, hj0, add_zero, add_zero, sub_zero, sub_zero, sign_mul, sign_mul, hij]
 #align sign_eq_of_affine_combination_mem_affine_span_pair sign_eq_of_affineCombination_mem_affineSpan_pair
+-/
 
+#print sign_eq_of_affineCombination_mem_affineSpan_single_lineMap /-
 /-- Given an affinely independent family of points, suppose that an affine combination lies in
 the span of one point of that family and a combination of another two points of that family given
 by `line_map` with coefficient between 0 and 1. Then the coefficients of those two points in the
@@ -787,6 +856,7 @@ theorem sign_eq_of_affineCombination_mem_affineSpan_single_lineMap {p : ι → P
     Finset.affineCombinationLineMapWeights_apply_right h₂₃]
   simp [hc0, sub_pos.2 hc1]
 #align sign_eq_of_affine_combination_mem_affine_span_single_line_map sign_eq_of_affineCombination_mem_affineSpan_single_lineMap
+-/
 
 end Ordered
 
@@ -796,8 +866,6 @@ variable (k : Type _) {V : Type _} (P : Type _) [Ring k] [AddCommGroup V] [Modul
 
 variable [affine_space V P]
 
-include V
-
 #print Affine.Simplex /-
 /-- A `simplex k P n` is a collection of `n + 1` affinely
 independent points. -/
@@ -825,11 +893,13 @@ def mkOfPoint (p : P) : Simplex k P 0 :=
 #align affine.simplex.mk_of_point Affine.Simplex.mkOfPoint
 -/
 
+#print Affine.Simplex.mkOfPoint_points /-
 /-- The point in a simplex constructed with `mk_of_point`. -/
 @[simp]
 theorem mkOfPoint_points (p : P) (i : Fin 1) : (mkOfPoint k p).points i = p :=
   rfl
 #align affine.simplex.mk_of_point_points Affine.Simplex.mkOfPoint_points
+-/
 
 instance [Inhabited P] : Inhabited (Simplex k P 0) :=
   ⟨mkOfPoint k default⟩
@@ -842,6 +912,7 @@ instance nonempty : Nonempty (Simplex k P 0) :=
 
 variable {k V}
 
+#print Affine.Simplex.ext /-
 /-- Two simplices are equal if they have the same points. -/
 @[ext]
 theorem ext {n : ℕ} {s1 s2 : Simplex k P n} (h : ∀ i, s1.points i = s2.points i) : s1 = s2 :=
@@ -851,11 +922,14 @@ theorem ext {n : ℕ} {s1 s2 : Simplex k P n} (h : ∀ i, s1.points i = s2.point
   congr with i
   exact h i
 #align affine.simplex.ext Affine.Simplex.ext
+-/
 
+#print Affine.Simplex.ext_iff /-
 /-- Two simplices are equal if and only if they have the same points. -/
 theorem ext_iff {n : ℕ} (s1 s2 : Simplex k P n) : s1 = s2 ↔ ∀ i, s1.points i = s2.points i :=
   ⟨fun h _ => h ▸ rfl, ext⟩
 #align affine.simplex.ext_iff Affine.Simplex.ext_iff
+-/
 
 #print Affine.Simplex.face /-
 /-- A face of a simplex is a simplex with the given subset of
@@ -866,32 +940,40 @@ def face {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ} (h
 #align affine.simplex.face Affine.Simplex.face
 -/
 
+#print Affine.Simplex.face_points /-
 /-- The points of a face of a simplex are given by `mono_of_fin`. -/
 theorem face_points {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ}
     (h : fs.card = m + 1) (i : Fin (m + 1)) :
     (s.face h).points i = s.points (fs.orderEmbOfFin h i) :=
   rfl
 #align affine.simplex.face_points Affine.Simplex.face_points
+-/
 
+#print Affine.Simplex.face_points' /-
 /-- The points of a face of a simplex are given by `mono_of_fin`. -/
 theorem face_points' {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ}
     (h : fs.card = m + 1) : (s.face h).points = s.points ∘ fs.orderEmbOfFin h :=
   rfl
 #align affine.simplex.face_points' Affine.Simplex.face_points'
+-/
 
+#print Affine.Simplex.face_eq_mkOfPoint /-
 /-- A single-point face equals the 0-simplex constructed with
 `mk_of_point`. -/
 @[simp]
 theorem face_eq_mkOfPoint {n : ℕ} (s : Simplex k P n) (i : Fin (n + 1)) :
     s.face (Finset.card_singleton i) = mkOfPoint k (s.points i) := by ext; simp [face_points]
 #align affine.simplex.face_eq_mk_of_point Affine.Simplex.face_eq_mkOfPoint
+-/
 
+#print Affine.Simplex.range_face_points /-
 /-- The set of points of a face. -/
 @[simp]
 theorem range_face_points {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ}
     (h : fs.card = m + 1) : Set.range (s.face h).points = s.points '' ↑fs := by
   rw [face_points', Set.range_comp, Finset.range_orderEmbOfFin]
 #align affine.simplex.range_face_points Affine.Simplex.range_face_points
+-/
 
 #print Affine.Simplex.reindex /-
 /-- Remap a simplex along an `equiv` of index types. -/
@@ -901,12 +983,15 @@ def reindex {m n : ℕ} (s : Simplex k P m) (e : Fin (m + 1) ≃ Fin (n + 1)) :
 #align affine.simplex.reindex Affine.Simplex.reindex
 -/
 
+#print Affine.Simplex.reindex_refl /-
 /-- Reindexing by `equiv.refl` yields the original simplex. -/
 @[simp]
 theorem reindex_refl {n : ℕ} (s : Simplex k P n) : s.reindex (Equiv.refl (Fin (n + 1))) = s :=
   ext fun _ => rfl
 #align affine.simplex.reindex_refl Affine.Simplex.reindex_refl
+-/
 
+#print Affine.Simplex.reindex_trans /-
 /-- Reindexing by the composition of two equivalences is the same as reindexing twice. -/
 @[simp]
 theorem reindex_trans {n₁ n₂ n₃ : ℕ} (e₁₂ : Fin (n₁ + 1) ≃ Fin (n₂ + 1))
@@ -914,25 +999,32 @@ theorem reindex_trans {n₁ n₂ n₃ : ℕ} (e₁₂ : Fin (n₁ + 1) ≃ Fin (
     s.reindex (e₁₂.trans e₂₃) = (s.reindex e₁₂).reindex e₂₃ :=
   rfl
 #align affine.simplex.reindex_trans Affine.Simplex.reindex_trans
+-/
 
+#print Affine.Simplex.reindex_reindex_symm /-
 /-- Reindexing by an equivalence and its inverse yields the original simplex. -/
 @[simp]
 theorem reindex_reindex_symm {m n : ℕ} (s : Simplex k P m) (e : Fin (m + 1) ≃ Fin (n + 1)) :
     (s.reindex e).reindex e.symm = s := by rw [← reindex_trans, Equiv.self_trans_symm, reindex_refl]
 #align affine.simplex.reindex_reindex_symm Affine.Simplex.reindex_reindex_symm
+-/
 
+#print Affine.Simplex.reindex_symm_reindex /-
 /-- Reindexing by the inverse of an equivalence and that equivalence yields the original simplex. -/
 @[simp]
 theorem reindex_symm_reindex {m n : ℕ} (s : Simplex k P m) (e : Fin (n + 1) ≃ Fin (m + 1)) :
     (s.reindex e.symm).reindex e = s := by rw [← reindex_trans, Equiv.symm_trans_self, reindex_refl]
 #align affine.simplex.reindex_symm_reindex Affine.Simplex.reindex_symm_reindex
+-/
 
+#print Affine.Simplex.reindex_range_points /-
 /-- Reindexing a simplex produces one with the same set of points. -/
 @[simp]
 theorem reindex_range_points {m n : ℕ} (s : Simplex k P m) (e : Fin (m + 1) ≃ Fin (n + 1)) :
     Set.range (s.reindex e).points = Set.range s.points := by
   rw [reindex, Set.range_comp, Equiv.range_eq_univ, Set.image_univ]
 #align affine.simplex.reindex_range_points Affine.Simplex.reindex_range_points
+-/
 
 end Simplex
 
@@ -945,8 +1037,7 @@ namespace Simplex
 variable {k : Type _} {V : Type _} {P : Type _} [DivisionRing k] [AddCommGroup V] [Module k V]
   [affine_space V P]
 
-include V
-
+#print Affine.Simplex.face_centroid_eq_centroid /-
 /-- The centroid of a face of a simplex as the centroid of a subset of
 the points. -/
 @[simp]
@@ -957,7 +1048,9 @@ theorem face_centroid_eq_centroid {n : ℕ} (s : Simplex k P n) {fs : Finset (Fi
   rw [← Finset.coe_inj, Finset.coe_map, Finset.coe_univ, Set.image_univ]
   simp
 #align affine.simplex.face_centroid_eq_centroid Affine.Simplex.face_centroid_eq_centroid
+-/
 
+#print Affine.Simplex.centroid_eq_iff /-
 /-- Over a characteristic-zero division ring, the centroids given by
 two subsets of the points of a simplex are equal if and only if those
 faces are given by the same subset of points. -/
@@ -986,7 +1079,9 @@ theorem centroid_eq_iff [CharZero k] {n : ℕ} (s : Simplex k P n) {fs₁ fs₂
   · simpa [hni, hi, key] using ha
   · simpa [hni, hi, key] using ha.symm
 #align affine.simplex.centroid_eq_iff Affine.Simplex.centroid_eq_iff
+-/
 
+#print Affine.Simplex.face_centroid_eq_iff /-
 /-- Over a characteristic-zero division ring, the centroids of two
 faces of a simplex are equal if and only if those faces are given by
 the same subset of points. -/
@@ -998,7 +1093,9 @@ theorem face_centroid_eq_iff [CharZero k] {n : ℕ} (s : Simplex k P n)
   rw [face_centroid_eq_centroid, face_centroid_eq_centroid]
   exact s.centroid_eq_iff h₁ h₂
 #align affine.simplex.face_centroid_eq_iff Affine.Simplex.face_centroid_eq_iff
+-/
 
+#print Affine.Simplex.centroid_eq_of_range_eq /-
 /-- Two simplices with the same points have the same centroid. -/
 theorem centroid_eq_of_range_eq {n : ℕ} {s₁ s₂ : Simplex k P n}
     (h : Set.range s₁.points = Set.range s₂.points) :
@@ -1010,6 +1107,7 @@ theorem centroid_eq_of_range_eq {n : ℕ} {s₁ s₂ : Simplex k P n}
       (fun _ _ _ _ he => AffineIndependent.injective s₁.independent he)
       (fun _ _ _ _ he => AffineIndependent.injective s₂.independent he) h
 #align affine.simplex.centroid_eq_of_range_eq Affine.Simplex.centroid_eq_of_range_eq
+-/
 
 end Simplex
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

@@ -60,8 +60,7 @@ include V
 nontrivial weighted subtractions (where the sum of weights is 0) are
 0. -/
 def AffineIndependent (p : ι → P) : Prop :=
-  ∀ (s : Finset ι) (w : ι → k),
-    (∑ i in s, w i) = 0 → s.weightedVSub p w = (0 : V) → ∀ i ∈ s, w i = 0
+  ∀ (s : Finset ι) (w : ι → k), ∑ i in s, w i = 0 → s.weightedVSub p w = (0 : V) → ∀ i ∈ s, w i = 0
 #align affine_independent AffineIndependent
 -/
 
@@ -69,7 +68,7 @@ def AffineIndependent (p : ι → P) : Prop :=
 theorem affineIndependent_def (p : ι → P) :
     AffineIndependent k p ↔
       ∀ (s : Finset ι) (w : ι → k),
-        (∑ i in s, w i) = 0 → s.weightedVSub p w = (0 : V) → ∀ i ∈ s, w i = 0 :=
+        ∑ i in s, w i = 0 → s.weightedVSub p w = (0 : V) → ∀ i ∈ s, w i = 0 :=
   Iff.rfl
 #align affine_independent_def affineIndependent_def
 
@@ -83,7 +82,7 @@ only if no nontrivial weighted subtractions over `finset.univ` (where
 the sum of the weights is 0) are 0. -/
 theorem affineIndependent_iff_of_fintype [Fintype ι] (p : ι → P) :
     AffineIndependent k p ↔
-      ∀ w : ι → k, (∑ i, w i) = 0 → Finset.univ.weightedVSub p w = (0 : V) → ∀ i, w i = 0 :=
+      ∀ w : ι → k, ∑ i, w i = 0 → Finset.univ.weightedVSub p w = (0 : V) → ∀ i, w i = 0 :=
   by
   constructor
   · exact fun h w hw hs i => h Finset.univ w hw hs i (Finset.mem_univ _)
@@ -112,7 +111,7 @@ theorem affineIndependent_iff_linearIndependent_vsub (p : ι → P) (i1 : ι) :
       dsimp only
       erw [dif_neg x.property, Subtype.coe_eta]
     rw [hfg]
-    have hf : (∑ ι in s2, f ι) = 0 :=
+    have hf : ∑ ι in s2, f ι = 0 :=
       by
       rw [Finset.sum_insert
           (Finset.not_mem_map_subtype_of_not_property s (Classical.not_not.2 rfl)),
@@ -140,7 +139,7 @@ theorem affineIndependent_iff_linearIndependent_vsub (p : ι → P) (i1 : ι) :
     rw [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero s w p hw (p i1), ←
       s.weighted_vsub_of_point_erase w p i1, Finset.weightedVSubOfPoint_apply] at hs 
     let f : ι → V := fun i => w i • (p i -ᵥ p i1)
-    have hs2 : (∑ i in (s.erase i1).Subtype fun i => i ≠ i1, f i) = 0 :=
+    have hs2 : ∑ i in (s.erase i1).Subtype fun i => i ≠ i1, f i = 0 :=
       by
       rw [← hs]
       convert Finset.sum_subtype_of_mem f fun x => Finset.ne_of_mem_erase
@@ -201,8 +200,8 @@ have equal `set.indicator`. -/
 theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P) :
     AffineIndependent k p ↔
       ∀ (s1 s2 : Finset ι) (w1 w2 : ι → k),
-        (∑ i in s1, w1 i) = 1 →
-          (∑ i in s2, w2 i) = 1 →
+        ∑ i in s1, w1 i = 1 →
+          ∑ i in s2, w2 i = 1 →
             s1.affineCombination k p w1 = s2.affineCombination k p w2 →
               Set.indicator (↑s1) w1 = Set.indicator (↑s2) w2 :=
   by
@@ -214,7 +213,7 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
     · rw [← sub_eq_zero]
       rw [Set.sum_indicator_subset _ (Finset.subset_union_left s1 s2)] at hw1 
       rw [Set.sum_indicator_subset _ (Finset.subset_union_right s1 s2)] at hw2 
-      have hws : (∑ i in s1 ∪ s2, (Set.indicator (↑s1) w1 - Set.indicator (↑s2) w2) i) = 0 := by
+      have hws : ∑ i in s1 ∪ s2, (Set.indicator (↑s1) w1 - Set.indicator (↑s2) w2) i = 0 := by
         simp [hw1, hw2]
       rw [Finset.affineCombination_indicator_subset _ _ (Finset.subset_union_left s1 s2),
         Finset.affineCombination_indicator_subset _ _ (Finset.subset_union_right s1 s2), ←
@@ -224,13 +223,13 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
       simp [mt (Set.mem_union_left ↑s2) hi, mt (Set.mem_union_right ↑s1) hi]
   · intro ha s w hw hs i0 hi0
     let w1 : ι → k := Function.update (Function.const ι 0) i0 1
-    have hw1 : (∑ i in s, w1 i) = 1 := by
+    have hw1 : ∑ i in s, w1 i = 1 := by
       rw [Finset.sum_update_of_mem hi0, Finset.sum_const_zero, add_zero]
     have hw1s : s.affine_combination k p w1 = p i0 :=
       s.affine_combination_of_eq_one_of_eq_zero w1 p hi0 (Function.update_same _ _ _) fun _ _ hne =>
         Function.update_noteq hne _ _
     let w2 := w + w1
-    have hw2 : (∑ i in s, w2 i) = 1 := by simp [w2, Finset.sum_add_distrib, hw, hw1]
+    have hw2 : ∑ i in s, w2 i = 1 := by simp [w2, Finset.sum_add_distrib, hw, hw1]
     have hw2s : s.affine_combination k p w2 = p i0 := by
       simp [w2, ← Finset.weightedVSub_vadd_affineCombination, hs, hw1s]
     replace ha := ha s s w2 w1 hw2 hw1 (hw1s.symm ▸ hw2s)
@@ -245,8 +244,8 @@ combinations (with sum of weights 1) that evaluate to the same point are equal.
 theorem affineIndependent_iff_eq_of_fintype_affineCombination_eq [Fintype ι] (p : ι → P) :
     AffineIndependent k p ↔
       ∀ w1 w2 : ι → k,
-        (∑ i, w1 i) = 1 →
-          (∑ i, w2 i) = 1 →
+        ∑ i, w1 i = 1 →
+          ∑ i, w2 i = 1 →
             Finset.univ.affineCombination k p w1 = Finset.univ.affineCombination k p w2 → w1 = w2 :=
   by
   rw [affineIndependent_iff_indicator_eq_of_affineCombination_eq]
@@ -254,9 +253,9 @@ theorem affineIndependent_iff_eq_of_fintype_affineCombination_eq [Fintype ι] (p
   · intro h w1 w2 hw1 hw2 hweq
     simpa only [Set.indicator_univ, Finset.coe_univ] using h _ _ w1 w2 hw1 hw2 hweq
   · intro h s1 s2 w1 w2 hw1 hw2 hweq
-    have hw1' : (∑ i, (s1 : Set ι).indicator w1 i) = 1 := by
+    have hw1' : ∑ i, (s1 : Set ι).indicator w1 i = 1 := by
       rwa [Set.sum_indicator_subset _ (Finset.subset_univ s1)] at hw1 
-    have hw2' : (∑ i, (s2 : Set ι).indicator w2 i) = 1 := by
+    have hw2' : ∑ i, (s2 : Set ι).indicator w2 i = 1 := by
       rwa [Set.sum_indicator_subset _ (Finset.subset_univ s2)] at hw2 
     rw [Finset.affineCombination_indicator_subset w1 p (Finset.subset_univ s1),
       Finset.affineCombination_indicator_subset w2 p (Finset.subset_univ s2)] at hweq 
@@ -279,8 +278,8 @@ theorem AffineIndependent.units_lineMap {p : ι → P} (hp : AffineIndependent k
 #align affine_independent.units_line_map AffineIndependent.units_lineMap
 
 theorem AffineIndependent.indicator_eq_of_affineCombination_eq {p : ι → P}
-    (ha : AffineIndependent k p) (s₁ s₂ : Finset ι) (w₁ w₂ : ι → k) (hw₁ : (∑ i in s₁, w₁ i) = 1)
-    (hw₂ : (∑ i in s₂, w₂ i) = 1) (h : s₁.affineCombination k p w₁ = s₂.affineCombination k p w₂) :
+    (ha : AffineIndependent k p) (s₁ s₂ : Finset ι) (w₁ w₂ : ι → k) (hw₁ : ∑ i in s₁, w₁ i = 1)
+    (hw₂ : ∑ i in s₂, w₂ i = 1) (h : s₁.affineCombination k p w₁ = s₂.affineCombination k p w₂) :
     Set.indicator (↑s₁) w₁ = Set.indicator (↑s₂) w₂ :=
   (affineIndependent_iff_indicator_eq_of_affineCombination_eq k p).1 ha s₁ s₂ w₁ w₂ hw₁ hw₂ h
 #align affine_independent.indicator_eq_of_affine_combination_eq AffineIndependent.indicator_eq_of_affineCombination_eq
@@ -310,8 +309,7 @@ theorem AffineIndependent.comp_embedding {ι2 : Type _} (f : ι2 ↪ ι) {p : ι
     have h : ∃ i : ι2, f i = f i2 := ⟨i2, rfl⟩
     have hs : h.some = i2 := f.injective h.some_spec
     simp_rw [w', dif_pos h, hs]
-  have hw's : (∑ i in fs', w' i) = 0 :=
-    by
+  have hw's : ∑ i in fs', w' i = 0 := by
     rw [← hw, Finset.sum_map]
     simp [hw']
   have hs' : fs'.weighted_vsub p w' = (0 : V) :=
@@ -438,7 +436,7 @@ theorem AffineIndependent.exists_mem_inter_of_exists_mem_inter_affineSpan [Nontr
   rcases hp0s2 with ⟨fs2, hfs2, w2, hw2, hp0s2⟩
   rw [affineIndependent_iff_indicator_eq_of_affineCombination_eq] at ha 
   replace ha := ha fs1 fs2 w1 w2 hw1 hw2 (hp0s1 ▸ hp0s2)
-  have hnz : (∑ i in fs1, w1 i) ≠ 0 := hw1.symm ▸ one_ne_zero
+  have hnz : ∑ i in fs1, w1 i ≠ 0 := hw1.symm ▸ one_ne_zero
   rcases Finset.exists_ne_zero_of_sum_ne_zero hnz with ⟨i, hifs1, hinz⟩
   simp_rw [← Set.indicator_of_mem (Finset.mem_coe.2 hifs1) w1, ha] at hinz 
   use i, hfs1 hifs1, hfs2 (Set.mem_of_indicator_ne_zero hinz)
@@ -483,7 +481,7 @@ theorem AffineIndependent.not_mem_affineSpan_diff [Nontrivial k] {p : ι → P}
 
 theorem exists_nontrivial_relation_sum_zero_of_not_affine_ind {t : Finset V}
     (h : ¬AffineIndependent k (coe : t → V)) :
-    ∃ f : V → k, (∑ e in t, f e • e) = 0 ∧ (∑ e in t, f e) = 0 ∧ ∃ x ∈ t, f x ≠ 0 := by
+    ∃ f : V → k, ∑ e in t, f e • e = 0 ∧ ∑ e in t, f e = 0 ∧ ∃ x ∈ t, f x ≠ 0 := by
   classical
   rw [affineIndependent_iff_of_fintype] at h 
   simp only [exists_prop, not_forall] at h 
@@ -502,7 +500,7 @@ theorem exists_nontrivial_relation_sum_zero_of_not_affine_ind {t : Finset V}
 in terms of linear combinations. -/
 theorem affineIndependent_iff {ι} {p : ι → V} :
     AffineIndependent k p ↔
-      ∀ (s : Finset ι) (w : ι → k), s.Sum w = 0 → (∑ e in s, w e • p e) = 0 → ∀ e ∈ s, w e = 0 :=
+      ∀ (s : Finset ι) (w : ι → k), s.Sum w = 0 → ∑ e in s, w e • p e = 0 → ∀ e ∈ s, w e = 0 :=
   forall₃_congr fun s w hw => by simp [s.weighted_vsub_eq_linear_combination hw]
 #align affine_independent_iff affineIndependent_iff
 
@@ -510,8 +508,7 @@ theorem affineIndependent_iff {ι} {p : ι → V} :
 `vector_span` of two points given as affine combinations if and only if it is a weighted
 subtraction with weights a multiple of the difference between the weights of the two points. -/
 theorem weightedVSub_mem_vectorSpan_pair {p : ι → P} (h : AffineIndependent k p) {w w₁ w₂ : ι → k}
-    {s : Finset ι} (hw : (∑ i in s, w i) = 0) (hw₁ : (∑ i in s, w₁ i) = 1)
-    (hw₂ : (∑ i in s, w₂ i) = 1) :
+    {s : Finset ι} (hw : ∑ i in s, w i = 0) (hw₁ : ∑ i in s, w₁ i = 1) (hw₂ : ∑ i in s, w₂ i = 1) :
     s.weightedVSub p w ∈
         vectorSpan k ({s.affineCombination k p w₁, s.affineCombination k p w₂} : Set P) ↔
       ∃ r : k, ∀ i ∈ s, w i = r * (w₁ i - w₂ i) :=
@@ -521,7 +518,7 @@ theorem weightedVSub_mem_vectorSpan_pair {p : ι → P} (h : AffineIndependent k
   · rcases h with ⟨r, hr⟩
     refine' ⟨r, fun i hi => _⟩
     rw [s.affine_combination_vsub, ← s.weighted_vsub_const_smul, ← sub_eq_zero, ← map_sub] at hr 
-    have hw' : (∑ j in s, (r • (w₁ - w₂) - w) j) = 0 := by
+    have hw' : ∑ j in s, (r • (w₁ - w₂) - w) j = 0 := by
       simp_rw [Pi.sub_apply, Pi.smul_apply, Pi.sub_apply, smul_sub, Finset.sum_sub_distrib, ←
         Finset.smul_sum, hw, hw₁, hw₂, sub_self]
     have hr' := h s _ hw' hr i hi
@@ -541,8 +538,8 @@ span of two points given as affine combinations if and only if it is an affine c
 with weights those of one point plus a multiple of the difference between the weights of the
 two points. -/
 theorem affineCombination_mem_affineSpan_pair {p : ι → P} (h : AffineIndependent k p)
-    {w w₁ w₂ : ι → k} {s : Finset ι} (hw : (∑ i in s, w i) = 1) (hw₁ : (∑ i in s, w₁ i) = 1)
-    (hw₂ : (∑ i in s, w₂ i) = 1) :
+    {w w₁ w₂ : ι → k} {s : Finset ι} (hw : ∑ i in s, w i = 1) (hw₁ : ∑ i in s, w₁ i = 1)
+    (hw₂ : ∑ i in s, w₂ i = 1) :
     s.affineCombination k p w ∈ line[k, s.affineCombination k p w₁, s.affineCombination k p w₂] ↔
       ∃ r : k, ∀ i ∈ s, w i = r * (w₂ i - w₁ i) + w₁ i :=
   by
@@ -656,10 +653,10 @@ theorem AffineIndependent.affineIndependent_of_not_mem_span {p : ι → P} {i :
   · refine' False.elim (hi _)
     let wm : ι → k := -(w i)⁻¹ • w
     have hms : s.weighted_vsub p wm = (0 : V) := by simp [wm, hs]
-    have hwm : (∑ i in s, wm i) = 0 := by simp [wm, ← Finset.mul_sum, hw]
+    have hwm : ∑ i in s, wm i = 0 := by simp [wm, ← Finset.mul_sum, hw]
     have hwmi : wm i = -1 := by simp [wm, his.2]
     let w' : { y // y ≠ i } → k := fun x => wm x
-    have hw' : (∑ x in s', w' x) = 1 :=
+    have hw' : ∑ x in s', w' x = 1 :=
       by
       simp_rw [w', Finset.sum_subtype_eq_sum_filter]
       rw [← s.sum_filter_add_sum_filter_not (· ≠ i)] at hwm 
@@ -672,7 +669,7 @@ theorem AffineIndependent.affineIndependent_of_not_mem_span {p : ι → P} {i :
     exact affineCombination_mem_affineSpan hw' p'
   · rw [not_and_or, Classical.not_not] at his 
     let w' : { y // y ≠ i } → k := fun x => w x
-    have hw' : (∑ x in s', w' x) = 0 :=
+    have hw' : ∑ x in s', w' x = 0 :=
       by
       simp_rw [Finset.sum_subtype_eq_sum_filter]
       rw [Finset.sum_filter_of_ne, hw]
@@ -753,8 +750,8 @@ coefficients in the first point in the span are zero and those in the second poi
 have the same sign. Then the coefficients in the combination lying in the span have the same
 sign. -/
 theorem sign_eq_of_affineCombination_mem_affineSpan_pair {p : ι → P} (h : AffineIndependent k p)
-    {w w₁ w₂ : ι → k} {s : Finset ι} (hw : (∑ i in s, w i) = 1) (hw₁ : (∑ i in s, w₁ i) = 1)
-    (hw₂ : (∑ i in s, w₂ i) = 1)
+    {w w₁ w₂ : ι → k} {s : Finset ι} (hw : ∑ i in s, w i = 1) (hw₁ : ∑ i in s, w₁ i = 1)
+    (hw₂ : ∑ i in s, w₂ i = 1)
     (hs :
       s.affineCombination k p w ∈ line[k, s.affineCombination k p w₁, s.affineCombination k p w₂])
     {i j : ι} (hi : i ∈ s) (hj : j ∈ s) (hi0 : w₁ i = 0) (hj0 : w₁ j = 0)
@@ -772,7 +769,7 @@ the span of one point of that family and a combination of another two points of
 by `line_map` with coefficient between 0 and 1. Then the coefficients of those two points in the
 combination lying in the span have the same sign. -/
 theorem sign_eq_of_affineCombination_mem_affineSpan_single_lineMap {p : ι → P}
-    (h : AffineIndependent k p) {w : ι → k} {s : Finset ι} (hw : (∑ i in s, w i) = 1) {i₁ i₂ i₃ : ι}
+    (h : AffineIndependent k p) {w : ι → k} {s : Finset ι} (hw : ∑ i in s, w i = 1) {i₁ i₂ i₃ : ι}
     (h₁ : i₁ ∈ s) (h₂ : i₂ ∈ s) (h₃ : i₃ ∈ s) (h₁₂ : i₁ ≠ i₂) (h₁₃ : i₁ ≠ i₃) (h₂₃ : i₂ ≠ i₃)
     {c : k} (hc0 : 0 < c) (hc1 : c < 1)
     (hs : s.affineCombination k p w ∈ line[k, p i₁, AffineMap.lineMap (p i₂) (p i₃) c]) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

@@ -598,7 +598,7 @@ theorem exists_subset_affineIndependent_affineSpan_eq_top {s : Set P}
 
 variable (k V)
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem exists_affineIndependent (s : Set P) :
     ∃ (t : _) (_ : t ⊆ s), affineSpan k t = affineSpan k s ∧ AffineIndependent k (coe : t → P) :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -99,56 +99,56 @@ from a base point in that family are linearly independent. -/
 theorem affineIndependent_iff_linearIndependent_vsub (p : ι → P) (i1 : ι) :
     AffineIndependent k p ↔ LinearIndependent k fun i : { x // x ≠ i1 } => (p i -ᵥ p i1 : V) := by
   classical
-    constructor
-    · intro h
-      rw [linearIndependent_iff']
-      intro s g hg i hi
-      set f : ι → k := fun x => if hx : x = i1 then -∑ y in s, g y else g ⟨x, hx⟩ with hfdef
-      let s2 : Finset ι := insert i1 (s.map (embedding.subtype _))
-      have hfg : ∀ x : { x // x ≠ i1 }, g x = f x :=
-        by
-        intro x
-        rw [hfdef]
-        dsimp only
-        erw [dif_neg x.property, Subtype.coe_eta]
-      rw [hfg]
-      have hf : (∑ ι in s2, f ι) = 0 :=
-        by
-        rw [Finset.sum_insert
-            (Finset.not_mem_map_subtype_of_not_property s (Classical.not_not.2 rfl)),
-          Finset.sum_subtype_map_embedding fun x hx => (hfg x).symm]
-        rw [hfdef]
-        dsimp only
-        rw [dif_pos rfl]
-        exact neg_add_self _
-      have hs2 : s2.weighted_vsub p f = (0 : V) :=
-        by
-        set f2 : ι → V := fun x => f x • (p x -ᵥ p i1) with hf2def
-        set g2 : { x // x ≠ i1 } → V := fun x => g x • (p x -ᵥ p i1) with hg2def
-        have hf2g2 : ∀ x : { x // x ≠ i1 }, f2 x = g2 x :=
-          by
-          simp_rw [hf2def, hg2def, hfg]
-          exact fun x => rfl
-        rw [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero s2 f p hf (p i1),
-          Finset.weightedVSubOfPoint_insert, Finset.weightedVSubOfPoint_apply,
-          Finset.sum_subtype_map_embedding fun x hx => hf2g2 x]
-        exact hg
-      exact h s2 f hf hs2 i (Finset.mem_insert_of_mem (Finset.mem_map.2 ⟨i, hi, rfl⟩))
-    · intro h
-      rw [linearIndependent_iff'] at h 
-      intro s w hw hs i hi
-      rw [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero s w p hw (p i1), ←
-        s.weighted_vsub_of_point_erase w p i1, Finset.weightedVSubOfPoint_apply] at hs 
-      let f : ι → V := fun i => w i • (p i -ᵥ p i1)
-      have hs2 : (∑ i in (s.erase i1).Subtype fun i => i ≠ i1, f i) = 0 :=
+  constructor
+  · intro h
+    rw [linearIndependent_iff']
+    intro s g hg i hi
+    set f : ι → k := fun x => if hx : x = i1 then -∑ y in s, g y else g ⟨x, hx⟩ with hfdef
+    let s2 : Finset ι := insert i1 (s.map (embedding.subtype _))
+    have hfg : ∀ x : { x // x ≠ i1 }, g x = f x :=
+      by
+      intro x
+      rw [hfdef]
+      dsimp only
+      erw [dif_neg x.property, Subtype.coe_eta]
+    rw [hfg]
+    have hf : (∑ ι in s2, f ι) = 0 :=
+      by
+      rw [Finset.sum_insert
+          (Finset.not_mem_map_subtype_of_not_property s (Classical.not_not.2 rfl)),
+        Finset.sum_subtype_map_embedding fun x hx => (hfg x).symm]
+      rw [hfdef]
+      dsimp only
+      rw [dif_pos rfl]
+      exact neg_add_self _
+    have hs2 : s2.weighted_vsub p f = (0 : V) :=
+      by
+      set f2 : ι → V := fun x => f x • (p x -ᵥ p i1) with hf2def
+      set g2 : { x // x ≠ i1 } → V := fun x => g x • (p x -ᵥ p i1) with hg2def
+      have hf2g2 : ∀ x : { x // x ≠ i1 }, f2 x = g2 x :=
         by
-        rw [← hs]
-        convert Finset.sum_subtype_of_mem f fun x => Finset.ne_of_mem_erase
-      have h2 := h ((s.erase i1).Subtype fun i => i ≠ i1) (fun x => w x) hs2
-      simp_rw [Finset.mem_subtype] at h2 
-      have h2b : ∀ i ∈ s, i ≠ i1 → w i = 0 := fun i his hi =>
-        h2 ⟨i, hi⟩ (Finset.mem_erase_of_ne_of_mem hi his)
-      exact Finset.eq_zero_of_sum_eq_zero hw h2b i hi
+        simp_rw [hf2def, hg2def, hfg]
+        exact fun x => rfl
+      rw [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero s2 f p hf (p i1),
+        Finset.weightedVSubOfPoint_insert, Finset.weightedVSubOfPoint_apply,
+        Finset.sum_subtype_map_embedding fun x hx => hf2g2 x]
+      exact hg
+    exact h s2 f hf hs2 i (Finset.mem_insert_of_mem (Finset.mem_map.2 ⟨i, hi, rfl⟩))
+  · intro h
+    rw [linearIndependent_iff'] at h 
+    intro s w hw hs i hi
+    rw [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero s w p hw (p i1), ←
+      s.weighted_vsub_of_point_erase w p i1, Finset.weightedVSubOfPoint_apply] at hs 
+    let f : ι → V := fun i => w i • (p i -ᵥ p i1)
+    have hs2 : (∑ i in (s.erase i1).Subtype fun i => i ≠ i1, f i) = 0 :=
+      by
+      rw [← hs]
+      convert Finset.sum_subtype_of_mem f fun x => Finset.ne_of_mem_erase
+    have h2 := h ((s.erase i1).Subtype fun i => i ≠ i1) (fun x => w x) hs2
+    simp_rw [Finset.mem_subtype] at h2 
+    have h2b : ∀ i ∈ s, i ≠ i1 → w i = 0 := fun i his hi =>
+      h2 ⟨i, hi⟩ (Finset.mem_erase_of_ne_of_mem hi his)
+    exact Finset.eq_zero_of_sum_eq_zero hw h2b i hi
 #align affine_independent_iff_linear_independent_vsub affineIndependent_iff_linearIndependent_vsub
 
 /-- A set is affinely independent if and only if the differences from
@@ -165,15 +165,16 @@ theorem affineIndependent_set_iff_linearIndependent_vsub {s : Set P} {p₁ : P}
     let f : (fun p : P => (p -ᵥ p₁ : V)) '' (s \ {p₁}) → { x : s // x ≠ ⟨p₁, hp₁⟩ } := fun x =>
       ⟨⟨(x : V) +ᵥ p₁, Set.mem_of_mem_diff (hv x)⟩, fun hx =>
         Set.not_mem_of_mem_diff (hv x) (Subtype.ext_iff.1 hx)⟩
-    convert h.comp f fun x1 x2 hx =>
+    convert
+      h.comp f fun x1 x2 hx =>
         Subtype.ext (vadd_right_cancel p₁ (Subtype.ext_iff.1 (Subtype.ext_iff.1 hx)))
     ext v
     exact (vadd_vsub (v : V) p₁).symm
   · intro h
     let f : { x : s // x ≠ ⟨p₁, hp₁⟩ } → (fun p : P => (p -ᵥ p₁ : V)) '' (s \ {p₁}) := fun x =>
       ⟨((x : s) : P) -ᵥ p₁, ⟨x, ⟨⟨(x : s).property, fun hx => x.property (Subtype.ext hx)⟩, rfl⟩⟩⟩
-    convert h.comp f fun x1 x2 hx =>
-        Subtype.ext (Subtype.ext (vsub_left_cancel (Subtype.ext_iff.1 hx)))
+    convert
+      h.comp f fun x1 x2 hx => Subtype.ext (Subtype.ext (vsub_left_cancel (Subtype.ext_iff.1 hx)))
 #align affine_independent_set_iff_linear_independent_vsub affineIndependent_set_iff_linearIndependent_vsub
 
 /-- A set of nonzero vectors is linearly independent if and only if,
@@ -206,37 +207,37 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
               Set.indicator (↑s1) w1 = Set.indicator (↑s2) w2 :=
   by
   classical
-    constructor
-    · intro ha s1 s2 w1 w2 hw1 hw2 heq
-      ext i
-      by_cases hi : i ∈ s1 ∪ s2
-      · rw [← sub_eq_zero]
-        rw [Set.sum_indicator_subset _ (Finset.subset_union_left s1 s2)] at hw1 
-        rw [Set.sum_indicator_subset _ (Finset.subset_union_right s1 s2)] at hw2 
-        have hws : (∑ i in s1 ∪ s2, (Set.indicator (↑s1) w1 - Set.indicator (↑s2) w2) i) = 0 := by
-          simp [hw1, hw2]
-        rw [Finset.affineCombination_indicator_subset _ _ (Finset.subset_union_left s1 s2),
-          Finset.affineCombination_indicator_subset _ _ (Finset.subset_union_right s1 s2), ←
-          @vsub_eq_zero_iff_eq V, Finset.affineCombination_vsub] at heq 
-        exact ha (s1 ∪ s2) (Set.indicator (↑s1) w1 - Set.indicator (↑s2) w2) hws HEq i hi
-      · rw [← Finset.mem_coe, Finset.coe_union] at hi 
-        simp [mt (Set.mem_union_left ↑s2) hi, mt (Set.mem_union_right ↑s1) hi]
-    · intro ha s w hw hs i0 hi0
-      let w1 : ι → k := Function.update (Function.const ι 0) i0 1
-      have hw1 : (∑ i in s, w1 i) = 1 := by
-        rw [Finset.sum_update_of_mem hi0, Finset.sum_const_zero, add_zero]
-      have hw1s : s.affine_combination k p w1 = p i0 :=
-        s.affine_combination_of_eq_one_of_eq_zero w1 p hi0 (Function.update_same _ _ _)
-          fun _ _ hne => Function.update_noteq hne _ _
-      let w2 := w + w1
-      have hw2 : (∑ i in s, w2 i) = 1 := by simp [w2, Finset.sum_add_distrib, hw, hw1]
-      have hw2s : s.affine_combination k p w2 = p i0 := by
-        simp [w2, ← Finset.weightedVSub_vadd_affineCombination, hs, hw1s]
-      replace ha := ha s s w2 w1 hw2 hw1 (hw1s.symm ▸ hw2s)
-      have hws : w2 i0 - w1 i0 = 0 := by
-        rw [← Finset.mem_coe] at hi0 
-        rw [← Set.indicator_of_mem hi0 w2, ← Set.indicator_of_mem hi0 w1, ha, sub_self]
-      simpa [w2] using hws
+  constructor
+  · intro ha s1 s2 w1 w2 hw1 hw2 heq
+    ext i
+    by_cases hi : i ∈ s1 ∪ s2
+    · rw [← sub_eq_zero]
+      rw [Set.sum_indicator_subset _ (Finset.subset_union_left s1 s2)] at hw1 
+      rw [Set.sum_indicator_subset _ (Finset.subset_union_right s1 s2)] at hw2 
+      have hws : (∑ i in s1 ∪ s2, (Set.indicator (↑s1) w1 - Set.indicator (↑s2) w2) i) = 0 := by
+        simp [hw1, hw2]
+      rw [Finset.affineCombination_indicator_subset _ _ (Finset.subset_union_left s1 s2),
+        Finset.affineCombination_indicator_subset _ _ (Finset.subset_union_right s1 s2), ←
+        @vsub_eq_zero_iff_eq V, Finset.affineCombination_vsub] at heq 
+      exact ha (s1 ∪ s2) (Set.indicator (↑s1) w1 - Set.indicator (↑s2) w2) hws HEq i hi
+    · rw [← Finset.mem_coe, Finset.coe_union] at hi 
+      simp [mt (Set.mem_union_left ↑s2) hi, mt (Set.mem_union_right ↑s1) hi]
+  · intro ha s w hw hs i0 hi0
+    let w1 : ι → k := Function.update (Function.const ι 0) i0 1
+    have hw1 : (∑ i in s, w1 i) = 1 := by
+      rw [Finset.sum_update_of_mem hi0, Finset.sum_const_zero, add_zero]
+    have hw1s : s.affine_combination k p w1 = p i0 :=
+      s.affine_combination_of_eq_one_of_eq_zero w1 p hi0 (Function.update_same _ _ _) fun _ _ hne =>
+        Function.update_noteq hne _ _
+    let w2 := w + w1
+    have hw2 : (∑ i in s, w2 i) = 1 := by simp [w2, Finset.sum_add_distrib, hw, hw1]
+    have hw2s : s.affine_combination k p w2 = p i0 := by
+      simp [w2, ← Finset.weightedVSub_vadd_affineCombination, hs, hw1s]
+    replace ha := ha s s w2 w1 hw2 hw1 (hw1s.symm ▸ hw2s)
+    have hws : w2 i0 - w1 i0 = 0 := by
+      rw [← Finset.mem_coe] at hi0 
+      rw [← Set.indicator_of_mem hi0 w2, ← Set.indicator_of_mem hi0 w1, ha, sub_self]
+    simpa [w2] using hws
 #align affine_independent_iff_indicator_eq_of_affine_combination_eq affineIndependent_iff_indicator_eq_of_affineCombination_eq
 
 /-- A finite family is affinely independent if and only if any affine
@@ -301,24 +302,24 @@ family. -/
 theorem AffineIndependent.comp_embedding {ι2 : Type _} (f : ι2 ↪ ι) {p : ι → P}
     (ha : AffineIndependent k p) : AffineIndependent k (p ∘ f) := by
   classical
-    intro fs w hw hs i0 hi0
-    let fs' := fs.map f
-    let w' i := if h : ∃ i2, f i2 = i then w h.some else 0
-    have hw' : ∀ i2 : ι2, w' (f i2) = w i2 := by
-      intro i2
-      have h : ∃ i : ι2, f i = f i2 := ⟨i2, rfl⟩
-      have hs : h.some = i2 := f.injective h.some_spec
-      simp_rw [w', dif_pos h, hs]
-    have hw's : (∑ i in fs', w' i) = 0 :=
-      by
-      rw [← hw, Finset.sum_map]
-      simp [hw']
-    have hs' : fs'.weighted_vsub p w' = (0 : V) :=
-      by
-      rw [← hs, Finset.weightedVSub_map]
-      congr with i
-      simp [hw']
-    rw [← ha fs' w' hw's hs' (f i0) ((Finset.mem_map' _).2 hi0), hw']
+  intro fs w hw hs i0 hi0
+  let fs' := fs.map f
+  let w' i := if h : ∃ i2, f i2 = i then w h.some else 0
+  have hw' : ∀ i2 : ι2, w' (f i2) = w i2 := by
+    intro i2
+    have h : ∃ i : ι2, f i = f i2 := ⟨i2, rfl⟩
+    have hs : h.some = i2 := f.injective h.some_spec
+    simp_rw [w', dif_pos h, hs]
+  have hw's : (∑ i in fs', w' i) = 0 :=
+    by
+    rw [← hw, Finset.sum_map]
+    simp [hw']
+  have hs' : fs'.weighted_vsub p w' = (0 : V) :=
+    by
+    rw [← hs, Finset.weightedVSub_map]
+    congr with i
+    simp [hw']
+  rw [← ha fs' w' hw's hs' (f i0) ((Finset.mem_map' _).2 hi0), hw']
 #align affine_independent.comp_embedding AffineIndependent.comp_embedding
 
 /-- If a family is affinely independent, so is any subfamily indexed
@@ -484,18 +485,17 @@ theorem exists_nontrivial_relation_sum_zero_of_not_affine_ind {t : Finset V}
     (h : ¬AffineIndependent k (coe : t → V)) :
     ∃ f : V → k, (∑ e in t, f e • e) = 0 ∧ (∑ e in t, f e) = 0 ∧ ∃ x ∈ t, f x ≠ 0 := by
   classical
-    rw [affineIndependent_iff_of_fintype] at h 
-    simp only [exists_prop, not_forall] at h 
-    obtain ⟨w, hw, hwt, i, hi⟩ := h
-    simp only [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero _ w (coe : t → V) hw 0,
-      vsub_eq_sub, Finset.weightedVSubOfPoint_apply, sub_zero] at hwt 
-    let f : ∀ x : V, x ∈ t → k := fun x hx => w ⟨x, hx⟩
-    refine' ⟨fun x => if hx : x ∈ t then f x hx else (0 : k), _, _, by use i; simp [hi, f]⟩
-    suffices (∑ e : V in t, dite (e ∈ t) (fun hx => f e hx • e) fun hx => 0) = 0 by convert this;
-      ext; by_cases hx : x ∈ t <;> simp [hx]
-    all_goals
-      simp only [Finset.sum_dite_of_true fun x h => h, Subtype.val_eq_coe, Finset.mk_coe, f, hwt,
-        hw]
+  rw [affineIndependent_iff_of_fintype] at h 
+  simp only [exists_prop, not_forall] at h 
+  obtain ⟨w, hw, hwt, i, hi⟩ := h
+  simp only [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero _ w (coe : t → V) hw 0,
+    vsub_eq_sub, Finset.weightedVSubOfPoint_apply, sub_zero] at hwt 
+  let f : ∀ x : V, x ∈ t → k := fun x hx => w ⟨x, hx⟩
+  refine' ⟨fun x => if hx : x ∈ t then f x hx else (0 : k), _, _, by use i; simp [hi, f]⟩
+  suffices (∑ e : V in t, dite (e ∈ t) (fun hx => f e hx • e) fun hx => 0) = 0 by convert this; ext;
+    by_cases hx : x ∈ t <;> simp [hx]
+  all_goals
+    simp only [Finset.sum_dite_of_true fun x h => h, Subtype.val_eq_coe, Finset.mk_coe, f, hwt, hw]
 #align exists_nontrivial_relation_sum_zero_of_not_affine_ind exists_nontrivial_relation_sum_zero_of_not_affine_ind
 
 /-- Viewing a module as an affine space modelled on itself, we can characterise affine independence
@@ -647,48 +647,48 @@ variable {k V P}
 the affine span of that family, the family is affinely independent. -/
 theorem AffineIndependent.affineIndependent_of_not_mem_span {p : ι → P} {i : ι}
     (ha : AffineIndependent k fun x : { y // y ≠ i } => p x)
-    (hi : p i ∉ affineSpan k (p '' { x | x ≠ i })) : AffineIndependent k p := by
+    (hi : p i ∉ affineSpan k (p '' {x | x ≠ i})) : AffineIndependent k p := by
   classical
-    intro s w hw hs
-    let s' : Finset { y // y ≠ i } := s.subtype (· ≠ i)
-    let p' : { y // y ≠ i } → P := fun x => p x
-    by_cases his : i ∈ s ∧ w i ≠ 0
-    · refine' False.elim (hi _)
-      let wm : ι → k := -(w i)⁻¹ • w
-      have hms : s.weighted_vsub p wm = (0 : V) := by simp [wm, hs]
-      have hwm : (∑ i in s, wm i) = 0 := by simp [wm, ← Finset.mul_sum, hw]
-      have hwmi : wm i = -1 := by simp [wm, his.2]
-      let w' : { y // y ≠ i } → k := fun x => wm x
-      have hw' : (∑ x in s', w' x) = 1 :=
-        by
-        simp_rw [w', Finset.sum_subtype_eq_sum_filter]
-        rw [← s.sum_filter_add_sum_filter_not (· ≠ i)] at hwm 
-        simp_rw [Classical.not_not, Finset.filter_eq', if_pos his.1, Finset.sum_singleton, ← wm,
-          hwmi, ← sub_eq_add_neg, sub_eq_zero] at hwm 
-        exact hwm
-      rw [← s.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one hms his.1 hwmi, ←
-        (Subtype.range_coe : _ = { x | x ≠ i }), ← Set.range_comp, ←
-        s.affine_combination_subtype_eq_filter]
-      exact affineCombination_mem_affineSpan hw' p'
-    · rw [not_and_or, Classical.not_not] at his 
-      let w' : { y // y ≠ i } → k := fun x => w x
-      have hw' : (∑ x in s', w' x) = 0 :=
-        by
-        simp_rw [Finset.sum_subtype_eq_sum_filter]
-        rw [Finset.sum_filter_of_ne, hw]
-        rintro x hxs hwx rfl
-        exact hwx (his.neg_resolve_left hxs)
-      have hs' : s'.weighted_vsub p' w' = (0 : V) :=
-        by
-        simp_rw [Finset.weightedVSub_subtype_eq_filter]
-        rw [Finset.weightedVSub_filter_of_ne, hs]
-        rintro x hxs hwx rfl
-        exact hwx (his.neg_resolve_left hxs)
-      intro j hj
-      by_cases hji : j = i
-      · rw [hji] at hj 
-        exact hji.symm ▸ his.neg_resolve_left hj
-      · exact ha s' w' hw' hs' ⟨j, hji⟩ (Finset.mem_subtype.2 hj)
+  intro s w hw hs
+  let s' : Finset { y // y ≠ i } := s.subtype (· ≠ i)
+  let p' : { y // y ≠ i } → P := fun x => p x
+  by_cases his : i ∈ s ∧ w i ≠ 0
+  · refine' False.elim (hi _)
+    let wm : ι → k := -(w i)⁻¹ • w
+    have hms : s.weighted_vsub p wm = (0 : V) := by simp [wm, hs]
+    have hwm : (∑ i in s, wm i) = 0 := by simp [wm, ← Finset.mul_sum, hw]
+    have hwmi : wm i = -1 := by simp [wm, his.2]
+    let w' : { y // y ≠ i } → k := fun x => wm x
+    have hw' : (∑ x in s', w' x) = 1 :=
+      by
+      simp_rw [w', Finset.sum_subtype_eq_sum_filter]
+      rw [← s.sum_filter_add_sum_filter_not (· ≠ i)] at hwm 
+      simp_rw [Classical.not_not, Finset.filter_eq', if_pos his.1, Finset.sum_singleton, ← wm, hwmi,
+        ← sub_eq_add_neg, sub_eq_zero] at hwm 
+      exact hwm
+    rw [← s.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one hms his.1 hwmi, ←
+      (Subtype.range_coe : _ = {x | x ≠ i}), ← Set.range_comp, ←
+      s.affine_combination_subtype_eq_filter]
+    exact affineCombination_mem_affineSpan hw' p'
+  · rw [not_and_or, Classical.not_not] at his 
+    let w' : { y // y ≠ i } → k := fun x => w x
+    have hw' : (∑ x in s', w' x) = 0 :=
+      by
+      simp_rw [Finset.sum_subtype_eq_sum_filter]
+      rw [Finset.sum_filter_of_ne, hw]
+      rintro x hxs hwx rfl
+      exact hwx (his.neg_resolve_left hxs)
+    have hs' : s'.weighted_vsub p' w' = (0 : V) :=
+      by
+      simp_rw [Finset.weightedVSub_subtype_eq_filter]
+      rw [Finset.weightedVSub_filter_of_ne, hs]
+      rintro x hxs hwx rfl
+      exact hwx (his.neg_resolve_left hxs)
+    intro j hj
+    by_cases hji : j = i
+    · rw [hji] at hj 
+      exact hji.symm ▸ his.neg_resolve_left hj
+    · exact ha s' w' hw' hs' ⟨j, hji⟩ (Finset.mem_subtype.2 hj)
 #align affine_independent.affine_independent_of_not_mem_span AffineIndependent.affineIndependent_of_not_mem_span
 
 /-- If distinct points `p₁` and `p₂` lie in `s` but `p₃` does not, the three points are affinely
@@ -778,17 +778,17 @@ theorem sign_eq_of_affineCombination_mem_affineSpan_single_lineMap {p : ι → P
     (hs : s.affineCombination k p w ∈ line[k, p i₁, AffineMap.lineMap (p i₂) (p i₃) c]) :
     SignType.sign (w i₂) = SignType.sign (w i₃) := by
   classical
-    rw [← s.affine_combination_affine_combination_single_weights k p h₁, ←
-      s.affine_combination_affine_combination_line_map_weights p h₂ h₃ c] at hs 
-    refine'
-      sign_eq_of_affineCombination_mem_affineSpan_pair h hw
-        (s.sum_affine_combination_single_weights k h₁)
-        (s.sum_affine_combination_line_map_weights h₂ h₃ c) hs h₂ h₃
-        (Finset.affineCombinationSingleWeights_apply_of_ne k h₁₂.symm)
-        (Finset.affineCombinationSingleWeights_apply_of_ne k h₁₃.symm) _
-    rw [Finset.affineCombinationLineMapWeights_apply_left h₂₃,
-      Finset.affineCombinationLineMapWeights_apply_right h₂₃]
-    simp [hc0, sub_pos.2 hc1]
+  rw [← s.affine_combination_affine_combination_single_weights k p h₁, ←
+    s.affine_combination_affine_combination_line_map_weights p h₂ h₃ c] at hs 
+  refine'
+    sign_eq_of_affineCombination_mem_affineSpan_pair h hw
+      (s.sum_affine_combination_single_weights k h₁)
+      (s.sum_affine_combination_line_map_weights h₂ h₃ c) hs h₂ h₃
+      (Finset.affineCombinationSingleWeights_apply_of_ne k h₁₂.symm)
+      (Finset.affineCombinationSingleWeights_apply_of_ne k h₁₃.symm) _
+  rw [Finset.affineCombinationLineMapWeights_apply_left h₂₃,
+    Finset.affineCombinationLineMapWeights_apply_right h₂₃]
+  simp [hc0, sub_pos.2 hc1]
 #align sign_eq_of_affine_combination_mem_affine_span_single_line_map sign_eq_of_affineCombination_mem_affineSpan_single_lineMap
 
 end Ordered
@@ -956,7 +956,7 @@ the points. -/
 theorem face_centroid_eq_centroid {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ}
     (h : fs.card = m + 1) : Finset.univ.centroid k (s.face h).points = fs.centroid k s.points :=
   by
-  convert(finset.univ.centroid_map k (fs.order_emb_of_fin h).toEmbedding s.points).symm
+  convert (finset.univ.centroid_map k (fs.order_emb_of_fin h).toEmbedding s.points).symm
   rw [← Finset.coe_inj, Finset.coe_map, Finset.coe_univ, Set.image_univ]
   simp
 #align affine.simplex.face_centroid_eq_centroid Affine.Simplex.face_centroid_eq_centroid
@@ -980,7 +980,7 @@ theorem centroid_eq_iff [CharZero k] {n : ℕ} (s : Simplex k P n) {fs₁ fs₂
     Finset.centroidWeightsIndicator_def, Finset.centroidWeights, h₁, h₂] at ha 
   ext i
   specialize ha i
-  have key : ∀ n : ℕ, (n : k) + 1 ≠ 0 := fun n h => by norm_cast  at h 
+  have key : ∀ n : ℕ, (n : k) + 1 ≠ 0 := fun n h => by norm_cast at h 
   -- we should be able to golf this to `refine ⟨λ hi, decidable.by_contradiction (λ hni, _), ...⟩`,
       -- but for some unknown reason it doesn't work.
       constructor <;>

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -88,8 +88,8 @@ theorem affineIndependent_iff_of_fintype [Fintype ι] (p : ι → P) :
   constructor
   · exact fun h w hw hs i => h Finset.univ w hw hs i (Finset.mem_univ _)
   · intro h s w hw hs i hi
-    rw [Finset.weightedVSub_indicator_subset _ _ (Finset.subset_univ s)] at hs
-    rw [Set.sum_indicator_subset _ (Finset.subset_univ s)] at hw
+    rw [Finset.weightedVSub_indicator_subset _ _ (Finset.subset_univ s)] at hs 
+    rw [Set.sum_indicator_subset _ (Finset.subset_univ s)] at hw 
     replace h := h ((↑s : Set ι).indicator w) hw hs i
     simpa [hi] using h
 #align affine_independent_iff_of_fintype affineIndependent_iff_of_fintype
@@ -135,17 +135,17 @@ theorem affineIndependent_iff_linearIndependent_vsub (p : ι → P) (i1 : ι) :
         exact hg
       exact h s2 f hf hs2 i (Finset.mem_insert_of_mem (Finset.mem_map.2 ⟨i, hi, rfl⟩))
     · intro h
-      rw [linearIndependent_iff'] at h
+      rw [linearIndependent_iff'] at h 
       intro s w hw hs i hi
       rw [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero s w p hw (p i1), ←
-        s.weighted_vsub_of_point_erase w p i1, Finset.weightedVSubOfPoint_apply] at hs
+        s.weighted_vsub_of_point_erase w p i1, Finset.weightedVSubOfPoint_apply] at hs 
       let f : ι → V := fun i => w i • (p i -ᵥ p i1)
       have hs2 : (∑ i in (s.erase i1).Subtype fun i => i ≠ i1, f i) = 0 :=
         by
         rw [← hs]
         convert Finset.sum_subtype_of_mem f fun x => Finset.ne_of_mem_erase
       have h2 := h ((s.erase i1).Subtype fun i => i ≠ i1) (fun x => w x) hs2
-      simp_rw [Finset.mem_subtype] at h2
+      simp_rw [Finset.mem_subtype] at h2 
       have h2b : ∀ i ∈ s, i ≠ i1 → w i = 0 := fun i his hi =>
         h2 ⟨i, hi⟩ (Finset.mem_erase_of_ne_of_mem hi his)
       exact Finset.eq_zero_of_sum_eq_zero hw h2b i hi
@@ -211,15 +211,15 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
       ext i
       by_cases hi : i ∈ s1 ∪ s2
       · rw [← sub_eq_zero]
-        rw [Set.sum_indicator_subset _ (Finset.subset_union_left s1 s2)] at hw1
-        rw [Set.sum_indicator_subset _ (Finset.subset_union_right s1 s2)] at hw2
+        rw [Set.sum_indicator_subset _ (Finset.subset_union_left s1 s2)] at hw1 
+        rw [Set.sum_indicator_subset _ (Finset.subset_union_right s1 s2)] at hw2 
         have hws : (∑ i in s1 ∪ s2, (Set.indicator (↑s1) w1 - Set.indicator (↑s2) w2) i) = 0 := by
           simp [hw1, hw2]
         rw [Finset.affineCombination_indicator_subset _ _ (Finset.subset_union_left s1 s2),
           Finset.affineCombination_indicator_subset _ _ (Finset.subset_union_right s1 s2), ←
-          @vsub_eq_zero_iff_eq V, Finset.affineCombination_vsub] at heq
+          @vsub_eq_zero_iff_eq V, Finset.affineCombination_vsub] at heq 
         exact ha (s1 ∪ s2) (Set.indicator (↑s1) w1 - Set.indicator (↑s2) w2) hws HEq i hi
-      · rw [← Finset.mem_coe, Finset.coe_union] at hi
+      · rw [← Finset.mem_coe, Finset.coe_union] at hi 
         simp [mt (Set.mem_union_left ↑s2) hi, mt (Set.mem_union_right ↑s1) hi]
     · intro ha s w hw hs i0 hi0
       let w1 : ι → k := Function.update (Function.const ι 0) i0 1
@@ -234,7 +234,7 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
         simp [w2, ← Finset.weightedVSub_vadd_affineCombination, hs, hw1s]
       replace ha := ha s s w2 w1 hw2 hw1 (hw1s.symm ▸ hw2s)
       have hws : w2 i0 - w1 i0 = 0 := by
-        rw [← Finset.mem_coe] at hi0
+        rw [← Finset.mem_coe] at hi0 
         rw [← Set.indicator_of_mem hi0 w2, ← Set.indicator_of_mem hi0 w1, ha, sub_self]
       simpa [w2] using hws
 #align affine_independent_iff_indicator_eq_of_affine_combination_eq affineIndependent_iff_indicator_eq_of_affineCombination_eq
@@ -254,11 +254,11 @@ theorem affineIndependent_iff_eq_of_fintype_affineCombination_eq [Fintype ι] (p
     simpa only [Set.indicator_univ, Finset.coe_univ] using h _ _ w1 w2 hw1 hw2 hweq
   · intro h s1 s2 w1 w2 hw1 hw2 hweq
     have hw1' : (∑ i, (s1 : Set ι).indicator w1 i) = 1 := by
-      rwa [Set.sum_indicator_subset _ (Finset.subset_univ s1)] at hw1
+      rwa [Set.sum_indicator_subset _ (Finset.subset_univ s1)] at hw1 
     have hw2' : (∑ i, (s2 : Set ι).indicator w2 i) = 1 := by
-      rwa [Set.sum_indicator_subset _ (Finset.subset_univ s2)] at hw2
+      rwa [Set.sum_indicator_subset _ (Finset.subset_univ s2)] at hw2 
     rw [Finset.affineCombination_indicator_subset w1 p (Finset.subset_univ s1),
-      Finset.affineCombination_indicator_subset w2 p (Finset.subset_univ s2)] at hweq
+      Finset.affineCombination_indicator_subset w2 p (Finset.subset_univ s2)] at hweq 
     exact h _ _ hw1' hw2' hweq
 #align affine_independent_iff_eq_of_fintype_affine_combination_eq affineIndependent_iff_eq_of_fintype_affineCombination_eq
 
@@ -272,7 +272,7 @@ This is the affine version of `linear_independent.units_smul`. -/
 theorem AffineIndependent.units_lineMap {p : ι → P} (hp : AffineIndependent k p) (j : ι)
     (w : ι → Units k) : AffineIndependent k fun i => AffineMap.lineMap (p j) (p i) (w i : k) :=
   by
-  rw [affineIndependent_iff_linearIndependent_vsub k _ j] at hp⊢
+  rw [affineIndependent_iff_linearIndependent_vsub k _ j] at hp ⊢
   simp only [AffineMap.lineMap_vsub_left, AffineMap.coe_const, AffineMap.lineMap_same]
   exact hp.units_smul fun i => w i
 #align affine_independent.units_line_map AffineIndependent.units_lineMap
@@ -290,7 +290,7 @@ protected theorem AffineIndependent.injective [Nontrivial k] {p : ι → P}
     (ha : AffineIndependent k p) : Function.Injective p :=
   by
   intro i j hij
-  rw [affineIndependent_iff_linearIndependent_vsub _ _ j] at ha
+  rw [affineIndependent_iff_linearIndependent_vsub _ _ j] at ha 
   by_contra hij'
   exact ha.ne_zero ⟨i, hij'⟩ (vsub_eq_zero_iff_eq.mpr hij)
 #align affine_independent.injective AffineIndependent.injective
@@ -382,7 +382,7 @@ theorem AffineIndependent.of_comp {p : ι → P} (f : P →ᵃ[k] P₂) (hai : A
   obtain ⟨i⟩ := h
   rw [affineIndependent_iff_linearIndependent_vsub k p i]
   simp_rw [affineIndependent_iff_linearIndependent_vsub k (f ∘ p) i, Function.comp_apply, ←
-    f.linear_map_vsub] at hai
+    f.linear_map_vsub] at hai 
   exact LinearIndependent.of_comp f.linear hai
 #align affine_independent.of_comp AffineIndependent.of_comp
 
@@ -393,7 +393,7 @@ theorem AffineIndependent.map' {p : ι → P} (hai : AffineIndependent k p) (f :
   by
   cases' isEmpty_or_nonempty ι with h h; · haveI := h; apply affineIndependent_of_subsingleton
   obtain ⟨i⟩ := h
-  rw [affineIndependent_iff_linearIndependent_vsub k p i] at hai
+  rw [affineIndependent_iff_linearIndependent_vsub k p i] at hai 
   simp_rw [affineIndependent_iff_linearIndependent_vsub k (f ∘ p) i, Function.comp_apply, ←
     f.linear_map_vsub]
   have hf' : f.linear.ker = ⊥ := by rwa [LinearMap.ker_eq_bot, f.linear_injective_iff]
@@ -430,16 +430,16 @@ theorem AffineIndependent.exists_mem_inter_of_exists_mem_inter_affineSpan [Nontr
     (ha : AffineIndependent k p) {s1 s2 : Set ι} {p0 : P} (hp0s1 : p0 ∈ affineSpan k (p '' s1))
     (hp0s2 : p0 ∈ affineSpan k (p '' s2)) : ∃ i : ι, i ∈ s1 ∩ s2 :=
   by
-  rw [Set.image_eq_range] at hp0s1 hp0s2
+  rw [Set.image_eq_range] at hp0s1 hp0s2 
   rw [mem_affineSpan_iff_eq_affineCombination, ←
-    Finset.eq_affineCombination_subset_iff_eq_affineCombination_subtype] at hp0s1 hp0s2
+    Finset.eq_affineCombination_subset_iff_eq_affineCombination_subtype] at hp0s1 hp0s2 
   rcases hp0s1 with ⟨fs1, hfs1, w1, hw1, hp0s1⟩
   rcases hp0s2 with ⟨fs2, hfs2, w2, hw2, hp0s2⟩
-  rw [affineIndependent_iff_indicator_eq_of_affineCombination_eq] at ha
+  rw [affineIndependent_iff_indicator_eq_of_affineCombination_eq] at ha 
   replace ha := ha fs1 fs2 w1 w2 hw1 hw2 (hp0s1 ▸ hp0s2)
   have hnz : (∑ i in fs1, w1 i) ≠ 0 := hw1.symm ▸ one_ne_zero
   rcases Finset.exists_ne_zero_of_sum_ne_zero hnz with ⟨i, hifs1, hinz⟩
-  simp_rw [← Set.indicator_of_mem (Finset.mem_coe.2 hifs1) w1, ha] at hinz
+  simp_rw [← Set.indicator_of_mem (Finset.mem_coe.2 hifs1) w1, ha] at hinz 
   use i, hfs1 hifs1, hfs2 (Set.mem_of_indicator_ne_zero hinz)
 #align affine_independent.exists_mem_inter_of_exists_mem_inter_affine_span AffineIndependent.exists_mem_inter_of_exists_mem_inter_affineSpan
 
@@ -468,7 +468,7 @@ protected theorem AffineIndependent.mem_affineSpan_iff [Nontrivial k] {p : ι 
     have h :=
       AffineIndependent.exists_mem_inter_of_exists_mem_inter_affineSpan ha hs
         (mem_affineSpan k (Set.mem_image_of_mem _ (Set.mem_singleton _)))
-    rwa [← Set.nonempty_def, Set.inter_singleton_nonempty] at h
+    rwa [← Set.nonempty_def, Set.inter_singleton_nonempty] at h 
   · exact fun h => mem_affineSpan k (Set.mem_image_of_mem p h)
 #align affine_independent.mem_affine_span_iff AffineIndependent.mem_affineSpan_iff
 
@@ -484,11 +484,11 @@ theorem exists_nontrivial_relation_sum_zero_of_not_affine_ind {t : Finset V}
     (h : ¬AffineIndependent k (coe : t → V)) :
     ∃ f : V → k, (∑ e in t, f e • e) = 0 ∧ (∑ e in t, f e) = 0 ∧ ∃ x ∈ t, f x ≠ 0 := by
   classical
-    rw [affineIndependent_iff_of_fintype] at h
-    simp only [exists_prop, not_forall] at h
+    rw [affineIndependent_iff_of_fintype] at h 
+    simp only [exists_prop, not_forall] at h 
     obtain ⟨w, hw, hwt, i, hi⟩ := h
     simp only [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero _ w (coe : t → V) hw 0,
-      vsub_eq_sub, Finset.weightedVSubOfPoint_apply, sub_zero] at hwt
+      vsub_eq_sub, Finset.weightedVSubOfPoint_apply, sub_zero] at hwt 
     let f : ∀ x : V, x ∈ t → k := fun x hx => w ⟨x, hx⟩
     refine' ⟨fun x => if hx : x ∈ t then f x hx else (0 : k), _, _, by use i; simp [hi, f]⟩
     suffices (∑ e : V in t, dite (e ∈ t) (fun hx => f e hx • e) fun hx => 0) = 0 by convert this;
@@ -520,7 +520,7 @@ theorem weightedVSub_mem_vectorSpan_pair {p : ι → P} (h : AffineIndependent k
   refine' ⟨fun h => _, fun h => _⟩
   · rcases h with ⟨r, hr⟩
     refine' ⟨r, fun i hi => _⟩
-    rw [s.affine_combination_vsub, ← s.weighted_vsub_const_smul, ← sub_eq_zero, ← map_sub] at hr
+    rw [s.affine_combination_vsub, ← s.weighted_vsub_const_smul, ← sub_eq_zero, ← map_sub] at hr 
     have hw' : (∑ j in s, (r • (w₁ - w₂) - w) j) = 0 := by
       simp_rw [Pi.sub_apply, Pi.smul_apply, Pi.sub_apply, smul_sub, Finset.sum_sub_distrib, ←
         Finset.smul_sum, hw, hw₁, hw₂, sub_self]
@@ -530,7 +530,7 @@ theorem weightedVSub_mem_vectorSpan_pair {p : ι → P} (h : AffineIndependent k
   · rcases h with ⟨r, hr⟩
     refine' ⟨r, _⟩
     let w' i := r * (w₁ i - w₂ i)
-    change ∀ i ∈ s, w i = w' i at hr
+    change ∀ i ∈ s, w i = w' i at hr 
     rw [s.weighted_vsub_congr hr fun _ _ => rfl, s.affine_combination_vsub, ←
       s.weighted_vsub_const_smul]
     congr
@@ -575,21 +575,21 @@ theorem exists_subset_affineIndependent_affineSpan_eq_top {s : Set P}
     let hsv := Basis.ofVectorSpace k V
     have hsvi := hsv.linear_independent
     have hsvt := hsv.span_eq
-    rw [Basis.coe_ofVectorSpace] at hsvi hsvt
+    rw [Basis.coe_ofVectorSpace] at hsvi hsvt 
     have h0 : ∀ v : V, v ∈ Basis.ofVectorSpaceIndex _ _ → v ≠ 0 := by intro v hv;
       simpa using hsv.ne_zero ⟨v, hv⟩
-    rw [linearIndependent_set_iff_affineIndependent_vadd_union_singleton k h0 p₁] at hsvi
+    rw [linearIndependent_set_iff_affineIndependent_vadd_union_singleton k h0 p₁] at hsvi 
     exact
       ⟨{p₁} ∪ (fun v => v +ᵥ p₁) '' _, Set.empty_subset _, hsvi,
         affineSpan_singleton_union_vadd_eq_top_of_span_eq_top p₁ hsvt⟩
-  · rw [affineIndependent_set_iff_linearIndependent_vsub k hp₁] at h
+  · rw [affineIndependent_set_iff_linearIndependent_vsub k hp₁] at h 
     let bsv := Basis.extend h
     have hsvi := bsv.linear_independent
     have hsvt := bsv.span_eq
-    rw [Basis.coe_extend] at hsvi hsvt
+    rw [Basis.coe_extend] at hsvi hsvt 
     have hsv := h.subset_extend (Set.subset_univ _)
     have h0 : ∀ v : V, v ∈ h.extend _ → v ≠ 0 := by intro v hv; simpa using bsv.ne_zero ⟨v, hv⟩
-    rw [linearIndependent_set_iff_affineIndependent_vadd_union_singleton k h0 p₁] at hsvi
+    rw [linearIndependent_set_iff_affineIndependent_vadd_union_singleton k h0 p₁] at hsvi 
     refine' ⟨{p₁} ∪ (fun v => v +ᵥ p₁) '' h.extend (Set.subset_univ _), _, _⟩
     · refine' Set.Subset.trans _ (Set.union_subset_union_right _ (Set.image_subset _ hsv))
       simp [Set.image_image]
@@ -600,17 +600,17 @@ variable (k V)
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem exists_affineIndependent (s : Set P) :
-    ∃ (t : _)(_ : t ⊆ s), affineSpan k t = affineSpan k s ∧ AffineIndependent k (coe : t → P) :=
+    ∃ (t : _) (_ : t ⊆ s), affineSpan k t = affineSpan k s ∧ AffineIndependent k (coe : t → P) :=
   by
   rcases s.eq_empty_or_nonempty with (rfl | ⟨p, hp⟩)
   · exact ⟨∅, Set.empty_subset ∅, rfl, affineIndependent_of_subsingleton k _⟩
   obtain ⟨b, hb₁, hb₂, hb₃⟩ := exists_linearIndependent k ((Equiv.vaddConst p).symm '' s)
   have hb₀ : ∀ v : V, v ∈ b → v ≠ 0 := fun v hv => hb₃.ne_zero (⟨v, hv⟩ : b)
-  rw [linearIndependent_set_iff_affineIndependent_vadd_union_singleton k hb₀ p] at hb₃
+  rw [linearIndependent_set_iff_affineIndependent_vadd_union_singleton k hb₀ p] at hb₃ 
   refine' ⟨{p} ∪ Equiv.vaddConst p '' b, _, _, hb₃⟩
   · apply Set.union_subset (set.singleton_subset_iff.mpr hp)
     rwa [← (Equiv.vaddConst p).subset_image' b s]
-  · rw [Equiv.coe_vaddConst_symm, ← vectorSpan_eq_span_vsub_set_right k hp] at hb₂
+  · rw [Equiv.coe_vaddConst_symm, ← vectorSpan_eq_span_vsub_set_right k hp] at hb₂ 
     apply AffineSubspace.ext_of_direction_eq
     · have : Submodule.span k b = Submodule.span k (insert 0 b) := by simp
       simp only [direction_affineSpan, ← hb₂, Equiv.coe_vaddConst, Set.singleton_union,
@@ -662,15 +662,15 @@ theorem AffineIndependent.affineIndependent_of_not_mem_span {p : ι → P} {i :
       have hw' : (∑ x in s', w' x) = 1 :=
         by
         simp_rw [w', Finset.sum_subtype_eq_sum_filter]
-        rw [← s.sum_filter_add_sum_filter_not (· ≠ i)] at hwm
+        rw [← s.sum_filter_add_sum_filter_not (· ≠ i)] at hwm 
         simp_rw [Classical.not_not, Finset.filter_eq', if_pos his.1, Finset.sum_singleton, ← wm,
-          hwmi, ← sub_eq_add_neg, sub_eq_zero] at hwm
+          hwmi, ← sub_eq_add_neg, sub_eq_zero] at hwm 
         exact hwm
       rw [← s.affine_combination_eq_of_weighted_vsub_eq_zero_of_eq_neg_one hms his.1 hwmi, ←
         (Subtype.range_coe : _ = { x | x ≠ i }), ← Set.range_comp, ←
         s.affine_combination_subtype_eq_filter]
       exact affineCombination_mem_affineSpan hw' p'
-    · rw [not_and_or, Classical.not_not] at his
+    · rw [not_and_or, Classical.not_not] at his 
       let w' : { y // y ≠ i } → k := fun x => w x
       have hw' : (∑ x in s', w' x) = 0 :=
         by
@@ -686,7 +686,7 @@ theorem AffineIndependent.affineIndependent_of_not_mem_span {p : ι → P} {i :
         exact hwx (his.neg_resolve_left hxs)
       intro j hj
       by_cases hji : j = i
-      · rw [hji] at hj
+      · rw [hji] at hj 
         exact hji.symm ▸ his.neg_resolve_left hj
       · exact ha s' w' hw' hs' ⟨j, hji⟩ (Finset.mem_subtype.2 hj)
 #align affine_independent.affine_independent_of_not_mem_span AffineIndependent.affineIndependent_of_not_mem_span
@@ -761,9 +761,9 @@ theorem sign_eq_of_affineCombination_mem_affineSpan_pair {p : ι → P} (h : Aff
     (hij : SignType.sign (w₂ i) = SignType.sign (w₂ j)) :
     SignType.sign (w i) = SignType.sign (w j) :=
   by
-  rw [affineCombination_mem_affineSpan_pair h hw hw₁ hw₂] at hs
+  rw [affineCombination_mem_affineSpan_pair h hw hw₁ hw₂] at hs 
   rcases hs with ⟨r, hr⟩
-  dsimp only at hr
+  dsimp only at hr 
   rw [hr i hi, hr j hj, hi0, hj0, add_zero, add_zero, sub_zero, sub_zero, sign_mul, sign_mul, hij]
 #align sign_eq_of_affine_combination_mem_affine_span_pair sign_eq_of_affineCombination_mem_affineSpan_pair
 
@@ -779,7 +779,7 @@ theorem sign_eq_of_affineCombination_mem_affineSpan_single_lineMap {p : ι → P
     SignType.sign (w i₂) = SignType.sign (w i₃) := by
   classical
     rw [← s.affine_combination_affine_combination_single_weights k p h₁, ←
-      s.affine_combination_affine_combination_line_map_weights p h₂ h₃ c] at hs
+      s.affine_combination_affine_combination_line_map_weights p h₂ h₃ c] at hs 
     refine'
       sign_eq_of_affineCombination_mem_affineSpan_pair h hw
         (s.sum_affine_combination_single_weights k h₁)
@@ -971,16 +971,16 @@ theorem centroid_eq_iff [CharZero k] {n : ℕ} (s : Simplex k P n) {fs₁ fs₂
   by
   refine' ⟨fun h => _, congr_arg _⟩
   rw [Finset.centroid_eq_affineCombination_fintype, Finset.centroid_eq_affineCombination_fintype] at
-    h
+    h 
   have ha :=
     (affineIndependent_iff_indicator_eq_of_affineCombination_eq k s.points).1 s.independent _ _ _ _
       (fs₁.sum_centroid_weights_indicator_eq_one_of_card_eq_add_one k h₁)
       (fs₂.sum_centroid_weights_indicator_eq_one_of_card_eq_add_one k h₂) h
   simp_rw [Finset.coe_univ, Set.indicator_univ, Function.funext_iff,
-    Finset.centroidWeightsIndicator_def, Finset.centroidWeights, h₁, h₂] at ha
+    Finset.centroidWeightsIndicator_def, Finset.centroidWeights, h₁, h₂] at ha 
   ext i
   specialize ha i
-  have key : ∀ n : ℕ, (n : k) + 1 ≠ 0 := fun n h => by norm_cast  at h
+  have key : ∀ n : ℕ, (n : k) + 1 ≠ 0 := fun n h => by norm_cast  at h 
   -- we should be able to golf this to `refine ⟨λ hi, decidable.by_contradiction (λ hni, _), ...⟩`,
       -- but for some unknown reason it doesn't work.
       constructor <;>
@@ -1007,7 +1007,7 @@ theorem centroid_eq_of_range_eq {n : ℕ} {s₁ s₂ : Simplex k P n}
     (h : Set.range s₁.points = Set.range s₂.points) :
     Finset.univ.centroid k s₁.points = Finset.univ.centroid k s₂.points :=
   by
-  rw [← Set.image_univ, ← Set.image_univ, ← Finset.coe_univ] at h
+  rw [← Set.image_univ, ← Set.image_univ, ← Finset.coe_univ] at h 
   exact
     finset.univ.centroid_eq_of_inj_on_of_image_eq k _
       (fun _ _ _ _ he => AffineIndependent.injective s₁.independent he)

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -43,7 +43,7 @@ This file defines affinely independent families of points.
 
 noncomputable section
 
-open BigOperators Affine
+open scoped BigOperators Affine
 
 open Function
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -65,9 +65,6 @@ def AffineIndependent (p : ι → P) : Prop :=
 #align affine_independent AffineIndependent
 -/
 
-/- warning: affine_independent_def -> affineIndependent_def is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_independent_def affineIndependent_defₓ'. -/
 /-- The definition of `affine_independent`. -/
 theorem affineIndependent_def (p : ι → P) :
     AffineIndependent k p ↔
@@ -76,20 +73,11 @@ theorem affineIndependent_def (p : ι → P) :
   Iff.rfl
 #align affine_independent_def affineIndependent_def
 
-/- warning: affine_independent_of_subsingleton -> affineIndependent_of_subsingleton is a dubious translation:
-lean 3 declaration is
-  forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Subsingleton.{succ u4} ι] (p : ι -> P), AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p
-but is expected to have type
-  forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Subsingleton.{succ u4} ι] (p : ι -> P), AffineIndependent.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p
-Case conversion may be inaccurate. Consider using '#align affine_independent_of_subsingleton affineIndependent_of_subsingletonₓ'. -/
 /-- A family with at most one point is affinely independent. -/
 theorem affineIndependent_of_subsingleton [Subsingleton ι] (p : ι → P) : AffineIndependent k p :=
   fun s w h hs i hi => Fintype.eq_of_subsingleton_of_sum_eq h i hi
 #align affine_independent_of_subsingleton affineIndependent_of_subsingleton
 
-/- warning: affine_independent_iff_of_fintype -> affineIndependent_iff_of_fintype is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_independent_iff_of_fintype affineIndependent_iff_of_fintypeₓ'. -/
 /-- A family indexed by a `fintype` is affinely independent if and
 only if no nontrivial weighted subtractions over `finset.univ` (where
 the sum of the weights is 0) are 0. -/
@@ -106,9 +94,6 @@ theorem affineIndependent_iff_of_fintype [Fintype ι] (p : ι → P) :
     simpa [hi] using h
 #align affine_independent_iff_of_fintype affineIndependent_iff_of_fintype
 
-/- warning: affine_independent_iff_linear_independent_vsub -> affineIndependent_iff_linearIndependent_vsub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_independent_iff_linear_independent_vsub affineIndependent_iff_linearIndependent_vsubₓ'. -/
 /-- A family is affinely independent if and only if the differences
 from a base point in that family are linearly independent. -/
 theorem affineIndependent_iff_linearIndependent_vsub (p : ι → P) (i1 : ι) :
@@ -166,9 +151,6 @@ theorem affineIndependent_iff_linearIndependent_vsub (p : ι → P) (i1 : ι) :
       exact Finset.eq_zero_of_sum_eq_zero hw h2b i hi
 #align affine_independent_iff_linear_independent_vsub affineIndependent_iff_linearIndependent_vsub
 
-/- warning: affine_independent_set_iff_linear_independent_vsub -> affineIndependent_set_iff_linearIndependent_vsub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_independent_set_iff_linear_independent_vsub affineIndependent_set_iff_linearIndependent_vsubₓ'. -/
 /-- A set is affinely independent if and only if the differences from
 a base point in that set are linearly independent. -/
 theorem affineIndependent_set_iff_linearIndependent_vsub {s : Set P} {p₁ : P} (hp₁ : p₁ ∈ s) :
@@ -194,9 +176,6 @@ theorem affineIndependent_set_iff_linearIndependent_vsub {s : Set P} {p₁ : P}
         Subtype.ext (Subtype.ext (vsub_left_cancel (Subtype.ext_iff.1 hx)))
 #align affine_independent_set_iff_linear_independent_vsub affineIndependent_set_iff_linearIndependent_vsub
 
-/- warning: linear_independent_set_iff_affine_independent_vadd_union_singleton -> linearIndependent_set_iff_affineIndependent_vadd_union_singleton is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_independent_set_iff_affine_independent_vadd_union_singleton linearIndependent_set_iff_affineIndependent_vadd_union_singletonₓ'. -/
 /-- A set of nonzero vectors is linearly independent if and only if,
 given a point `p₁`, the vectors added to `p₁` and `p₁` itself are
 affinely independent. -/
@@ -215,9 +194,6 @@ theorem linearIndependent_set_iff_affineIndependent_vadd_union_singleton {s : Se
   rw [h]
 #align linear_independent_set_iff_affine_independent_vadd_union_singleton linearIndependent_set_iff_affineIndependent_vadd_union_singleton
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_independent_iff_indicator_eq_of_affine_combination_eq affineIndependent_iff_indicator_eq_of_affineCombination_eqₓ'. -/
 /-- A family is affinely independent if and only if any affine
 combinations (with sum of weights 1) that evaluate to the same point
 have equal `set.indicator`. -/
@@ -263,9 +239,6 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
       simpa [w2] using hws
 #align affine_independent_iff_indicator_eq_of_affine_combination_eq affineIndependent_iff_indicator_eq_of_affineCombination_eq
 
-/- warning: affine_independent_iff_eq_of_fintype_affine_combination_eq -> affineIndependent_iff_eq_of_fintype_affineCombination_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_independent_iff_eq_of_fintype_affine_combination_eq affineIndependent_iff_eq_of_fintype_affineCombination_eqₓ'. -/
 /-- A finite family is affinely independent if and only if any affine
 combinations (with sum of weights 1) that evaluate to the same point are equal. -/
 theorem affineIndependent_iff_eq_of_fintype_affineCombination_eq [Fintype ι] (p : ι → P) :
@@ -291,9 +264,6 @@ theorem affineIndependent_iff_eq_of_fintype_affineCombination_eq [Fintype ι] (p
 
 variable {k}
 
-/- warning: affine_independent.units_line_map -> AffineIndependent.units_lineMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_independent.units_line_map AffineIndependent.units_lineMapₓ'. -/
 /-- If we single out one member of an affine-independent family of points and affinely transport
 all others along the line joining them to this member, the resulting new family of points is affine-
 independent.
@@ -307,9 +277,6 @@ theorem AffineIndependent.units_lineMap {p : ι → P} (hp : AffineIndependent k
   exact hp.units_smul fun i => w i
 #align affine_independent.units_line_map AffineIndependent.units_lineMap
 
-/- warning: affine_independent.indicator_eq_of_affine_combination_eq -> AffineIndependent.indicator_eq_of_affineCombination_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_independent.indicator_eq_of_affine_combination_eq AffineIndependent.indicator_eq_of_affineCombination_eqₓ'. -/
 theorem AffineIndependent.indicator_eq_of_affineCombination_eq {p : ι → P}
     (ha : AffineIndependent k p) (s₁ s₂ : Finset ι) (w₁ w₂ : ι → k) (hw₁ : (∑ i in s₁, w₁ i) = 1)
     (hw₂ : (∑ i in s₂, w₂ i) = 1) (h : s₁.affineCombination k p w₁ = s₂.affineCombination k p w₂) :
@@ -317,12 +284,6 @@ theorem AffineIndependent.indicator_eq_of_affineCombination_eq {p : ι → P}
   (affineIndependent_iff_indicator_eq_of_affineCombination_eq k p).1 ha s₁ s₂ w₁ w₂ hw₁ hw₂ h
 #align affine_independent.indicator_eq_of_affine_combination_eq AffineIndependent.indicator_eq_of_affineCombination_eq
 
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 /-- An affinely independent family is injective, if the underlying
 ring is nontrivial. -/
 protected theorem AffineIndependent.injective [Nontrivial k] {p : ι → P}
@@ -334,12 +295,6 @@ protected theorem AffineIndependent.injective [Nontrivial k] {p : ι → P}
   exact ha.ne_zero ⟨i, hij'⟩ (vsub_eq_zero_iff_eq.mpr hij)
 #align affine_independent.injective AffineIndependent.injective
 
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 /-- If a family is affinely independent, so is any subfamily given by
 composition of an embedding into index type with the original
 family. -/
@@ -366,12 +321,6 @@ theorem AffineIndependent.comp_embedding {ι2 : Type _} (f : ι2 ↪ ι) {p : ι
     rw [← ha fs' w' hw's hs' (f i0) ((Finset.mem_map' _).2 hi0), hw']
 #align affine_independent.comp_embedding AffineIndependent.comp_embedding
 
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 /-- If a family is affinely independent, so is any subfamily indexed
 by a subtype of the index type. -/
 protected theorem AffineIndependent.subtype {p : ι → P} (ha : AffineIndependent k p) (s : Set ι) :
@@ -379,12 +328,6 @@ protected theorem AffineIndependent.subtype {p : ι → P} (ha : AffineIndepende
   ha.comp_embedding (Embedding.subtype _)
 #align affine_independent.subtype AffineIndependent.subtype
 
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 /-- If an indexed family of points is affinely independent, so is the
 corresponding set of points. -/
 protected theorem AffineIndependent.range {p : ι → P} (ha : AffineIndependent k p) :
@@ -398,12 +341,6 @@ protected theorem AffineIndependent.range {p : ι → P} (ha : AffineIndependent
   simp [hf]
 #align affine_independent.range AffineIndependent.range
 
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 theorem affineIndependent_equiv {ι' : Type _} (e : ι ≃ ι') {p : ι' → P} :
     AffineIndependent k (p ∘ e) ↔ AffineIndependent k p :=
   by
@@ -414,12 +351,6 @@ theorem affineIndependent_equiv {ι' : Type _} (e : ι ≃ ι') {p : ι' → P}
   exact h.comp_embedding e.symm.to_embedding
 #align affine_independent_equiv affineIndependent_equiv
 
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 /-- If a set of points is affinely independent, so is any subset. -/
 protected theorem AffineIndependent.mono {s t : Set P}
     (ha : AffineIndependent k (fun x => x : t → P)) (hs : s ⊆ t) :
@@ -427,12 +358,6 @@ protected theorem AffineIndependent.mono {s t : Set P}
   ha.comp_embedding (s.embeddingOfSubset t hs)
 #align affine_independent.mono AffineIndependent.mono
 
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 /-- If the range of an injective indexed family of points is affinely
 independent, so is that family. -/
 theorem AffineIndependent.of_set_of_injective {p : ι → P}
@@ -449,9 +374,6 @@ variable {V₂ P₂ : Type _} [AddCommGroup V₂] [Module k V₂] [affine_space
 
 include V₂
 
-/- warning: affine_independent.of_comp -> AffineIndependent.of_comp is a dubious translation:
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 /-- If the image of a family of points in affine space under an affine transformation is affine-
 independent, then the original family of points is also affine-independent. -/
 theorem AffineIndependent.of_comp {p : ι → P} (f : P →ᵃ[k] P₂) (hai : AffineIndependent k (f ∘ p)) :
@@ -464,9 +386,6 @@ theorem AffineIndependent.of_comp {p : ι → P} (f : P →ᵃ[k] P₂) (hai : A
   exact LinearIndependent.of_comp f.linear hai
 #align affine_independent.of_comp AffineIndependent.of_comp
 
-/- warning: affine_independent.map' -> AffineIndependent.map' is a dubious translation:
-<too large>
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 /-- The image of a family of points in affine space, under an injective affine transformation, is
 affine-independent. -/
 theorem AffineIndependent.map' {p : ι → P} (hai : AffineIndependent k p) (f : P →ᵃ[k] P₂)
@@ -481,27 +400,18 @@ theorem AffineIndependent.map' {p : ι → P} (hai : AffineIndependent k p) (f :
   exact LinearIndependent.map' hai f.linear hf'
 #align affine_independent.map' AffineIndependent.map'
 
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 /-- Injective affine maps preserve affine independence. -/
 theorem AffineMap.affineIndependent_iff {p : ι → P} (f : P →ᵃ[k] P₂) (hf : Function.Injective f) :
     AffineIndependent k (f ∘ p) ↔ AffineIndependent k p :=
   ⟨AffineIndependent.of_comp f, fun hai => AffineIndependent.map' hai f hf⟩
 #align affine_map.affine_independent_iff AffineMap.affineIndependent_iff
 
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 /-- Affine equivalences preserve affine independence of families of points. -/
 theorem AffineEquiv.affineIndependent_iff {p : ι → P} (e : P ≃ᵃ[k] P₂) :
     AffineIndependent k (e ∘ p) ↔ AffineIndependent k p :=
   e.toAffineMap.affineIndependent_iff e.toEquiv.Injective
 #align affine_equiv.affine_independent_iff AffineEquiv.affineIndependent_iff
 
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-<too large>
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 /-- Affine equivalences preserve affine independence of subsets. -/
 theorem AffineEquiv.affineIndependent_set_of_eq_iff {s : Set P} (e : P ≃ᵃ[k] P₂) :
     AffineIndependent k (coe : e '' s → P₂) ↔ AffineIndependent k (coe : s → P) :=
@@ -512,12 +422,6 @@ theorem AffineEquiv.affineIndependent_set_of_eq_iff {s : Set P} (e : P ≃ᵃ[k]
 
 end Composition
 
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 /-- If a family is affinely independent, and the spans of points
 indexed by two subsets of the index type have a point in common, those
 subsets of the index type have an element in common, if the underlying
@@ -539,12 +443,6 @@ theorem AffineIndependent.exists_mem_inter_of_exists_mem_inter_affineSpan [Nontr
   use i, hfs1 hifs1, hfs2 (Set.mem_of_indicator_ne_zero hinz)
 #align affine_independent.exists_mem_inter_of_exists_mem_inter_affine_span AffineIndependent.exists_mem_inter_of_exists_mem_inter_affineSpan
 
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 /-- If a family is affinely independent, the spans of points indexed
 by disjoint subsets of the index type are disjoint, if the underlying
 ring is nontrivial. -/
@@ -557,12 +455,6 @@ theorem AffineIndependent.affineSpan_disjoint_of_disjoint [Nontrivial k] {p : ι
   exact Set.disjoint_iff.1 hd hi
 #align affine_independent.affine_span_disjoint_of_disjoint AffineIndependent.affineSpan_disjoint_of_disjoint
 
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 /-- If a family is affinely independent, a point in the family is in
 the span of some of the points given by a subset of the index type if
 and only if that point's index is in the subset, if the underlying
@@ -580,12 +472,6 @@ protected theorem AffineIndependent.mem_affineSpan_iff [Nontrivial k] {p : ι 
   · exact fun h => mem_affineSpan k (Set.mem_image_of_mem p h)
 #align affine_independent.mem_affine_span_iff AffineIndependent.mem_affineSpan_iff
 
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 /-- If a family is affinely independent, a point in the family is not
 in the affine span of the other points, if the underlying ring is
 nontrivial. -/
@@ -594,12 +480,6 @@ theorem AffineIndependent.not_mem_affineSpan_diff [Nontrivial k] {p : ι → P}
   simp [ha]
 #align affine_independent.not_mem_affine_span_diff AffineIndependent.not_mem_affineSpan_diff
 
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 theorem exists_nontrivial_relation_sum_zero_of_not_affine_ind {t : Finset V}
     (h : ¬AffineIndependent k (coe : t → V)) :
     ∃ f : V → k, (∑ e in t, f e • e) = 0 ∧ (∑ e in t, f e) = 0 ∧ ∃ x ∈ t, f x ≠ 0 := by
@@ -618,12 +498,6 @@ theorem exists_nontrivial_relation_sum_zero_of_not_affine_ind {t : Finset V}
         hw]
 #align exists_nontrivial_relation_sum_zero_of_not_affine_ind exists_nontrivial_relation_sum_zero_of_not_affine_ind
 
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 /-- Viewing a module as an affine space modelled on itself, we can characterise affine independence
 in terms of linear combinations. -/
 theorem affineIndependent_iff {ι} {p : ι → V} :
@@ -632,9 +506,6 @@ theorem affineIndependent_iff {ι} {p : ι → V} :
   forall₃_congr fun s w hw => by simp [s.weighted_vsub_eq_linear_combination hw]
 #align affine_independent_iff affineIndependent_iff
 
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 /-- Given an affinely independent family of points, a weighted subtraction lies in the
 `vector_span` of two points given as affine combinations if and only if it is a weighted
 subtraction with weights a multiple of the difference between the weights of the two points. -/
@@ -665,9 +536,6 @@ theorem weightedVSub_mem_vectorSpan_pair {p : ι → P} (h : AffineIndependent k
     congr
 #align weighted_vsub_mem_vector_span_pair weightedVSub_mem_vectorSpan_pair
 
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 /-- Given an affinely independent family of points, an affine combination lies in the
 span of two points given as affine combinations if and only if it is an affine combination
 with weights those of one point plus a multiple of the difference between the weights of the
@@ -696,12 +564,6 @@ variable [affine_space V P] {ι : Type _}
 
 include V
 
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 /-- An affinely independent set of points can be extended to such a
 set that spans the whole space. -/
 theorem exists_subset_affineIndependent_affineSpan_eq_top {s : Set P}
@@ -736,12 +598,6 @@ theorem exists_subset_affineIndependent_affineSpan_eq_top {s : Set P}
 
 variable (k V)
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem exists_affineIndependent (s : Set P) :
     ∃ (t : _)(_ : t ⊆ s), affineSpan k t = affineSpan k s ∧ AffineIndependent k (coe : t → P) :=
@@ -770,12 +626,6 @@ theorem exists_affineIndependent (s : Set P) :
 
 variable (k) {V P}
 
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 /-- Two different points are affinely independent. -/
 theorem affineIndependent_of_ne {p₁ p₂ : P} (h : p₁ ≠ p₂) : AffineIndependent k ![p₁, p₂] :=
   by
@@ -793,12 +643,6 @@ theorem affineIndependent_of_ne {p₁ p₂ : P} (h : p₁ ≠ p₂) : AffineInde
 
 variable {k V P}
 
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 /-- If all but one point of a family are affinely independent, and that point does not lie in
 the affine span of that family, the family is affinely independent. -/
 theorem AffineIndependent.affineIndependent_of_not_mem_span {p : ι → P} {i : ι}
@@ -847,12 +691,6 @@ theorem AffineIndependent.affineIndependent_of_not_mem_span {p : ι → P} {i :
       · exact ha s' w' hw' hs' ⟨j, hji⟩ (Finset.mem_subtype.2 hj)
 #align affine_independent.affine_independent_of_not_mem_span AffineIndependent.affineIndependent_of_not_mem_span
 
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 /-- If distinct points `p₁` and `p₂` lie in `s` but `p₃` does not, the three points are affinely
 independent. -/
 theorem affineIndependent_of_ne_of_mem_of_mem_of_not_mem {s : AffineSubspace k P} {p₁ p₂ p₃ : P}
@@ -873,12 +711,6 @@ theorem affineIndependent_of_ne_of_mem_of_mem_of_not_mem {s : AffineSubspace k P
   fin_cases x <;> simp [hp₁, hp₂]
 #align affine_independent_of_ne_of_mem_of_mem_of_not_mem affineIndependent_of_ne_of_mem_of_mem_of_not_mem
 
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 /-- If distinct points `p₁` and `p₃` lie in `s` but `p₂` does not, the three points are affinely
 independent. -/
 theorem affineIndependent_of_ne_of_mem_of_not_mem_of_mem {s : AffineSubspace k P} {p₁ p₂ p₃ : P}
@@ -891,12 +723,6 @@ theorem affineIndependent_of_ne_of_mem_of_not_mem_of_mem {s : AffineSubspace k P
   fin_cases x <;> rfl
 #align affine_independent_of_ne_of_mem_of_not_mem_of_mem affineIndependent_of_ne_of_mem_of_not_mem_of_mem
 
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-Case conversion may be inaccurate. Consider using '#align affine_independent_of_ne_of_not_mem_of_mem_of_mem affineIndependent_of_ne_of_not_mem_of_mem_of_memₓ'. -/
 /-- If distinct points `p₂` and `p₃` lie in `s` but `p₁` does not, the three points are affinely
 independent. -/
 theorem affineIndependent_of_ne_of_not_mem_of_mem_of_mem {s : AffineSubspace k P} {p₁ p₂ p₃ : P}
@@ -921,9 +747,6 @@ include V
 
 attribute [local instance] LinearOrderedRing.decidableLt
 
-/- warning: sign_eq_of_affine_combination_mem_affine_span_pair -> sign_eq_of_affineCombination_mem_affineSpan_pair is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align sign_eq_of_affine_combination_mem_affine_span_pair sign_eq_of_affineCombination_mem_affineSpan_pairₓ'. -/
 /-- Given an affinely independent family of points, suppose that an affine combination lies in
 the span of two points given as affine combinations, and suppose that, for two indices, the
 coefficients in the first point in the span are zero and those in the second point in the span
@@ -944,9 +767,6 @@ theorem sign_eq_of_affineCombination_mem_affineSpan_pair {p : ι → P} (h : Aff
   rw [hr i hi, hr j hj, hi0, hj0, add_zero, add_zero, sub_zero, sub_zero, sign_mul, sign_mul, hij]
 #align sign_eq_of_affine_combination_mem_affine_span_pair sign_eq_of_affineCombination_mem_affineSpan_pair
 
-/- warning: sign_eq_of_affine_combination_mem_affine_span_single_line_map -> sign_eq_of_affineCombination_mem_affineSpan_single_lineMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align sign_eq_of_affine_combination_mem_affine_span_single_line_map sign_eq_of_affineCombination_mem_affineSpan_single_lineMapₓ'. -/
 /-- Given an affinely independent family of points, suppose that an affine combination lies in
 the span of one point of that family and a combination of another two points of that family given
 by `line_map` with coefficient between 0 and 1. Then the coefficients of those two points in the
@@ -1008,12 +828,6 @@ def mkOfPoint (p : P) : Simplex k P 0 :=
 #align affine.simplex.mk_of_point Affine.Simplex.mkOfPoint
 -/
 
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 /-- The point in a simplex constructed with `mk_of_point`. -/
 @[simp]
 theorem mkOfPoint_points (p : P) (i : Fin 1) : (mkOfPoint k p).points i = p :=
@@ -1031,12 +845,6 @@ instance nonempty : Nonempty (Simplex k P 0) :=
 
 variable {k V}
 
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 /-- Two simplices are equal if they have the same points. -/
 @[ext]
 theorem ext {n : ℕ} {s1 s2 : Simplex k P n} (h : ∀ i, s1.points i = s2.points i) : s1 = s2 :=
@@ -1047,12 +855,6 @@ theorem ext {n : ℕ} {s1 s2 : Simplex k P n} (h : ∀ i, s1.points i = s2.point
   exact h i
 #align affine.simplex.ext Affine.Simplex.ext
 
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 /-- Two simplices are equal if and only if they have the same points. -/
 theorem ext_iff {n : ℕ} (s1 s2 : Simplex k P n) : s1 = s2 ↔ ∀ i, s1.points i = s2.points i :=
   ⟨fun h _ => h ▸ rfl, ext⟩
@@ -1067,9 +869,6 @@ def face {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ} (h
 #align affine.simplex.face Affine.Simplex.face
 -/
 
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 /-- The points of a face of a simplex are given by `mono_of_fin`. -/
 theorem face_points {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ}
     (h : fs.card = m + 1) (i : Fin (m + 1)) :
@@ -1077,21 +876,12 @@ theorem face_points {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m
   rfl
 #align affine.simplex.face_points Affine.Simplex.face_points
 
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 /-- The points of a face of a simplex are given by `mono_of_fin`. -/
 theorem face_points' {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ}
     (h : fs.card = m + 1) : (s.face h).points = s.points ∘ fs.orderEmbOfFin h :=
   rfl
 #align affine.simplex.face_points' Affine.Simplex.face_points'
 
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 /-- A single-point face equals the 0-simplex constructed with
 `mk_of_point`. -/
 @[simp]
@@ -1099,12 +889,6 @@ theorem face_eq_mkOfPoint {n : ℕ} (s : Simplex k P n) (i : Fin (n + 1)) :
     s.face (Finset.card_singleton i) = mkOfPoint k (s.points i) := by ext; simp [face_points]
 #align affine.simplex.face_eq_mk_of_point Affine.Simplex.face_eq_mkOfPoint
 
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 /-- The set of points of a face. -/
 @[simp]
 theorem range_face_points {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ}
@@ -1120,24 +904,12 @@ def reindex {m n : ℕ} (s : Simplex k P m) (e : Fin (m + 1) ≃ Fin (n + 1)) :
 #align affine.simplex.reindex Affine.Simplex.reindex
 -/
 
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 /-- Reindexing by `equiv.refl` yields the original simplex. -/
 @[simp]
 theorem reindex_refl {n : ℕ} (s : Simplex k P n) : s.reindex (Equiv.refl (Fin (n + 1))) = s :=
   ext fun _ => rfl
 #align affine.simplex.reindex_refl Affine.Simplex.reindex_refl
 
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 /-- Reindexing by the composition of two equivalences is the same as reindexing twice. -/
 @[simp]
 theorem reindex_trans {n₁ n₂ n₃ : ℕ} (e₁₂ : Fin (n₁ + 1) ≃ Fin (n₂ + 1))
@@ -1146,36 +918,18 @@ theorem reindex_trans {n₁ n₂ n₃ : ℕ} (e₁₂ : Fin (n₁ + 1) ≃ Fin (
   rfl
 #align affine.simplex.reindex_trans Affine.Simplex.reindex_trans
 
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 /-- Reindexing by an equivalence and its inverse yields the original simplex. -/
 @[simp]
 theorem reindex_reindex_symm {m n : ℕ} (s : Simplex k P m) (e : Fin (m + 1) ≃ Fin (n + 1)) :
     (s.reindex e).reindex e.symm = s := by rw [← reindex_trans, Equiv.self_trans_symm, reindex_refl]
 #align affine.simplex.reindex_reindex_symm Affine.Simplex.reindex_reindex_symm
 
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 /-- Reindexing by the inverse of an equivalence and that equivalence yields the original simplex. -/
 @[simp]
 theorem reindex_symm_reindex {m n : ℕ} (s : Simplex k P m) (e : Fin (n + 1) ≃ Fin (m + 1)) :
     (s.reindex e.symm).reindex e = s := by rw [← reindex_trans, Equiv.symm_trans_self, reindex_refl]
 #align affine.simplex.reindex_symm_reindex Affine.Simplex.reindex_symm_reindex
 
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 /-- Reindexing a simplex produces one with the same set of points. -/
 @[simp]
 theorem reindex_range_points {m n : ℕ} (s : Simplex k P m) (e : Fin (m + 1) ≃ Fin (n + 1)) :
@@ -1196,12 +950,6 @@ variable {k : Type _} {V : Type _} {P : Type _} [DivisionRing k] [AddCommGroup V
 
 include V
 
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-Case conversion may be inaccurate. Consider using '#align affine.simplex.face_centroid_eq_centroid Affine.Simplex.face_centroid_eq_centroidₓ'. -/
 /-- The centroid of a face of a simplex as the centroid of a subset of
 the points. -/
 @[simp]
@@ -1213,12 +961,6 @@ theorem face_centroid_eq_centroid {n : ℕ} (s : Simplex k P n) {fs : Finset (Fi
   simp
 #align affine.simplex.face_centroid_eq_centroid Affine.Simplex.face_centroid_eq_centroid
 
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-Case conversion may be inaccurate. Consider using '#align affine.simplex.centroid_eq_iff Affine.Simplex.centroid_eq_iffₓ'. -/
 /-- Over a characteristic-zero division ring, the centroids given by
 two subsets of the points of a simplex are equal if and only if those
 faces are given by the same subset of points. -/
@@ -1248,9 +990,6 @@ theorem centroid_eq_iff [CharZero k] {n : ℕ} (s : Simplex k P n) {fs₁ fs₂
   · simpa [hni, hi, key] using ha.symm
 #align affine.simplex.centroid_eq_iff Affine.Simplex.centroid_eq_iff
 
-/- warning: affine.simplex.face_centroid_eq_iff -> Affine.Simplex.face_centroid_eq_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine.simplex.face_centroid_eq_iff Affine.Simplex.face_centroid_eq_iffₓ'. -/
 /-- Over a characteristic-zero division ring, the centroids of two
 faces of a simplex are equal if and only if those faces are given by
 the same subset of points. -/
@@ -1263,12 +1002,6 @@ theorem face_centroid_eq_iff [CharZero k] {n : ℕ} (s : Simplex k P n)
   exact s.centroid_eq_iff h₁ h₂
 #align affine.simplex.face_centroid_eq_iff Affine.Simplex.face_centroid_eq_iff
 
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 /-- Two simplices with the same points have the same centroid. -/
 theorem centroid_eq_of_range_eq {n : ℕ} {s₁ s₂ : Simplex k P n}
     (h : Set.range s₁.points = Set.range s₂.points) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -409,9 +409,7 @@ theorem affineIndependent_equiv {ι' : Type _} (e : ι ≃ ι') {p : ι' → P}
   by
   refine' ⟨_, AffineIndependent.comp_embedding e.to_embedding⟩
   intro h
-  have : p = p ∘ e ∘ e.symm.to_embedding := by
-    ext
-    simp
+  have : p = p ∘ e ∘ e.symm.to_embedding := by ext; simp
   rw [this]
   exact h.comp_embedding e.symm.to_embedding
 #align affine_independent_equiv affineIndependent_equiv
@@ -458,9 +456,7 @@ Case conversion may be inaccurate. Consider using '#align affine_independent.of_
 independent, then the original family of points is also affine-independent. -/
 theorem AffineIndependent.of_comp {p : ι → P} (f : P →ᵃ[k] P₂) (hai : AffineIndependent k (f ∘ p)) :
     AffineIndependent k p := by
-  cases' isEmpty_or_nonempty ι with h h;
-  · haveI := h
-    apply affineIndependent_of_subsingleton
+  cases' isEmpty_or_nonempty ι with h h; · haveI := h; apply affineIndependent_of_subsingleton
   obtain ⟨i⟩ := h
   rw [affineIndependent_iff_linearIndependent_vsub k p i]
   simp_rw [affineIndependent_iff_linearIndependent_vsub k (f ∘ p) i, Function.comp_apply, ←
@@ -476,9 +472,7 @@ affine-independent. -/
 theorem AffineIndependent.map' {p : ι → P} (hai : AffineIndependent k p) (f : P →ᵃ[k] P₂)
     (hf : Function.Injective f) : AffineIndependent k (f ∘ p) :=
   by
-  cases' isEmpty_or_nonempty ι with h h
-  · haveI := h
-    apply affineIndependent_of_subsingleton
+  cases' isEmpty_or_nonempty ι with h h; · haveI := h; apply affineIndependent_of_subsingleton
   obtain ⟨i⟩ := h
   rw [affineIndependent_iff_linearIndependent_vsub k p i] at hai
   simp_rw [affineIndependent_iff_linearIndependent_vsub k (f ∘ p) i, Function.comp_apply, ←
@@ -616,16 +610,9 @@ theorem exists_nontrivial_relation_sum_zero_of_not_affine_ind {t : Finset V}
     simp only [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero _ w (coe : t → V) hw 0,
       vsub_eq_sub, Finset.weightedVSubOfPoint_apply, sub_zero] at hwt
     let f : ∀ x : V, x ∈ t → k := fun x hx => w ⟨x, hx⟩
-    refine'
-      ⟨fun x => if hx : x ∈ t then f x hx else (0 : k), _, _,
-        by
-        use i
-        simp [hi, f]⟩
-    suffices (∑ e : V in t, dite (e ∈ t) (fun hx => f e hx • e) fun hx => 0) = 0
-      by
-      convert this
-      ext
-      by_cases hx : x ∈ t <;> simp [hx]
+    refine' ⟨fun x => if hx : x ∈ t then f x hx else (0 : k), _, _, by use i; simp [hi, f]⟩
+    suffices (∑ e : V in t, dite (e ∈ t) (fun hx => f e hx • e) fun hx => 0) = 0 by convert this;
+      ext; by_cases hx : x ∈ t <;> simp [hx]
     all_goals
       simp only [Finset.sum_dite_of_true fun x h => h, Subtype.val_eq_coe, Finset.mk_coe, f, hwt,
         hw]
@@ -727,9 +714,7 @@ theorem exists_subset_affineIndependent_affineSpan_eq_top {s : Set P}
     have hsvi := hsv.linear_independent
     have hsvt := hsv.span_eq
     rw [Basis.coe_ofVectorSpace] at hsvi hsvt
-    have h0 : ∀ v : V, v ∈ Basis.ofVectorSpaceIndex _ _ → v ≠ 0 :=
-      by
-      intro v hv
+    have h0 : ∀ v : V, v ∈ Basis.ofVectorSpaceIndex _ _ → v ≠ 0 := by intro v hv;
       simpa using hsv.ne_zero ⟨v, hv⟩
     rw [linearIndependent_set_iff_affineIndependent_vadd_union_singleton k h0 p₁] at hsvi
     exact
@@ -741,10 +726,7 @@ theorem exists_subset_affineIndependent_affineSpan_eq_top {s : Set P}
     have hsvt := bsv.span_eq
     rw [Basis.coe_extend] at hsvi hsvt
     have hsv := h.subset_extend (Set.subset_univ _)
-    have h0 : ∀ v : V, v ∈ h.extend _ → v ≠ 0 :=
-      by
-      intro v hv
-      simpa using bsv.ne_zero ⟨v, hv⟩
+    have h0 : ∀ v : V, v ∈ h.extend _ → v ≠ 0 := by intro v hv; simpa using bsv.ne_zero ⟨v, hv⟩
     rw [linearIndependent_set_iff_affineIndependent_vadd_union_singleton k h0 p₁] at hsvi
     refine' ⟨{p₁} ∪ (fun v => v +ᵥ p₁) '' h.extend (Set.subset_univ _), _, _⟩
     · refine' Set.Subset.trans _ (Set.union_subset_union_right _ (Set.image_subset _ hsv))
@@ -805,10 +787,7 @@ theorem affineIndependent_of_ne {p₁ p₂ : P} (h : p₁ ≠ p₂) : AffineInde
     fin_cases i
     · simpa using hi
   haveI : Unique { x // x ≠ (0 : Fin 2) } := ⟨⟨i₁⟩, he'⟩
-  have hz : (![p₁, p₂] ↑default -ᵥ ![p₁, p₂] 0 : V) ≠ 0 :=
-    by
-    rw [he' default]
-    simpa using h.symm
+  have hz : (![p₁, p₂] ↑default -ᵥ ![p₁, p₂] 0 : V) ≠ 0 := by rw [he' default]; simpa using h.symm
   exact linearIndependent_unique _ hz
 #align affine_independent_of_ne affineIndependent_of_ne
 
@@ -1117,10 +1096,7 @@ Case conversion may be inaccurate. Consider using '#align affine.simplex.face_eq
 `mk_of_point`. -/
 @[simp]
 theorem face_eq_mkOfPoint {n : ℕ} (s : Simplex k P n) (i : Fin (n + 1)) :
-    s.face (Finset.card_singleton i) = mkOfPoint k (s.points i) :=
-  by
-  ext
-  simp [face_points]
+    s.face (Finset.card_singleton i) = mkOfPoint k (s.points i) := by ext; simp [face_points]
 #align affine.simplex.face_eq_mk_of_point Affine.Simplex.face_eq_mkOfPoint
 
 /- warning: affine.simplex.range_face_points -> Affine.Simplex.range_face_points is a dubious translation:

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -66,10 +66,7 @@ def AffineIndependent (p : ι → P) : Prop :=
 -/
 
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 Case conversion may be inaccurate. Consider using '#align affine_independent_def affineIndependent_defₓ'. -/
 /-- The definition of `affine_independent`. -/
 theorem affineIndependent_def (p : ι → P) :
@@ -91,10 +88,7 @@ theorem affineIndependent_of_subsingleton [Subsingleton ι] (p : ι → P) : Aff
 #align affine_independent_of_subsingleton affineIndependent_of_subsingleton
 
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 Case conversion may be inaccurate. Consider using '#align affine_independent_iff_of_fintype affineIndependent_iff_of_fintypeₓ'. -/
 /-- A family indexed by a `fintype` is affinely independent if and
 only if no nontrivial weighted subtractions over `finset.univ` (where
@@ -113,10 +107,7 @@ theorem affineIndependent_iff_of_fintype [Fintype ι] (p : ι → P) :
 #align affine_independent_iff_of_fintype affineIndependent_iff_of_fintype
 
 /- warning: affine_independent_iff_linear_independent_vsub -> affineIndependent_iff_linearIndependent_vsub is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align affine_independent_iff_linear_independent_vsub affineIndependent_iff_linearIndependent_vsubₓ'. -/
 /-- A family is affinely independent if and only if the differences
 from a base point in that family are linearly independent. -/
@@ -176,10 +167,7 @@ theorem affineIndependent_iff_linearIndependent_vsub (p : ι → P) (i1 : ι) :
 #align affine_independent_iff_linear_independent_vsub affineIndependent_iff_linearIndependent_vsub
 
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 Case conversion may be inaccurate. Consider using '#align affine_independent_set_iff_linear_independent_vsub affineIndependent_set_iff_linearIndependent_vsubₓ'. -/
 /-- A set is affinely independent if and only if the differences from
 a base point in that set are linearly independent. -/
@@ -207,10 +195,7 @@ theorem affineIndependent_set_iff_linearIndependent_vsub {s : Set P} {p₁ : P}
 #align affine_independent_set_iff_linear_independent_vsub affineIndependent_set_iff_linearIndependent_vsub
 
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 /-- A set of nonzero vectors is linearly independent if and only if,
 given a point `p₁`, the vectors added to `p₁` and `p₁` itself are
@@ -231,10 +216,7 @@ theorem linearIndependent_set_iff_affineIndependent_vadd_union_singleton {s : Se
 #align linear_independent_set_iff_affine_independent_vadd_union_singleton linearIndependent_set_iff_affineIndependent_vadd_union_singleton
 
 /- warning: affine_independent_iff_indicator_eq_of_affine_combination_eq -> affineIndependent_iff_indicator_eq_of_affineCombination_eq is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align affine_independent_iff_indicator_eq_of_affine_combination_eq affineIndependent_iff_indicator_eq_of_affineCombination_eqₓ'. -/
 /-- A family is affinely independent if and only if any affine
 combinations (with sum of weights 1) that evaluate to the same point
@@ -282,10 +264,7 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
 #align affine_independent_iff_indicator_eq_of_affine_combination_eq affineIndependent_iff_indicator_eq_of_affineCombination_eq
 
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 Case conversion may be inaccurate. Consider using '#align affine_independent_iff_eq_of_fintype_affine_combination_eq affineIndependent_iff_eq_of_fintype_affineCombination_eqₓ'. -/
 /-- A finite family is affinely independent if and only if any affine
 combinations (with sum of weights 1) that evaluate to the same point are equal. -/
@@ -313,10 +292,7 @@ theorem affineIndependent_iff_eq_of_fintype_affineCombination_eq [Fintype ι] (p
 variable {k}
 
 /- warning: affine_independent.units_line_map -> AffineIndependent.units_lineMap is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align affine_independent.units_line_map AffineIndependent.units_lineMapₓ'. -/
 /-- If we single out one member of an affine-independent family of points and affinely transport
 all others along the line joining them to this member, the resulting new family of points is affine-
@@ -332,10 +308,7 @@ theorem AffineIndependent.units_lineMap {p : ι → P} (hp : AffineIndependent k
 #align affine_independent.units_line_map AffineIndependent.units_lineMap
 
 /- warning: affine_independent.indicator_eq_of_affine_combination_eq -> AffineIndependent.indicator_eq_of_affineCombination_eq is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align affine_independent.indicator_eq_of_affine_combination_eq AffineIndependent.indicator_eq_of_affineCombination_eqₓ'. -/
 theorem AffineIndependent.indicator_eq_of_affineCombination_eq {p : ι → P}
     (ha : AffineIndependent k p) (s₁ s₂ : Finset ι) (w₁ w₂ : ι → k) (hw₁ : (∑ i in s₁, w₁ i) = 1)
@@ -479,10 +452,7 @@ variable {V₂ P₂ : Type _} [AddCommGroup V₂] [Module k V₂] [affine_space
 include V₂
 
 /- warning: affine_independent.of_comp -> AffineIndependent.of_comp is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align affine_independent.of_comp AffineIndependent.of_compₓ'. -/
 /-- If the image of a family of points in affine space under an affine transformation is affine-
 independent, then the original family of points is also affine-independent. -/
@@ -499,10 +469,7 @@ theorem AffineIndependent.of_comp {p : ι → P} (f : P →ᵃ[k] P₂) (hai : A
 #align affine_independent.of_comp AffineIndependent.of_comp
 
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 Case conversion may be inaccurate. Consider using '#align affine_independent.map' AffineIndependent.map'ₓ'. -/
 /-- The image of a family of points in affine space, under an injective affine transformation, is
 affine-independent. -/
@@ -521,10 +488,7 @@ theorem AffineIndependent.map' {p : ι → P} (hai : AffineIndependent k p) (f :
 #align affine_independent.map' AffineIndependent.map'
 
 /- warning: affine_map.affine_independent_iff -> AffineMap.affineIndependent_iff is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align affine_map.affine_independent_iff AffineMap.affineIndependent_iffₓ'. -/
 /-- Injective affine maps preserve affine independence. -/
 theorem AffineMap.affineIndependent_iff {p : ι → P} (f : P →ᵃ[k] P₂) (hf : Function.Injective f) :
@@ -533,10 +497,7 @@ theorem AffineMap.affineIndependent_iff {p : ι → P} (f : P →ᵃ[k] P₂) (h
 #align affine_map.affine_independent_iff AffineMap.affineIndependent_iff
 
 /- warning: affine_equiv.affine_independent_iff -> AffineEquiv.affineIndependent_iff is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align affine_equiv.affine_independent_iff AffineEquiv.affineIndependent_iffₓ'. -/
 /-- Affine equivalences preserve affine independence of families of points. -/
 theorem AffineEquiv.affineIndependent_iff {p : ι → P} (e : P ≃ᵃ[k] P₂) :
@@ -545,10 +506,7 @@ theorem AffineEquiv.affineIndependent_iff {p : ι → P} (e : P ≃ᵃ[k] P₂)
 #align affine_equiv.affine_independent_iff AffineEquiv.affineIndependent_iff
 
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 Case conversion may be inaccurate. Consider using '#align affine_equiv.affine_independent_set_of_eq_iff AffineEquiv.affineIndependent_set_of_eq_iffₓ'. -/
 /-- Affine equivalences preserve affine independence of subsets. -/
 theorem AffineEquiv.affineIndependent_set_of_eq_iff {s : Set P} (e : P ≃ᵃ[k] P₂) :
@@ -688,10 +646,7 @@ theorem affineIndependent_iff {ι} {p : ι → V} :
 #align affine_independent_iff affineIndependent_iff
 
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 Case conversion may be inaccurate. Consider using '#align weighted_vsub_mem_vector_span_pair weightedVSub_mem_vectorSpan_pairₓ'. -/
 /-- Given an affinely independent family of points, a weighted subtraction lies in the
 `vector_span` of two points given as affine combinations if and only if it is a weighted
@@ -724,10 +679,7 @@ theorem weightedVSub_mem_vectorSpan_pair {p : ι → P} (h : AffineIndependent k
 #align weighted_vsub_mem_vector_span_pair weightedVSub_mem_vectorSpan_pair
 
 /- warning: affine_combination_mem_affine_span_pair -> affineCombination_mem_affineSpan_pair is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align affine_combination_mem_affine_span_pair affineCombination_mem_affineSpan_pairₓ'. -/
 /-- Given an affinely independent family of points, an affine combination lies in the
 span of two points given as affine combinations if and only if it is an affine combination
@@ -991,10 +943,7 @@ include V
 attribute [local instance] LinearOrderedRing.decidableLt
 
 /- warning: sign_eq_of_affine_combination_mem_affine_span_pair -> sign_eq_of_affineCombination_mem_affineSpan_pair is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align sign_eq_of_affine_combination_mem_affine_span_pair sign_eq_of_affineCombination_mem_affineSpan_pairₓ'. -/
 /-- Given an affinely independent family of points, suppose that an affine combination lies in
 the span of two points given as affine combinations, and suppose that, for two indices, the
@@ -1017,10 +966,7 @@ theorem sign_eq_of_affineCombination_mem_affineSpan_pair {p : ι → P} (h : Aff
 #align sign_eq_of_affine_combination_mem_affine_span_pair sign_eq_of_affineCombination_mem_affineSpan_pair
 
 /- warning: sign_eq_of_affine_combination_mem_affine_span_single_line_map -> sign_eq_of_affineCombination_mem_affineSpan_single_lineMap is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align sign_eq_of_affine_combination_mem_affine_span_single_line_map sign_eq_of_affineCombination_mem_affineSpan_single_lineMapₓ'. -/
 /-- Given an affinely independent family of points, suppose that an affine combination lies in
 the span of one point of that family and a combination of another two points of that family given
@@ -1143,10 +1089,7 @@ def face {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ} (h
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align affine.simplex.face_points Affine.Simplex.face_pointsₓ'. -/
 /-- The points of a face of a simplex are given by `mono_of_fin`. -/
 theorem face_points {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ}
@@ -1156,10 +1099,7 @@ theorem face_points {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m
 #align affine.simplex.face_points Affine.Simplex.face_points
 
 /- warning: affine.simplex.face_points' -> Affine.Simplex.face_points' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align affine.simplex.face_points' Affine.Simplex.face_points'ₓ'. -/
 /-- The points of a face of a simplex are given by `mono_of_fin`. -/
 theorem face_points' {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ}
@@ -1333,10 +1273,7 @@ theorem centroid_eq_iff [CharZero k] {n : ℕ} (s : Simplex k P n) {fs₁ fs₂
 #align affine.simplex.centroid_eq_iff Affine.Simplex.centroid_eq_iff
 
 /- warning: affine.simplex.face_centroid_eq_iff -> Affine.Simplex.face_centroid_eq_iff is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align affine.simplex.face_centroid_eq_iff Affine.Simplex.face_centroid_eq_iffₓ'. -/
 /-- Over a characteristic-zero division ring, the centroids of two
 faces of a simplex are equal if and only if those faces are given by

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -69,7 +69,7 @@ def AffineIndependent (p : ι → P) : Prop :=
 lean 3 declaration is
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 but is expected to have type
-  forall (k : Type.{u4}) {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} (p : ι -> P), Iff (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (s : Finset.{u1} ι) (w : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u4), max (succ u1) (succ u4), succ u3} (LinearMap.{u4, u4, max u4 u1, u3} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u1 u4, u3} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u1, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (OfNat.ofNat.{u3} V 0 (Zero.toOfNat0.{u3} V (NegZeroClass.toZero.{u3} V (SubNegZeroMonoid.toNegZeroClass.{u3} V (SubtractionMonoid.toSubNegZeroMonoid.{u3} V (SubtractionCommMonoid.toSubtractionMonoid.{u3} V (AddCommGroup.toDivisionAddCommMonoid.{u3} V _inst_2)))))))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u4} k (w i) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))))))))
+  forall (k : Type.{u4}) {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} (p : ι -> P), Iff (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (s : Finset.{u1} ι) (w : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u4), max (succ u1) (succ u4), succ u3} (LinearMap.{u4, u4, max u4 u1, u3} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u1 u4, u3} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u1, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (OfNat.ofNat.{u3} V 0 (Zero.toOfNat0.{u3} V (NegZeroClass.toZero.{u3} V (SubNegZeroMonoid.toNegZeroClass.{u3} V (SubtractionMonoid.toSubNegZeroMonoid.{u3} V (SubtractionCommMonoid.toSubtractionMonoid.{u3} V (AddCommGroup.toDivisionAddCommMonoid.{u3} V _inst_2)))))))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u4} k (w i) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))))))))
 Case conversion may be inaccurate. Consider using '#align affine_independent_def affineIndependent_defₓ'. -/
 /-- The definition of `affine_independent`. -/
 theorem affineIndependent_def (p : ι → P) :
@@ -94,7 +94,7 @@ theorem affineIndependent_of_subsingleton [Subsingleton ι] (p : ι → P) : Aff
 lean 3 declaration is
   forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (forall (i : ι), Eq.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))))
 but is expected to have type
-  forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w : ι -> k), (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w) (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (forall (i : ι), Eq.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))))
+  forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w : ι -> k), (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w) (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (forall (i : ι), Eq.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align affine_independent_iff_of_fintype affineIndependent_iff_of_fintypeₓ'. -/
 /-- A family indexed by a `fintype` is affinely independent if and
 only if no nontrivial weighted subtractions over `finset.univ` (where
@@ -691,7 +691,7 @@ theorem affineIndependent_iff {ι} {p : ι → V} :
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u4} ι}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Iff (Membership.Mem.{u2, u2} V (Submodule.{u1, u2} 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 but is expected to have type
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+  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k 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(a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w₁) (Singleton.singleton.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (Set.{u2} P) (Set.instSingletonSet.{u2} P) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w₂))))) (Exists.{succ u4} k (fun (r : k) => forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u4} k (w i) (HMul.hMul.{u4, u4, u4} k k k (instHMul.{u4} k (NonUnitalNonAssocRing.toMul.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) r (HSub.hSub.{u4, u4, u4} k k k (instHSub.{u4} k (Ring.toSub.{u4} k _inst_1)) (w₁ i) (w₂ i))))))))
 Case conversion may be inaccurate. Consider using '#align weighted_vsub_mem_vector_span_pair weightedVSub_mem_vectorSpan_pairₓ'. -/
 /-- Given an affinely independent family of points, a weighted subtraction lies in the
 `vector_span` of two points given as affine combinations if and only if it is a weighted

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

@@ -429,7 +429,7 @@ protected theorem AffineIndependent.range {p : ι → P} (ha : AffineIndependent
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι' : Type.{u5}} (e : Equiv.{succ u4, succ u5} ι ι') {p : ι' -> P}, Iff (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Function.comp.{succ u4, succ u5, succ u3} ι ι' P p (coeFn.{max 1 (max (succ u4) (succ u5)) (succ u5) (succ u4), max (succ u4) (succ u5)} (Equiv.{succ u4, succ u5} ι ι') (fun (_x : Equiv.{succ u4, succ u5} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{succ u4, succ u5} ι ι') e))) (AffineIndependent.{u1, u2, u3, u5} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι' p)
 but is expected to have type
-  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι' : Type.{u5}} (e : Equiv.{succ u4, succ u5} ι ι') {p : ι' -> P}, Iff (AffineIndependent.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Function.comp.{succ u4, succ u5, succ u1} ι ι' P p (FunLike.coe.{max (succ u4) (succ u5), succ u4, succ u5} (Equiv.{succ u4, succ u5} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{succ u4, succ u5} ι ι') e))) (AffineIndependent.{u3, u2, u1, u5} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι' p)
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {ι' : Type.{u5}} (e : Equiv.{succ u4, succ u5} ι ι') {p : ι' -> P}, Iff (AffineIndependent.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Function.comp.{succ u4, succ u5, succ u1} ι ι' P p (FunLike.coe.{max (succ u4) (succ u5), succ u4, succ u5} (Equiv.{succ u4, succ u5} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{succ u4, succ u5} ι ι') e))) (AffineIndependent.{u3, u2, u1, u5} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι' p)
 Case conversion may be inaccurate. Consider using '#align affine_independent_equiv affineIndependent_equivₓ'. -/
 theorem affineIndependent_equiv {ι' : Type _} (e : ι ≃ ι') {p : ι' → P} :
     AffineIndependent k (p ∘ e) ↔ AffineIndependent k p :=
@@ -1146,7 +1146,7 @@ def face {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ} (h
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {n : Nat} (s : Affine.Simplex.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 n) {fs : Finset.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))} {m : Nat} (h : Eq.{1} Nat (Finset.card.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) fs) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), Eq.{succ u3} P (Affine.Simplex.points.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 m (Affine.Simplex.face.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s fs m h) i) (Affine.Simplex.points.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LinearOrder.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LinearOrder.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LinearOrder.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))))))) (Finset.orderEmbOfFin.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) fs (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) h) i))
 but is expected to have type
-  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {n : Nat} (s : Affine.Simplex.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 n) {fs : Finset.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))} {m : Nat} (h : Eq.{1} Nat (Finset.card.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) fs) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{succ u1} P (Affine.Simplex.points.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 m (Affine.Simplex.face.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s fs m h) i) (Affine.Simplex.points.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat 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+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {n : Nat} (s : Affine.Simplex.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 n) {fs : Finset.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))} {m : Nat} (h : Eq.{1} Nat (Finset.card.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) fs) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{succ u1} P (Affine.Simplex.points.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 m 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(OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Finset.orderEmbOfFin.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) fs (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) h) i))
 Case conversion may be inaccurate. Consider using '#align affine.simplex.face_points Affine.Simplex.face_pointsₓ'. -/
 /-- The points of a face of a simplex are given by `mono_of_fin`. -/
 theorem face_points {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ}
@@ -1159,7 +1159,7 @@ theorem face_points {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {n : Nat} (s : Affine.Simplex.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 n) {fs : Finset.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))} {m : Nat} (h : Eq.{1} Nat (Finset.card.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) fs) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), Eq.{succ u3} ((Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> P) (Affine.Simplex.points.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 m (Affine.Simplex.face.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s fs m h)) (Function.comp.{1, 1, succ u3} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) P (Affine.Simplex.points.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LinearOrder.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LinearOrder.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LinearOrder.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))))))) (Finset.orderEmbOfFin.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) fs (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) h)))
 but is expected to have type
-  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {n : Nat} (s : Affine.Simplex.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 n) {fs : Finset.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))} {m : Nat} (h : Eq.{1} Nat (Finset.card.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) fs) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{succ u1} ((Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> P) (Affine.Simplex.points.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 m (Affine.Simplex.face.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s fs m h)) (Function.comp.{1, 1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) P (Affine.Simplex.points.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} 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Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (OrderHomClass.toLatticeHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Finset.orderEmbOfFin.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) fs (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) h)))
 Case conversion may be inaccurate. Consider using '#align affine.simplex.face_points' Affine.Simplex.face_points'ₓ'. -/
 /-- The points of a face of a simplex are given by `mono_of_fin`. -/
 theorem face_points' {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ}

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

@@ -69,7 +69,7 @@ def AffineIndependent (p : ι → P) : Prop :=
 lean 3 declaration is
   forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (p : ι -> P), Iff (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (s : Finset.{u4} ι) (w : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))))))))
 but is expected to have type
-  forall (k : Type.{u4}) {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} (p : ι -> P), Iff (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (s : Finset.{u1} ι) (w : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u4), max (succ u1) (succ u4), succ u3} (LinearMap.{u4, u4, max u4 u1, u3} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u1 u4, u3} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u1, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (OfNat.ofNat.{u3} V 0 (Zero.toOfNat0.{u3} V (NegZeroClass.toZero.{u3} V (SubNegZeroMonoid.toNegZeroClass.{u3} V (SubtractionMonoid.toSubNegZeroMonoid.{u3} V (SubtractionCommMonoid.toSubtractionMonoid.{u3} V (AddCommGroup.toDivisionAddCommMonoid.{u3} V _inst_2)))))))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u4} k (w i) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))))))))
+  forall (k : Type.{u4}) {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} (p : ι -> P), Iff (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (s : Finset.{u1} ι) (w : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u4), max (succ u1) (succ u4), succ u3} (LinearMap.{u4, u4, max u4 u1, u3} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u1 u4, u3} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u1, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (OfNat.ofNat.{u3} V 0 (Zero.toOfNat0.{u3} V (NegZeroClass.toZero.{u3} V (SubNegZeroMonoid.toNegZeroClass.{u3} V (SubtractionMonoid.toSubNegZeroMonoid.{u3} V (SubtractionCommMonoid.toSubtractionMonoid.{u3} V (AddCommGroup.toDivisionAddCommMonoid.{u3} V _inst_2)))))))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u4} k (w i) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))))))))
 Case conversion may be inaccurate. Consider using '#align affine_independent_def affineIndependent_defₓ'. -/
 /-- The definition of `affine_independent`. -/
 theorem affineIndependent_def (p : ι → P) :
@@ -94,7 +94,7 @@ theorem affineIndependent_of_subsingleton [Subsingleton ι] (p : ι → P) : Aff
 lean 3 declaration is
   forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (forall (i : ι), Eq.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))))
 but is expected to have type
-  forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w : ι -> k), (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w) (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (forall (i : ι), Eq.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))))
+  forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w : ι -> k), (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w) (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (forall (i : ι), Eq.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align affine_independent_iff_of_fintype affineIndependent_iff_of_fintypeₓ'. -/
 /-- A family indexed by a `fintype` is affinely independent if and
 only if no nontrivial weighted subtractions over `finset.univ` (where
@@ -691,7 +691,7 @@ theorem affineIndependent_iff {ι} {p : ι → V} :
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u4} ι}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Iff (Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) 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(Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 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addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align weighted_vsub_mem_vector_span_pair weightedVSub_mem_vectorSpan_pairₓ'. -/
 /-- Given an affinely independent family of points, a weighted subtraction lies in the
 `vector_span` of two points given as affine combinations if and only if it is a weighted

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -69,7 +69,7 @@ def AffineIndependent (p : ι → P) : Prop :=
 lean 3 declaration is
   forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (p : ι -> P), Iff (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (s : Finset.{u4} ι) (w : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))))))))
 but is expected to have type
-  forall (k : Type.{u4}) {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} (p : ι -> P), Iff (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (s : Finset.{u1} ι) (w : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u4), max (succ u1) (succ u4), succ u3} (LinearMap.{u4, u4, max u4 u1, u3} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u1 u4, u3} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u1, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (OfNat.ofNat.{u3} V 0 (Zero.toOfNat0.{u3} V (NegZeroClass.toZero.{u3} V (SubNegZeroMonoid.toNegZeroClass.{u3} V (SubtractionMonoid.toSubNegZeroMonoid.{u3} V (SubtractionCommMonoid.toSubtractionMonoid.{u3} V (AddCommGroup.toDivisionAddCommMonoid.{u3} V _inst_2)))))))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u4} k (w i) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))))))))
+  forall (k : Type.{u4}) {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} (p : ι -> P), Iff (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (s : Finset.{u1} ι) (w : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u4), max (succ u1) (succ u4), succ u3} (LinearMap.{u4, u4, max u4 u1, u3} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u1 u4, u3} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u1, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (OfNat.ofNat.{u3} V 0 (Zero.toOfNat0.{u3} V (NegZeroClass.toZero.{u3} V (SubNegZeroMonoid.toNegZeroClass.{u3} V (SubtractionMonoid.toSubNegZeroMonoid.{u3} V (SubtractionCommMonoid.toSubtractionMonoid.{u3} V (AddCommGroup.toDivisionAddCommMonoid.{u3} V _inst_2)))))))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u4} k (w i) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))))))))
 Case conversion may be inaccurate. Consider using '#align affine_independent_def affineIndependent_defₓ'. -/
 /-- The definition of `affine_independent`. -/
 theorem affineIndependent_def (p : ι → P) :
@@ -94,7 +94,7 @@ theorem affineIndependent_of_subsingleton [Subsingleton ι] (p : ι → P) : Aff
 lean 3 declaration is
   forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (forall (i : ι), Eq.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))))
 but is expected to have type
-  forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w : ι -> k), (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w) (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (forall (i : ι), Eq.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))))
+  forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w : ι -> k), (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w) (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (forall (i : ι), Eq.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align affine_independent_iff_of_fintype affineIndependent_iff_of_fintypeₓ'. -/
 /-- A family indexed by a `fintype` is affinely independent if and
 only if no nontrivial weighted subtractions over `finset.univ` (where
@@ -234,7 +234,7 @@ theorem linearIndependent_set_iff_affineIndependent_vadd_union_singleton {s : Se
 lean 3 declaration is
   forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (p : ι -> P), Iff (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (s1 : Finset.{u4} ι) (s2 : Finset.{u4} ι) (w1 : ι -> k) (w2 : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s1 (fun (i : ι) => w1 i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s2 (fun (i : ι) => w2 i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k 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 but is expected to have type
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(NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s1 p) w1) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s2 p) w2)) -> (Eq.{max (succ u4) (succ u1)} (ι -> k) (Set.indicator.{u1, u4} ι k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.toSet.{u1} ι s1) w1) (Set.indicator.{u1, u4} ι k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.toSet.{u1} ι s2) w2)))
 Case conversion may be inaccurate. Consider using '#align affine_independent_iff_indicator_eq_of_affine_combination_eq affineIndependent_iff_indicator_eq_of_affineCombination_eqₓ'. -/
 /-- A family is affinely independent if and only if any affine
 combinations (with sum of weights 1) that evaluate to the same point
@@ -285,7 +285,7 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
 lean 3 declaration is
   forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w1 : ι -> k) (w2 : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w1 i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w2 i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => 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(Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w1) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w2)) -> (Eq.{max (succ u4) (succ u1)} (ι -> k) w1 w2))
 but is expected to have type
-  forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w1 : ι -> k) (w2 : ι -> k), (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w1 i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) -> (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k 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AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w1) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u2)) (succ u1), succ (max u3 u4), succ u1} (AffineMap.{u3, max u3 u4, max u3 u4, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w2)) -> (Eq.{max (succ u3) (succ u4)} (ι -> k) w1 w2))
+  forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w1 : ι -> k) (w2 : ι -> k), (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w1 i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) -> (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w2 i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w1) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u2)) (succ u1), succ (max u3 u4), succ u1} (AffineMap.{u3, max u3 u4, max u3 u4, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w1) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u2)) (succ u1), succ (max u3 u4), succ u1} (AffineMap.{u3, max u3 u4, max u3 u4, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w2)) -> (Eq.{max (succ u3) (succ u4)} (ι -> k) w1 w2))
 Case conversion may be inaccurate. Consider using '#align affine_independent_iff_eq_of_fintype_affine_combination_eq affineIndependent_iff_eq_of_fintype_affineCombination_eqₓ'. -/
 /-- A finite family is affinely independent if and only if any affine
 combinations (with sum of weights 1) that evaluate to the same point are equal. -/
@@ -316,7 +316,7 @@ variable {k}
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall (j : ι) (w : ι -> (Units.{u1} k (Ring.toMonoid.{u1} k _inst_1))), AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) => k -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (p j) (p i)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} k (Ring.toMonoid.{u1} k _inst_1)) k (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} k (Ring.toMonoid.{u1} k _inst_1)) k (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} k (Ring.toMonoid.{u1} k _inst_1)) k (coeBase.{succ u1, succ u1} (Units.{u1} k (Ring.toMonoid.{u1} k _inst_1)) k (Units.hasCoe.{u1} k (Ring.toMonoid.{u1} k _inst_1))))) (w i))))
 but is expected to have type
-  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall (j : ι) (w : ι -> (Units.{u4} k (MonoidWithZero.toMonoid.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))))), AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (fun (i : ι) => FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), succ u4, succ u2} (AffineMap.{u4, u4, u4, u3, u2} k k k V P _inst_1 (Ring.toAddCommGroup.{u4} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_1))) _inst_2 _inst_3 _inst_4) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) _x) (AffineMap.funLike.{u4, u4, u4, u3, u2} k k k V P _inst_1 (Ring.toAddCommGroup.{u4} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_1))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u4, u3, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (p j) (p i)) (Units.val.{u4} k (MonoidWithZero.toMonoid.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (w i))))
+  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall (j : ι) (w : ι -> (Units.{u4} k (MonoidWithZero.toMonoid.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))))), AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (fun (i : ι) => FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), succ u4, succ u2} (AffineMap.{u4, u4, u4, u3, u2} k k k V P _inst_1 (Ring.toAddCommGroup.{u4} k _inst_1) (Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_1))) _inst_2 _inst_3 _inst_4) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => P) _x) (AffineMap.funLike.{u4, u4, u4, u3, u2} k k k V P _inst_1 (Ring.toAddCommGroup.{u4} k _inst_1) (Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1)) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_1))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u4, u3, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (p j) (p i)) (Units.val.{u4} k (MonoidWithZero.toMonoid.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (w i))))
 Case conversion may be inaccurate. Consider using '#align affine_independent.units_line_map AffineIndependent.units_lineMapₓ'. -/
 /-- If we single out one member of an affine-independent family of points and affinely transport
 all others along the line joining them to this member, the resulting new family of points is affine-
@@ -335,7 +335,7 @@ theorem AffineIndependent.units_lineMap {p : ι → P} (hp : AffineIndependent k
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall (s₁ : Finset.{u4} ι) (s₂ : Finset.{u4} ι) (w₁ : ι -> k) (w₂ : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s₁ (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s₂ (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k 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 but is expected to have type
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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s₂ (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₁) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s₁ p) w₁) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s₂ p) w₂)) -> (Eq.{max (succ u4) (succ u1)} (ι -> k) (Set.indicator.{u1, u4} ι k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.toSet.{u1} ι s₁) w₁) (Set.indicator.{u1, u4} ι k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.toSet.{u1} ι s₂) w₂)))
 Case conversion may be inaccurate. Consider using '#align affine_independent.indicator_eq_of_affine_combination_eq AffineIndependent.indicator_eq_of_affineCombination_eqₓ'. -/
 theorem AffineIndependent.indicator_eq_of_affineCombination_eq {p : ι → P}
     (ha : AffineIndependent k p) (s₁ s₂ : Finset ι) (w₁ w₂ : ι → k) (hw₁ : (∑ i in s₁, w₁ i) = 1)
@@ -482,7 +482,7 @@ include V₂
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {V₂ : Type.{u5}} {P₂ : Type.{u6}} [_inst_5 : AddCommGroup.{u5} V₂] [_inst_6 : Module.{u1, u5} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u5} V₂ _inst_5)] [_inst_7 : AddTorsor.{u5, u6} V₂ P₂ (AddCommGroup.toAddGroup.{u5} V₂ _inst_5)] {p : ι -> P} (f : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), (AffineIndependent.{u1, u5, u6, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 ι (Function.comp.{succ u4, succ u3, succ u6} ι P P₂ (coeFn.{max (succ u2) (succ u3) (succ u5) (succ u6), max (succ u3) (succ u6)} (AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) p)) -> (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p)
 but is expected to have type
-  forall {k : Type.{u6}} {V : Type.{u5}} {P : Type.{u4}} [_inst_1 : Ring.{u6} k] [_inst_2 : AddCommGroup.{u5} V] [_inst_3 : Module.{u6, u5} k V (Ring.toSemiring.{u6} k _inst_1) (AddCommGroup.toAddCommMonoid.{u5} V _inst_2)] [_inst_4 : AddTorsor.{u5, u4} V P (AddCommGroup.toAddGroup.{u5} V _inst_2)] {ι : Type.{u1}} {V₂ : Type.{u3}} {P₂ : Type.{u2}} [_inst_5 : AddCommGroup.{u3} V₂] [_inst_6 : Module.{u6, u3} k V₂ (Ring.toSemiring.{u6} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_5)] [_inst_7 : AddTorsor.{u3, u2} V₂ P₂ (AddCommGroup.toAddGroup.{u3} V₂ _inst_5)] {p : ι -> P} (f : AffineMap.{u6, u5, u4, u3, u2} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), (AffineIndependent.{u6, u3, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 ι (Function.comp.{succ u1, succ u4, succ u2} ι P P₂ (FunLike.coe.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2), succ u4, succ u2} (AffineMap.{u6, u5, u4, u3, u2} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) _x) (AffineMap.funLike.{u6, u5, u4, u3, u2} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) p)) -> (AffineIndependent.{u6, u5, u4, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p)
+  forall {k : Type.{u6}} {V : Type.{u5}} {P : Type.{u4}} [_inst_1 : Ring.{u6} k] [_inst_2 : AddCommGroup.{u5} V] [_inst_3 : Module.{u6, u5} k V (Ring.toSemiring.{u6} k _inst_1) (AddCommGroup.toAddCommMonoid.{u5} V _inst_2)] [_inst_4 : AddTorsor.{u5, u4} V P (AddCommGroup.toAddGroup.{u5} V _inst_2)] {ι : Type.{u1}} {V₂ : Type.{u3}} {P₂ : Type.{u2}} [_inst_5 : AddCommGroup.{u3} V₂] [_inst_6 : Module.{u6, u3} k V₂ (Ring.toSemiring.{u6} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_5)] [_inst_7 : AddTorsor.{u3, u2} V₂ P₂ (AddCommGroup.toAddGroup.{u3} V₂ _inst_5)] {p : ι -> P} (f : AffineMap.{u6, u5, u4, u3, u2} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), (AffineIndependent.{u6, u3, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 ι (Function.comp.{succ u1, succ u4, succ u2} ι P P₂ (FunLike.coe.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2), succ u4, succ u2} (AffineMap.{u6, u5, u4, u3, u2} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P₂) _x) (AffineMap.funLike.{u6, u5, u4, u3, u2} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) p)) -> (AffineIndependent.{u6, u5, u4, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p)
 Case conversion may be inaccurate. Consider using '#align affine_independent.of_comp AffineIndependent.of_compₓ'. -/
 /-- If the image of a family of points in affine space under an affine transformation is affine-
 independent, then the original family of points is also affine-independent. -/
@@ -502,7 +502,7 @@ theorem AffineIndependent.of_comp {p : ι → P} (f : P →ᵃ[k] P₂) (hai : A
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {V₂ : Type.{u5}} {P₂ : Type.{u6}} [_inst_5 : AddCommGroup.{u5} V₂] [_inst_6 : Module.{u1, u5} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u5} V₂ _inst_5)] [_inst_7 : AddTorsor.{u5, u6} V₂ P₂ (AddCommGroup.toAddGroup.{u5} V₂ _inst_5)] {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall (f : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), (Function.Injective.{succ u3, succ u6} P P₂ (coeFn.{max (succ u2) (succ u3) (succ u5) (succ u6), max (succ u3) (succ u6)} (AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f)) -> (AffineIndependent.{u1, u5, u6, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 ι (Function.comp.{succ u4, succ u3, succ u6} ι P P₂ (coeFn.{max (succ u2) (succ u3) (succ u5) (succ u6), max (succ u3) (succ u6)} (AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) p)))
 but is expected to have type
-  forall {k : Type.{u6}} {V : Type.{u5}} {P : Type.{u4}} [_inst_1 : Ring.{u6} k] [_inst_2 : AddCommGroup.{u5} V] [_inst_3 : Module.{u6, u5} k V (Ring.toSemiring.{u6} k _inst_1) (AddCommGroup.toAddCommMonoid.{u5} V _inst_2)] [_inst_4 : AddTorsor.{u5, u4} V P (AddCommGroup.toAddGroup.{u5} V _inst_2)] {ι : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u6, u2} k V₂ (Ring.toSemiring.{u6} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] {p : ι -> P}, (AffineIndependent.{u6, u5, u4, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall (f : AffineMap.{u6, u5, u4, u2, u1} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), (Function.Injective.{succ u4, succ u1} P P₂ (FunLike.coe.{max (max (max (succ u5) (succ u4)) (succ u2)) (succ u1), succ u4, succ u1} (AffineMap.{u6, u5, u4, u2, u1} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) _x) (AffineMap.funLike.{u6, u5, u4, u2, u1} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f)) -> (AffineIndependent.{u6, u2, u1, u3} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 ι (Function.comp.{succ u3, succ u4, succ u1} ι P P₂ (FunLike.coe.{max (max (max (succ u5) (succ u4)) (succ u2)) (succ u1), succ u4, succ u1} (AffineMap.{u6, u5, u4, u2, u1} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) _x) (AffineMap.funLike.{u6, u5, u4, u2, u1} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) p)))
+  forall {k : Type.{u6}} {V : Type.{u5}} {P : Type.{u4}} [_inst_1 : Ring.{u6} k] [_inst_2 : AddCommGroup.{u5} V] [_inst_3 : Module.{u6, u5} k V (Ring.toSemiring.{u6} k _inst_1) (AddCommGroup.toAddCommMonoid.{u5} V _inst_2)] [_inst_4 : AddTorsor.{u5, u4} V P (AddCommGroup.toAddGroup.{u5} V _inst_2)] {ι : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u6, u2} k V₂ (Ring.toSemiring.{u6} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] {p : ι -> P}, (AffineIndependent.{u6, u5, u4, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall (f : AffineMap.{u6, u5, u4, u2, u1} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), (Function.Injective.{succ u4, succ u1} P P₂ (FunLike.coe.{max (max (max (succ u5) (succ u4)) (succ u2)) (succ u1), succ u4, succ u1} (AffineMap.{u6, u5, u4, u2, u1} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P₂) _x) (AffineMap.funLike.{u6, u5, u4, u2, u1} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f)) -> (AffineIndependent.{u6, u2, u1, u3} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 ι (Function.comp.{succ u3, succ u4, succ u1} ι P P₂ (FunLike.coe.{max (max (max (succ u5) (succ u4)) (succ u2)) (succ u1), succ u4, succ u1} (AffineMap.{u6, u5, u4, u2, u1} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P₂) _x) (AffineMap.funLike.{u6, u5, u4, u2, u1} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) p)))
 Case conversion may be inaccurate. Consider using '#align affine_independent.map' AffineIndependent.map'ₓ'. -/
 /-- The image of a family of points in affine space, under an injective affine transformation, is
 affine-independent. -/
@@ -524,7 +524,7 @@ theorem AffineIndependent.map' {p : ι → P} (hai : AffineIndependent k p) (f :
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {V₂ : Type.{u5}} {P₂ : Type.{u6}} [_inst_5 : AddCommGroup.{u5} V₂] [_inst_6 : Module.{u1, u5} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u5} V₂ _inst_5)] [_inst_7 : AddTorsor.{u5, u6} V₂ P₂ (AddCommGroup.toAddGroup.{u5} V₂ _inst_5)] {p : ι -> P} (f : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), (Function.Injective.{succ u3, succ u6} P P₂ (coeFn.{max (succ u2) (succ u3) (succ u5) (succ u6), max (succ u3) (succ u6)} (AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f)) -> (Iff (AffineIndependent.{u1, u5, u6, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 ι (Function.comp.{succ u4, succ u3, succ u6} ι P P₂ (coeFn.{max (succ u2) (succ u3) (succ u5) (succ u6), max (succ u3) (succ u6)} (AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineMap.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u5, u6} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) p)) (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p))
 but is expected to have type
-  forall {k : Type.{u6}} {V : Type.{u5}} {P : Type.{u4}} [_inst_1 : Ring.{u6} k] [_inst_2 : AddCommGroup.{u5} V] [_inst_3 : Module.{u6, u5} k V (Ring.toSemiring.{u6} k _inst_1) (AddCommGroup.toAddCommMonoid.{u5} V _inst_2)] [_inst_4 : AddTorsor.{u5, u4} V P (AddCommGroup.toAddGroup.{u5} V _inst_2)] {ι : Type.{u1}} {V₂ : Type.{u3}} {P₂ : Type.{u2}} [_inst_5 : AddCommGroup.{u3} V₂] [_inst_6 : Module.{u6, u3} k V₂ (Ring.toSemiring.{u6} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_5)] [_inst_7 : AddTorsor.{u3, u2} V₂ P₂ (AddCommGroup.toAddGroup.{u3} V₂ _inst_5)] {p : ι -> P} (f : AffineMap.{u6, u5, u4, u3, u2} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), (Function.Injective.{succ u4, succ u2} P P₂ (FunLike.coe.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2), succ u4, succ u2} (AffineMap.{u6, u5, u4, u3, u2} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) _x) (AffineMap.funLike.{u6, u5, u4, u3, u2} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f)) -> (Iff (AffineIndependent.{u6, u3, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 ι (Function.comp.{succ u1, succ u4, succ u2} ι P P₂ (FunLike.coe.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2), succ u4, succ u2} (AffineMap.{u6, u5, u4, u3, u2} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => P₂) _x) (AffineMap.funLike.{u6, u5, u4, u3, u2} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) p)) (AffineIndependent.{u6, u5, u4, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p))
+  forall {k : Type.{u6}} {V : Type.{u5}} {P : Type.{u4}} [_inst_1 : Ring.{u6} k] [_inst_2 : AddCommGroup.{u5} V] [_inst_3 : Module.{u6, u5} k V (Ring.toSemiring.{u6} k _inst_1) (AddCommGroup.toAddCommMonoid.{u5} V _inst_2)] [_inst_4 : AddTorsor.{u5, u4} V P (AddCommGroup.toAddGroup.{u5} V _inst_2)] {ι : Type.{u1}} {V₂ : Type.{u3}} {P₂ : Type.{u2}} [_inst_5 : AddCommGroup.{u3} V₂] [_inst_6 : Module.{u6, u3} k V₂ (Ring.toSemiring.{u6} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_5)] [_inst_7 : AddTorsor.{u3, u2} V₂ P₂ (AddCommGroup.toAddGroup.{u3} V₂ _inst_5)] {p : ι -> P} (f : AffineMap.{u6, u5, u4, u3, u2} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), (Function.Injective.{succ u4, succ u2} P P₂ (FunLike.coe.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2), succ u4, succ u2} (AffineMap.{u6, u5, u4, u3, u2} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P₂) _x) (AffineMap.funLike.{u6, u5, u4, u3, u2} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f)) -> (Iff (AffineIndependent.{u6, u3, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 ι (Function.comp.{succ u1, succ u4, succ u2} ι P P₂ (FunLike.coe.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2), succ u4, succ u2} (AffineMap.{u6, u5, u4, u3, u2} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P₂) _x) (AffineMap.funLike.{u6, u5, u4, u3, u2} k V P V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) p)) (AffineIndependent.{u6, u5, u4, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p))
 Case conversion may be inaccurate. Consider using '#align affine_map.affine_independent_iff AffineMap.affineIndependent_iffₓ'. -/
 /-- Injective affine maps preserve affine independence. -/
 theorem AffineMap.affineIndependent_iff {p : ι → P} (f : P →ᵃ[k] P₂) (hf : Function.Injective f) :
@@ -536,7 +536,7 @@ theorem AffineMap.affineIndependent_iff {p : ι → P} (f : P →ᵃ[k] P₂) (h
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {V₂ : Type.{u5}} {P₂ : Type.{u6}} [_inst_5 : AddCommGroup.{u5} V₂] [_inst_6 : Module.{u1, u5} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u5} V₂ _inst_5)] [_inst_7 : AddTorsor.{u5, u6} V₂ P₂ (AddCommGroup.toAddGroup.{u5} V₂ _inst_5)] {p : ι -> P} (e : AffineEquiv.{u1, u3, u6, u2, u5} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), Iff (AffineIndependent.{u1, u5, u6, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 ι (Function.comp.{succ u4, succ u3, succ u6} ι P P₂ (coeFn.{max (succ u3) (succ u6) (succ u2) (succ u5), max (succ u3) (succ u6)} (AffineEquiv.{u1, u3, u6, u2, u5} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineEquiv.{u1, u3, u6, u2, u5} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P -> P₂) (AffineEquiv.hasCoeToFun.{u1, u3, u6, u2, u5} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) e) p)) (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p)
 but is expected to have type
-  forall {k : Type.{u6}} {V : Type.{u3}} {P : Type.{u5}} [_inst_1 : Ring.{u6} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u6, u3} k V (Ring.toSemiring.{u6} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u5} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {V₂ : Type.{u2}} {P₂ : Type.{u4}} [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u6, u2} k V₂ (Ring.toSemiring.{u6} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u4} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] {p : ι -> P} (e : AffineEquiv.{u6, u5, u4, u3, u2} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), Iff (AffineIndependent.{u6, u2, u4, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 ι (Function.comp.{succ u1, succ u5, succ u4} ι P P₂ (FunLike.coe.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2), succ u5, succ u4} (AffineEquiv.{u6, u5, u4, u3, u2} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineEquiv._hyg.1471 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2), succ u5, succ u4} (AffineEquiv.{u6, u5, u4, u3, u2} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2), succ u5, succ u4} (AffineEquiv.{u6, u5, u4, u3, u2} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P P₂ (AffineEquiv.equivLike.{u6, u5, u4, u3, u2} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7))) e) p)) (AffineIndependent.{u6, u3, u5, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p)
+  forall {k : Type.{u6}} {V : Type.{u3}} {P : Type.{u5}} [_inst_1 : Ring.{u6} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u6, u3} k V (Ring.toSemiring.{u6} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u5} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {V₂ : Type.{u2}} {P₂ : Type.{u4}} [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u6, u2} k V₂ (Ring.toSemiring.{u6} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u4} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] {p : ι -> P} (e : AffineEquiv.{u6, u5, u4, u3, u2} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), Iff (AffineIndependent.{u6, u2, u4, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 ι (Function.comp.{succ u1, succ u5, succ u4} ι P P₂ (FunLike.coe.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2), succ u5, succ u4} (AffineEquiv.{u6, u5, u4, u3, u2} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineEquiv._hyg.1470 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2), succ u5, succ u4} (AffineEquiv.{u6, u5, u4, u3, u2} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2), succ u5, succ u4} (AffineEquiv.{u6, u5, u4, u3, u2} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P P₂ (AffineEquiv.equivLike.{u6, u5, u4, u3, u2} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7))) e) p)) (AffineIndependent.{u6, u3, u5, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p)
 Case conversion may be inaccurate. Consider using '#align affine_equiv.affine_independent_iff AffineEquiv.affineIndependent_iffₓ'. -/
 /-- Affine equivalences preserve affine independence of families of points. -/
 theorem AffineEquiv.affineIndependent_iff {p : ι → P} (e : P ≃ᵃ[k] P₂) :
@@ -548,7 +548,7 @@ theorem AffineEquiv.affineIndependent_iff {p : ι → P} (e : P ≃ᵃ[k] P₂)
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] {s : Set.{u3} P} (e : AffineEquiv.{u1, u3, u5, u2, u4} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), Iff (AffineIndependent.{u1, u4, u5, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 (coeSort.{succ u5, succ (succ u5)} (Set.{u5} P₂) Type.{u5} (Set.hasCoeToSort.{u5} P₂) (Set.image.{u3, u5} P P₂ (coeFn.{max (succ u3) (succ u5) (succ u2) (succ u4), max (succ u3) (succ u5)} (AffineEquiv.{u1, u3, u5, u2, u4} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineEquiv.{u1, u3, u5, u2, u4} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P -> P₂) (AffineEquiv.hasCoeToFun.{u1, u3, u5, u2, u4} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) e) s)) ((fun (a : Type.{u5}) (b : Type.{u5}) [self : HasLiftT.{succ u5, succ u5} a b] => self.0) (coeSort.{succ u5, succ (succ u5)} (Set.{u5} P₂) Type.{u5} (Set.hasCoeToSort.{u5} P₂) (Set.image.{u3, u5} P P₂ (coeFn.{max (succ u3) (succ u5) (succ u2) (succ u4), max (succ u3) (succ u5)} (AffineEquiv.{u1, u3, u5, u2, u4} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineEquiv.{u1, u3, u5, u2, u4} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P -> P₂) (AffineEquiv.hasCoeToFun.{u1, u3, u5, u2, u4} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) e) s)) P₂ (HasLiftT.mk.{succ u5, succ u5} (coeSort.{succ u5, succ (succ 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u2, u4} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) e) s)) P₂ (coeBase.{succ u5, succ u5} (coeSort.{succ u5, succ (succ u5)} (Set.{u5} P₂) Type.{u5} (Set.hasCoeToSort.{u5} P₂) (Set.image.{u3, u5} P P₂ (coeFn.{max (succ u3) (succ u5) (succ u2) (succ u4), max (succ u3) (succ u5)} (AffineEquiv.{u1, u3, u5, u2, u4} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineEquiv.{u1, u3, u5, u2, u4} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P -> P₂) (AffineEquiv.hasCoeToFun.{u1, u3, u5, u2, u4} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) e) s)) P₂ (coeSubtype.{succ u5} P₂ (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (Set.{u5} P₂) (Set.hasMem.{u5} P₂) x (Set.image.{u3, u5} P P₂ (coeFn.{max (succ u3) (succ u5) (succ u2) (succ u4), max (succ u3) (succ u5)} (AffineEquiv.{u1, u3, u5, u2, u4} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineEquiv.{u1, u3, u5, u2, u4} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P -> P₂) (AffineEquiv.hasCoeToFun.{u1, u3, u5, u2, u4} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) e) s)))))))) (AffineIndependent.{u1, u2, u3, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) P (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) P (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) P (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} P) Type.{u3} (Set.hasCoeToSort.{u3} P) s) P (coeSubtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (Set.{u3} P) (Set.hasMem.{u3} P) x s)))))))
 but is expected to have type
-  forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u5}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u5} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {V₂ : Type.{u1}} {P₂ : Type.{u3}} [_inst_5 : AddCommGroup.{u1} V₂] [_inst_6 : Module.{u4, u1} k V₂ (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V₂ _inst_5)] [_inst_7 : AddTorsor.{u1, u3} V₂ P₂ (AddCommGroup.toAddGroup.{u1} V₂ _inst_5)] {s : Set.{u5} P} (e : AffineEquiv.{u4, u5, u3, u2, u1} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), Iff (AffineIndependent.{u4, u1, u3, u3} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 (Subtype.{succ u3} P₂ (fun (x : P₂) => Membership.mem.{u3, u3} P₂ (Set.{u3} P₂) (Set.instMembershipSet.{u3} P₂) x (Set.image.{u5, u3} P P₂ (FunLike.coe.{max (max (max (succ u5) (succ u3)) (succ u2)) (succ u1), succ u5, succ u3} (AffineEquiv.{u4, u5, u3, u2, u1} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P (fun (a : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineEquiv._hyg.1471 : P) => P₂) a) (EmbeddingLike.toFunLike.{max (max (max (succ u5) (succ u3)) (succ u2)) (succ u1), succ u5, succ u3} (AffineEquiv.{u4, u5, u3, u2, u1} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u5) (succ u3)) (succ u2)) (succ u1), succ u5, succ u3} (AffineEquiv.{u4, u5, u3, u2, u1} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P P₂ (AffineEquiv.equivLike.{u4, u5, u3, u2, u1} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7))) e) s))) (Subtype.val.{succ u3} P₂ (fun (x : P₂) => Membership.mem.{u3, u3} P₂ (Set.{u3} P₂) (Set.instMembershipSet.{u3} P₂) x (Set.image.{u5, u3} P P₂ (FunLike.coe.{max (max (max (succ u5) (succ u3)) (succ u2)) (succ u1), succ u5, succ u3} (AffineEquiv.{u4, u5, u3, u2, u1} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P (fun (a : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineEquiv._hyg.1471 : P) => P₂) a) (EmbeddingLike.toFunLike.{max (max (max (succ u5) (succ u3)) (succ u2)) (succ u1), succ u5, succ u3} (AffineEquiv.{u4, u5, u3, u2, u1} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u5) (succ u3)) (succ u2)) (succ u1), succ u5, succ u3} (AffineEquiv.{u4, u5, u3, u2, u1} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P P₂ (AffineEquiv.equivLike.{u4, u5, u3, u2, u1} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7))) e) s)))) (AffineIndependent.{u4, u2, u5, u5} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Subtype.{succ u5} P (fun (x : P) => Membership.mem.{u5, u5} P (Set.{u5} P) (Set.instMembershipSet.{u5} P) x s)) (Subtype.val.{succ u5} P (fun (x : P) => Membership.mem.{u5, u5} P (Set.{u5} P) (Set.instMembershipSet.{u5} P) x s)))
+  forall {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u5}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u4, u2} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u5} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {V₂ : Type.{u1}} {P₂ : Type.{u3}} [_inst_5 : AddCommGroup.{u1} V₂] [_inst_6 : Module.{u4, u1} k V₂ (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V₂ _inst_5)] [_inst_7 : AddTorsor.{u1, u3} V₂ P₂ (AddCommGroup.toAddGroup.{u1} V₂ _inst_5)] {s : Set.{u5} P} (e : AffineEquiv.{u4, u5, u3, u2, u1} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), Iff (AffineIndependent.{u4, u1, u3, u3} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 (Subtype.{succ u3} P₂ (fun (x : P₂) => Membership.mem.{u3, u3} P₂ (Set.{u3} P₂) (Set.instMembershipSet.{u3} P₂) x (Set.image.{u5, u3} P P₂ (FunLike.coe.{max (max (max (succ u5) (succ u3)) (succ u2)) (succ u1), succ u5, succ u3} (AffineEquiv.{u4, u5, u3, u2, u1} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P (fun (a : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineEquiv._hyg.1470 : P) => P₂) a) (EmbeddingLike.toFunLike.{max (max (max (succ u5) (succ u3)) (succ u2)) (succ u1), succ u5, succ u3} (AffineEquiv.{u4, u5, u3, u2, u1} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u5) (succ u3)) (succ u2)) (succ u1), succ u5, succ u3} (AffineEquiv.{u4, u5, u3, u2, u1} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P P₂ (AffineEquiv.equivLike.{u4, u5, u3, u2, u1} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7))) e) s))) (Subtype.val.{succ u3} P₂ (fun (x : P₂) => Membership.mem.{u3, u3} P₂ (Set.{u3} P₂) (Set.instMembershipSet.{u3} P₂) x (Set.image.{u5, u3} P P₂ (FunLike.coe.{max (max (max (succ u5) (succ u3)) (succ u2)) (succ u1), succ u5, succ u3} (AffineEquiv.{u4, u5, u3, u2, u1} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P (fun (a : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineEquiv._hyg.1470 : P) => P₂) a) (EmbeddingLike.toFunLike.{max (max (max (succ u5) (succ u3)) (succ u2)) (succ u1), succ u5, succ u3} (AffineEquiv.{u4, u5, u3, u2, u1} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u5) (succ u3)) (succ u2)) (succ u1), succ u5, succ u3} (AffineEquiv.{u4, u5, u3, u2, u1} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P P₂ (AffineEquiv.equivLike.{u4, u5, u3, u2, u1} k P P₂ V V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7))) e) s)))) (AffineIndependent.{u4, u2, u5, u5} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Subtype.{succ u5} P (fun (x : P) => Membership.mem.{u5, u5} P (Set.{u5} P) (Set.instMembershipSet.{u5} P) x s)) (Subtype.val.{succ u5} P (fun (x : P) => Membership.mem.{u5, u5} P (Set.{u5} P) (Set.instMembershipSet.{u5} P) x s)))
 Case conversion may be inaccurate. Consider using '#align affine_equiv.affine_independent_set_of_eq_iff AffineEquiv.affineIndependent_set_of_eq_iffₓ'. -/
 /-- Affine equivalences preserve affine independence of subsets. -/
 theorem AffineEquiv.affineIndependent_set_of_eq_iff {s : Set P} (e : P ≃ᵃ[k] P₂) :
@@ -691,7 +691,7 @@ theorem affineIndependent_iff {ι} {p : ι → V} :
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u4} ι}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Iff (Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) 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_inst_1)))) r (HSub.hSub.{u4, u4, u4} k k k (instHSub.{u4} k (Ring.toSub.{u4} k _inst_1)) (w₁ i) (w₂ i))))))))
+  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k 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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u4, u3, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₁) (Set.{u2} P) (Set.instInsertSet.{u2} P) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun 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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w₁) (Singleton.singleton.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (Set.{u2} P) (Set.instSingletonSet.{u2} P) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w₂))))) (Exists.{succ u4} k (fun (r : k) => forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u4} k (w i) (HMul.hMul.{u4, u4, u4} k k k (instHMul.{u4} k (NonUnitalNonAssocRing.toMul.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) r (HSub.hSub.{u4, u4, u4} k k k (instHSub.{u4} k (Ring.toSub.{u4} k _inst_1)) (w₁ i) (w₂ i))))))))
 Case conversion may be inaccurate. Consider using '#align weighted_vsub_mem_vector_span_pair weightedVSub_mem_vectorSpan_pairₓ'. -/
 /-- Given an affinely independent family of points, a weighted subtraction lies in the
 `vector_span` of two points given as affine combinations if and only if it is a weighted
@@ -727,7 +727,7 @@ theorem weightedVSub_mem_vectorSpan_pair {p : ι → P} (h : AffineIndependent k
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u4} ι}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Iff (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) 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_inst_1)))) r (HSub.hSub.{u4, u4, u4} k k k (instHSub.{u4} k (Ring.toSub.{u4} k _inst_1)) (w₂ i) (w₁ i))) (w₁ i)))))))
 Case conversion may be inaccurate. Consider using '#align affine_combination_mem_affine_span_pair affineCombination_mem_affineSpan_pairₓ'. -/
 /-- Given an affinely independent family of points, an affine combination lies in the
 span of two points given as affine combinations if and only if it is an affine combination
@@ -994,7 +994,7 @@ attribute [local instance] LinearOrderedRing.decidableLt
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u4} ι}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) s (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) s (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4)) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k 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(fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k 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: ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₂))))) -> (forall {i : ι} {j : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) j s) -> (Eq.{succ u1} k (w₁ i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))))))) -> (Eq.{succ u1} k (w₁ j) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))))))) -> (Eq.{1} SignType (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w₂ i)) (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w₂ j))) -> (Eq.{1} SignType (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k 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(PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w i)) (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w j)))))
 but is expected to have type
-  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : LinearOrderedRing.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) -> (Membership.mem.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (AffineSubspace.instSetLikeAffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P 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(LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₁) (Singleton.singleton.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (Set.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (Set.instSingletonSet.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) 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(LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₂))))) -> (forall {i : ι} {j : ι}, (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) j s) -> (Eq.{succ u4} k (w₁ i) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1)))))))) -> (Eq.{succ u4} k (w₁ j) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k 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(PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w₂ j))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k 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+  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : LinearOrderedRing.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k 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_inst_1)) _inst_2 _inst_3 _inst_4) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (AffineSubspace.instSetLikeAffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k 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_inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) 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(a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₁) (Singleton.singleton.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂) (Set.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂)) (Set.instSingletonSet.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) w₂)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₂))))) -> (forall {i : ι} {j : ι}, (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) j s) -> (Eq.{succ u4} k (w₁ i) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1)))))))) -> (Eq.{succ u4} k (w₁ j) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1)))))))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w₂ i)) (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w₂ j))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w i)) (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w j)))))
 Case conversion may be inaccurate. Consider using '#align sign_eq_of_affine_combination_mem_affine_span_pair sign_eq_of_affineCombination_mem_affineSpan_pairₓ'. -/
 /-- Given an affinely independent family of points, suppose that an affine combination lies in
 the span of two points given as affine combinations, and suppose that, for two indices, the
@@ -1020,7 +1020,7 @@ theorem sign_eq_of_affineCombination_mem_affineSpan_pair {p : ι → P} (h : Aff
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {s : Finset.{u4} ι}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (forall {i₁ : ι} {i₂ : ι} {i₃ : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i₁ s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i₂ s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i₃ s) -> (Ne.{succ u4} ι i₁ i₂) -> (Ne.{succ u4} ι i₁ i₃) -> (Ne.{succ u4} ι i₂ i₃) -> (forall {c : k}, (LT.lt.{u1} k (Preorder.toHasLt.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) c) -> (LT.lt.{u1} k (Preorder.toHasLt.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) c (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4)) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => 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(OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w i₃))))))
 but is expected to have type
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(PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w i₃))))))
+  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : LinearOrderedRing.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : 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 Case conversion may be inaccurate. Consider using '#align sign_eq_of_affine_combination_mem_affine_span_single_line_map sign_eq_of_affineCombination_mem_affineSpan_single_lineMapₓ'. -/
 /-- Given an affinely independent family of points, suppose that an affine combination lies in
 the span of one point of that family and a combination of another two points of that family given

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -1018,7 +1018,7 @@ theorem sign_eq_of_affineCombination_mem_affineSpan_pair {p : ι → P} (h : Aff
 
 /- warning: sign_eq_of_affine_combination_mem_affine_span_single_line_map -> sign_eq_of_affineCombination_mem_affineSpan_single_lineMap is a dubious translation:
 lean 3 declaration is
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(OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w i₃))))))
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {s : Finset.{u4} ι}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (forall {i₁ : ι} {i₂ : ι} {i₃ : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i₁ s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i₂ s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i₃ s) -> (Ne.{succ u4} ι i₁ i₂) -> (Ne.{succ u4} ι i₁ i₃) -> (Ne.{succ u4} ι i₂ i₃) -> (forall {c : k}, (LT.lt.{u1} k (Preorder.toHasLt.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) c) -> (LT.lt.{u1} k (Preorder.toHasLt.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) c (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4)) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => 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max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k 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(AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) (p i₁) (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} k k k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} k k k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} 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(OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w i₃))))))
 but is expected to have type
   forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : LinearOrderedRing.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) -> (forall {i₁ : ι} {i₂ : ι} {i₃ : ι}, (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i₁ s) -> (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i₂ s) -> (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i₃ s) -> (Ne.{succ u1} ι i₁ i₂) -> (Ne.{succ u1} ι i₁ i₃) -> (Ne.{succ u1} ι i₂ i₃) -> (forall {c : k}, (LT.lt.{u4} k (Preorder.toLT.{u4} k (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) c) -> (LT.lt.{u4} k (Preorder.toLT.{u4} k (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) c (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) -> (Membership.mem.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c) (AffineSubspace.instSetLikeAffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 (Insert.insert.{u2, u2} P (Set.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c)) (Set.instInsertSet.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c)) (p i₁) (Singleton.singleton.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c) (Set.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c)) (Set.instSingletonSet.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), succ u4, succ u2} (AffineMap.{u4, u4, u4, u3, u2} k k k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))) _inst_2 _inst_3 _inst_4) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) _x) (AffineMap.funLike.{u4, u4, u4, u3, u2} k k k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u4, u3, u2} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 (p i₂) (p i₃)) c))))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w i₂)) (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w i₃))))))
 Case conversion may be inaccurate. Consider using '#align sign_eq_of_affine_combination_mem_affine_span_single_line_map sign_eq_of_affineCombination_mem_affineSpan_single_lineMapₓ'. -/
@@ -1144,7 +1144,7 @@ def face {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ} (h
 
 /- warning: affine.simplex.face_points -> Affine.Simplex.face_points is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {n : Nat} (s : Affine.Simplex.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 n) {fs : Finset.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))} {m : Nat} (h : Eq.{1} Nat (Finset.card.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) fs) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), Eq.{succ u3} P (Affine.Simplex.points.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 m (Affine.Simplex.face.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s fs m h) i) (Affine.Simplex.points.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LinearOrder.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LinearOrder.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin 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Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LinearOrder.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))))))) (Finset.orderEmbOfFin.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) fs (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) h) i))
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {n : Nat} (s : Affine.Simplex.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 n) {fs : Finset.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))} {m : Nat} (h : Eq.{1} Nat (Finset.card.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) fs) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 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(HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LinearOrder.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))))))) (Finset.orderEmbOfFin.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) fs (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) h) i))
 but is expected to have type
   forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {n : Nat} (s : Affine.Simplex.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 n) {fs : Finset.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))} {m : Nat} (h : Eq.{1} Nat (Finset.card.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) fs) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{succ u1} P (Affine.Simplex.points.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 m (Affine.Simplex.face.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s fs m h) i) (Affine.Simplex.points.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat 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 Case conversion may be inaccurate. Consider using '#align affine.simplex.face_points Affine.Simplex.face_pointsₓ'. -/
@@ -1157,7 +1157,7 @@ theorem face_points {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m
 
 /- warning: affine.simplex.face_points' -> Affine.Simplex.face_points' is a dubious translation:
 lean 3 declaration is
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(instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))))))) (Finset.orderEmbOfFin.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) fs (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) h)))
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {n : Nat} (s : Affine.Simplex.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 n) {fs : Finset.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))} {m : Nat} (h : Eq.{1} Nat (Finset.card.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) fs) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), Eq.{succ u3} ((Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> P) (Affine.Simplex.points.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 m (Affine.Simplex.face.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s fs m h)) (Function.comp.{1, 1, succ u3} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) P (Affine.Simplex.points.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LinearOrder.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LinearOrder.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toHasLe.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LinearOrder.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))))))) (Finset.orderEmbOfFin.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) fs (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) h)))
 but is expected to have type
   forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {n : Nat} (s : Affine.Simplex.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 n) {fs : Finset.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))} {m : Nat} (h : Eq.{1} Nat (Finset.card.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) fs) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{succ u1} ((Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> P) (Affine.Simplex.points.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 m (Affine.Simplex.face.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s fs m h)) (Function.comp.{1, 1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) P (Affine.Simplex.points.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (InfHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 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Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))))) (Finset.orderEmbOfFin.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) fs (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) h)))
 Case conversion may be inaccurate. Consider using '#align affine.simplex.face_points' Affine.Simplex.face_points'ₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -69,7 +69,7 @@ def AffineIndependent (p : ι → P) : Prop :=
 lean 3 declaration is
   forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (p : ι -> P), Iff (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (s : Finset.{u4} ι) (w : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))))))))
 but is expected to have type
-  forall (k : Type.{u4}) {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} (p : ι -> P), Iff (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (s : Finset.{u1} ι) (w : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u4), max (succ u1) (succ u4), succ u3} (LinearMap.{u4, u4, max u4 u1, u3} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u1 u4, u3} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u1, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (OfNat.ofNat.{u3} V 0 (Zero.toOfNat0.{u3} V (NegZeroClass.toZero.{u3} V (SubNegZeroMonoid.toNegZeroClass.{u3} V (SubtractionMonoid.toSubNegZeroMonoid.{u3} V (SubtractionCommMonoid.toSubtractionMonoid.{u3} V (AddCommGroup.toDivisionAddCommMonoid.{u3} V _inst_2)))))))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u4} k (w i) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))))))))
+  forall (k : Type.{u4}) {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} (p : ι -> P), Iff (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (s : Finset.{u1} ι) (w : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u4), max (succ u1) (succ u4), succ u3} (LinearMap.{u4, u4, max u4 u1, u3} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u1 u4, u3} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u1, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (OfNat.ofNat.{u3} V 0 (Zero.toOfNat0.{u3} V (NegZeroClass.toZero.{u3} V (SubNegZeroMonoid.toNegZeroClass.{u3} V (SubtractionMonoid.toSubNegZeroMonoid.{u3} V (SubtractionCommMonoid.toSubtractionMonoid.{u3} V (AddCommGroup.toDivisionAddCommMonoid.{u3} V _inst_2)))))))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u4} k (w i) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))))))))
 Case conversion may be inaccurate. Consider using '#align affine_independent_def affineIndependent_defₓ'. -/
 /-- The definition of `affine_independent`. -/
 theorem affineIndependent_def (p : ι → P) :
@@ -94,7 +94,7 @@ theorem affineIndependent_of_subsingleton [Subsingleton ι] (p : ι → P) : Aff
 lean 3 declaration is
   forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (forall (i : ι), Eq.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))))
 but is expected to have type
-  forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w : ι -> k), (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w) (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (forall (i : ι), Eq.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))))
+  forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w : ι -> k), (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w) (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (forall (i : ι), Eq.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align affine_independent_iff_of_fintype affineIndependent_iff_of_fintypeₓ'. -/
 /-- A family indexed by a `fintype` is affinely independent if and
 only if no nontrivial weighted subtractions over `finset.univ` (where
@@ -234,7 +234,7 @@ theorem linearIndependent_set_iff_affineIndependent_vadd_union_singleton {s : Se
 lean 3 declaration is
   forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (p : ι -> P), Iff (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (s1 : Finset.{u4} ι) (s2 : Finset.{u4} ι) (w1 : ι -> k) (w2 : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s1 (fun (i : ι) => w1 i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s2 (fun (i : ι) => w2 i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i 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 but is expected to have type
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(NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s1 p) w1) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s2 p) w2)) -> (Eq.{max (succ u4) (succ u1)} (ι -> k) (Set.indicator.{u1, u4} ι k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.toSet.{u1} ι s1) w1) (Set.indicator.{u1, u4} ι k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.toSet.{u1} ι s2) w2)))
 Case conversion may be inaccurate. Consider using '#align affine_independent_iff_indicator_eq_of_affine_combination_eq affineIndependent_iff_indicator_eq_of_affineCombination_eqₓ'. -/
 /-- A family is affinely independent if and only if any affine
 combinations (with sum of weights 1) that evaluate to the same point
@@ -285,7 +285,7 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
 lean 3 declaration is
   forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w1 : ι -> k) (w2 : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w1 i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w2 i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => 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(Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w1) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w2)) -> (Eq.{max (succ u4) (succ u1)} (ι -> k) w1 w2))
 but is expected to have type
-  forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w1 : ι -> k) (w2 : ι -> k), (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w1 i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) -> (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k 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(Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w2)) -> (Eq.{max (succ u3) (succ u4)} (ι -> k) w1 w2))
+  forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w1 : ι -> k) (w2 : ι -> k), (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w1 i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) -> (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w2 i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w1) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u2)) (succ u1), succ (max u3 u4), succ u1} (AffineMap.{u3, max u3 u4, max u3 u4, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w1) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u2)) (succ u1), succ (max u3 u4), succ u1} (AffineMap.{u3, max u3 u4, max u3 u4, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k 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AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w2)) -> (Eq.{max (succ u3) (succ u4)} (ι -> k) w1 w2))
 Case conversion may be inaccurate. Consider using '#align affine_independent_iff_eq_of_fintype_affine_combination_eq affineIndependent_iff_eq_of_fintype_affineCombination_eqₓ'. -/
 /-- A finite family is affinely independent if and only if any affine
 combinations (with sum of weights 1) that evaluate to the same point are equal. -/
@@ -335,7 +335,7 @@ theorem AffineIndependent.units_lineMap {p : ι → P} (hp : AffineIndependent k
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall (s₁ : Finset.{u4} ι) (s₂ : Finset.{u4} ι) (w₁ : ι -> k) (w₂ : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s₁ (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s₂ (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k 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(NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s₁ p) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => 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_inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s₂ p) w₂)) -> (Eq.{max (succ u4) (succ u1)} (ι -> k) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₁) w₁) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₂) w₂)))
 but is expected to have type
-  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall (s₁ : Finset.{u1} ι) (s₂ : Finset.{u1} ι) (w₁ : ι -> k) (w₂ : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s₁ (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s₂ (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s₁ p) w₁) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s₂ p) w₂)) -> (Eq.{max (succ u4) (succ u1)} (ι -> k) (Set.indicator.{u1, u4} ι k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.toSet.{u1} ι s₁) w₁) (Set.indicator.{u1, u4} ι k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.toSet.{u1} ι s₂) w₂)))
+  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall (s₁ : Finset.{u1} ι) (s₂ : Finset.{u1} ι) (w₁ : ι -> k) (w₂ : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s₁ (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s₂ (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s₁ p) w₁) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s₂ p) w₂)) -> (Eq.{max (succ u4) (succ u1)} (ι -> k) (Set.indicator.{u1, u4} ι k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.toSet.{u1} ι s₁) w₁) (Set.indicator.{u1, u4} ι k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.toSet.{u1} ι s₂) w₂)))
 Case conversion may be inaccurate. Consider using '#align affine_independent.indicator_eq_of_affine_combination_eq AffineIndependent.indicator_eq_of_affineCombination_eqₓ'. -/
 theorem AffineIndependent.indicator_eq_of_affineCombination_eq {p : ι → P}
     (ha : AffineIndependent k p) (s₁ s₂ : Finset ι) (w₁ w₂ : ι → k) (hw₁ : (∑ i in s₁, w₁ i) = 1)
@@ -691,7 +691,7 @@ theorem affineIndependent_iff {ι} {p : ι → V} :
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u4} ι}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k 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+  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k 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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u1 u4, u3} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u1, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2389 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u4, u3, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (Set.{u2} P) (Set.instInsertSet.{u2} P) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w₁) (Singleton.singleton.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (Set.{u2} P) (Set.instSingletonSet.{u2} P) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w₂))))) (Exists.{succ u4} k (fun (r : k) => forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u4} k (w i) (HMul.hMul.{u4, u4, u4} k k k (instHMul.{u4} k (NonUnitalNonAssocRing.toMul.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) r (HSub.hSub.{u4, u4, u4} k k k (instHSub.{u4} k (Ring.toSub.{u4} k _inst_1)) (w₁ i) (w₂ i))))))))
 Case conversion may be inaccurate. Consider using '#align weighted_vsub_mem_vector_span_pair weightedVSub_mem_vectorSpan_pairₓ'. -/
 /-- Given an affinely independent family of points, a weighted subtraction lies in the
 `vector_span` of two points given as affine combinations if and only if it is a weighted
@@ -727,7 +727,7 @@ theorem weightedVSub_mem_vectorSpan_pair {p : ι → P} (h : AffineIndependent k
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u4} ι}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι 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 but is expected to have type
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(Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w₂))))) (Exists.{succ u4} k (fun (r : k) => forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u4} k (w i) (HAdd.hAdd.{u4, u4, u4} k k k (instHAdd.{u4} k (Distrib.toAdd.{u4} k (NonUnitalNonAssocSemiring.toDistrib.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))))) (HMul.hMul.{u4, u4, u4} k k k (instHMul.{u4} k (NonUnitalNonAssocRing.toMul.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) r (HSub.hSub.{u4, u4, u4} k k k (instHSub.{u4} k (Ring.toSub.{u4} k _inst_1)) (w₂ i) (w₁ i))) (w₁ i)))))))
 Case conversion may be inaccurate. Consider using '#align affine_combination_mem_affine_span_pair affineCombination_mem_affineSpan_pairₓ'. -/
 /-- Given an affinely independent family of points, an affine combination lies in the
 span of two points given as affine combinations if and only if it is an affine combination
@@ -994,7 +994,7 @@ attribute [local instance] LinearOrderedRing.decidableLt
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u4} ι}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) s (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) s (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k 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(fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k 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(LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₁) (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k 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(StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₂))))) -> (forall {i : ι} {j : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) j s) -> (Eq.{succ u1} k (w₁ i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))))))) -> (Eq.{succ u1} k (w₁ j) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))))))) -> (Eq.{1} SignType (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w₂ i)) (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w₂ j))) -> (Eq.{1} SignType (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k 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(PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w i)) (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w j)))))
 but is expected to have type
-  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : LinearOrderedRing.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k 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AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₁) (Singleton.singleton.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (Set.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (Set.instSingletonSet.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) 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(LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₂))))) -> (forall {i : ι} {j : ι}, (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) j s) -> (Eq.{succ u4} k (w₁ i) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1)))))))) -> (Eq.{succ u4} k (w₁ j) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1)))))))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w₂ i)) (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w₂ j))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w i)) (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w j)))))
+  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : LinearOrderedRing.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) -> (Membership.mem.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (AffineSubspace.instSetLikeAffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k 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AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₁) (Singleton.singleton.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (Set.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (Set.instSingletonSet.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₂))))) -> (forall {i : ι} {j : ι}, (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) j s) -> (Eq.{succ u4} k (w₁ i) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1)))))))) -> (Eq.{succ u4} k (w₁ j) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1)))))))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w₂ i)) (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w₂ j))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w i)) (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w j)))))
 Case conversion may be inaccurate. Consider using '#align sign_eq_of_affine_combination_mem_affine_span_pair sign_eq_of_affineCombination_mem_affineSpan_pairₓ'. -/
 /-- Given an affinely independent family of points, suppose that an affine combination lies in
 the span of two points given as affine combinations, and suppose that, for two indices, the
@@ -1020,7 +1020,7 @@ theorem sign_eq_of_affineCombination_mem_affineSpan_pair {p : ι → P} (h : Aff
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {s : Finset.{u4} ι}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (forall {i₁ : ι} {i₂ : ι} {i₃ : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i₁ s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i₂ s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i₃ s) -> (Ne.{succ u4} ι i₁ i₂) -> (Ne.{succ u4} ι i₁ i₃) -> (Ne.{succ u4} ι i₂ i₃) -> (forall {c : k}, (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) c) -> (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) c (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4)) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) (p i₁) (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} k k k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} k k k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) => k -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} k k k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 (p i₂) (p i₃)) c))))) -> (Eq.{1} SignType (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w i₂)) (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w i₃))))))
 but is expected to have type
-  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : LinearOrderedRing.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) -> (forall {i₁ : ι} {i₂ : ι} {i₃ : ι}, (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i₁ s) -> (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i₂ s) -> (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i₃ s) -> (Ne.{succ u1} ι i₁ i₂) -> (Ne.{succ u1} ι i₁ i₃) -> (Ne.{succ u1} ι i₂ i₃) -> (forall {c : k}, (LT.lt.{u4} k (Preorder.toLT.{u4} k (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) c) -> (LT.lt.{u4} k (Preorder.toLT.{u4} k (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) c (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) -> (Membership.mem.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => 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+  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : LinearOrderedRing.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : 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(a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) _x) (AffineMap.funLike.{u4, u4, u4, u3, u2} k k k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u4, u3, u2} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 (p i₂) (p i₃)) c))))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w i₂)) (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w i₃))))))
 Case conversion may be inaccurate. Consider using '#align sign_eq_of_affine_combination_mem_affine_span_single_line_map sign_eq_of_affineCombination_mem_affineSpan_single_lineMapₓ'. -/
 /-- Given an affinely independent family of points, suppose that an affine combination lies in
 the span of one point of that family and a combination of another two points of that family given

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ad820c4997738e2f542f8a20f32911f52020e26

@@ -994,7 +994,7 @@ attribute [local instance] LinearOrderedRing.decidableLt
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u4} ι}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) s (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k 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(fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k 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(LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₁) (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k 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(StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₂))))) -> (forall {i : ι} {j : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) j s) -> (Eq.{succ u1} k (w₁ i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))))))) -> (Eq.{succ u1} k (w₁ j) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))))))) -> (Eq.{1} SignType (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w₂ i)) (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w₂ j))) -> (Eq.{1} SignType (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k 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(PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w i)) (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w j)))))
 but is expected to have type
-  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : LinearOrderedRing.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k 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AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₁) (Singleton.singleton.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (Set.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (Set.instSingletonSet.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₂))))) -> (forall {i : ι} {j : ι}, (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) j s) -> (Eq.{succ u4} k (w₁ i) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1)))))))) -> (Eq.{succ u4} k (w₁ j) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1)))))))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w₂ i)) (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w₂ j))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w i)) (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w j)))))
+  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : LinearOrderedRing.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) -> (Membership.mem.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (AffineSubspace.instSetLikeAffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k 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AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₁) (Singleton.singleton.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (Set.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (Set.instSingletonSet.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₂))))) -> (forall {i : ι} {j : ι}, (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) j s) -> (Eq.{succ u4} k (w₁ i) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1)))))))) -> (Eq.{succ u4} k (w₁ j) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1)))))))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w₂ i)) (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w₂ j))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w i)) (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w j)))))
 Case conversion may be inaccurate. Consider using '#align sign_eq_of_affine_combination_mem_affine_span_pair sign_eq_of_affineCombination_mem_affineSpan_pairₓ'. -/
 /-- Given an affinely independent family of points, suppose that an affine combination lies in
 the span of two points given as affine combinations, and suppose that, for two indices, the
@@ -1020,7 +1020,7 @@ theorem sign_eq_of_affineCombination_mem_affineSpan_pair {p : ι → P} (h : Aff
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {s : Finset.{u4} ι}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (forall {i₁ : ι} {i₂ : ι} {i₃ : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i₁ s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i₂ s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i₃ s) -> (Ne.{succ u4} ι i₁ i₂) -> (Ne.{succ u4} ι i₁ i₃) -> (Ne.{succ u4} ι i₂ i₃) -> (forall {c : k}, (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) c) -> (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) c (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4)) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) (p i₁) (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} k k k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} k k k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) => k -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} k k k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 (p i₂) (p i₃)) c))))) -> (Eq.{1} SignType (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w i₂)) (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w i₃))))))
 but is expected to have type
-  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : LinearOrderedRing.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) -> (forall {i₁ : ι} {i₂ : ι} {i₃ : ι}, (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i₁ s) -> (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i₂ s) -> (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i₃ s) -> (Ne.{succ u1} ι i₁ i₂) -> (Ne.{succ u1} ι i₁ i₃) -> (Ne.{succ u1} ι i₂ i₃) -> (forall {c : k}, (LT.lt.{u4} k (Preorder.toLT.{u4} k (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) c) -> (LT.lt.{u4} k (Preorder.toLT.{u4} k (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) c (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) -> (Membership.mem.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => 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+  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : LinearOrderedRing.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : 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(LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 (Insert.insert.{u2, u2} P (Set.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c)) (Set.instInsertSet.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c)) (p i₁) (Singleton.singleton.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c) (Set.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c)) (Set.instSingletonSet.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c)) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), succ u4, succ u2} (AffineMap.{u4, u4, u4, u3, u2} k k k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))) _inst_2 _inst_3 _inst_4) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) _x) (AffineMap.funLike.{u4, u4, u4, u3, u2} k k k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u4, u3, u2} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 (p i₂) (p i₃)) c))))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w i₂)) (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLT.{u4} k _inst_1 a b)) (w i₃))))))
 Case conversion may be inaccurate. Consider using '#align sign_eq_of_affine_combination_mem_affine_span_single_line_map sign_eq_of_affineCombination_mem_affineSpan_single_lineMapₓ'. -/
 /-- Given an affinely independent family of points, suppose that an affine combination lies in
 the span of one point of that family and a combination of another two points of that family given

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

@@ -69,7 +69,7 @@ def AffineIndependent (p : ι → P) : Prop :=
 lean 3 declaration is
   forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (p : ι -> P), Iff (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (s : Finset.{u4} ι) (w : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))))))))
 but is expected to have type
-  forall (k : Type.{u4}) {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} (p : ι -> P), Iff (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (s : Finset.{u1} ι) (w : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u4), max (succ u1) (succ u4), succ u3} (LinearMap.{u4, u4, max u4 u1, u3} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u1 u4, u3} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u1, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (OfNat.ofNat.{u3} V 0 (Zero.toOfNat0.{u3} V (NegZeroClass.toZero.{u3} V (SubNegZeroMonoid.toNegZeroClass.{u3} V (SubtractionMonoid.toSubNegZeroMonoid.{u3} V (SubtractionCommMonoid.toSubtractionMonoid.{u3} V (AddCommGroup.toDivisionAddCommMonoid.{u3} V _inst_2)))))))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u4} k (w i) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))))))))
+  forall (k : Type.{u4}) {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} (p : ι -> P), Iff (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (s : Finset.{u1} ι) (w : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u4), max (succ u1) (succ u4), succ u3} (LinearMap.{u4, u4, max u4 u1, u3} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u1 u4, u3} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u1, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (OfNat.ofNat.{u3} V 0 (Zero.toOfNat0.{u3} V (NegZeroClass.toZero.{u3} V (SubNegZeroMonoid.toNegZeroClass.{u3} V (SubtractionMonoid.toSubNegZeroMonoid.{u3} V (SubtractionCommMonoid.toSubtractionMonoid.{u3} V (AddCommGroup.toDivisionAddCommMonoid.{u3} V _inst_2)))))))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u4} k (w i) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))))))))
 Case conversion may be inaccurate. Consider using '#align affine_independent_def affineIndependent_defₓ'. -/
 /-- The definition of `affine_independent`. -/
 theorem affineIndependent_def (p : ι → P) :
@@ -94,7 +94,7 @@ theorem affineIndependent_of_subsingleton [Subsingleton ι] (p : ι → P) : Aff
 lean 3 declaration is
   forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (forall (i : ι), Eq.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))))
 but is expected to have type
-  forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w : ι -> k), (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w) (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (forall (i : ι), Eq.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))))
+  forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w : ι -> k), (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w) (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (forall (i : ι), Eq.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align affine_independent_iff_of_fintype affineIndependent_iff_of_fintypeₓ'. -/
 /-- A family indexed by a `fintype` is affinely independent if and
 only if no nontrivial weighted subtractions over `finset.univ` (where
@@ -234,7 +234,7 @@ theorem linearIndependent_set_iff_affineIndependent_vadd_union_singleton {s : Se
 lean 3 declaration is
   forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (p : ι -> P), Iff (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (s1 : Finset.{u4} ι) (s2 : Finset.{u4} ι) (w1 : ι -> k) (w2 : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s1 (fun (i : ι) => w1 i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s2 (fun (i : ι) => w2 i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k 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 but is expected to have type
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(NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s1 p) w1) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s2 p) w2)) -> (Eq.{max (succ u4) (succ u1)} (ι -> k) (Set.indicator.{u1, u4} ι k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.toSet.{u1} ι s1) w1) (Set.indicator.{u1, u4} ι k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.toSet.{u1} ι s2) w2)))
 Case conversion may be inaccurate. Consider using '#align affine_independent_iff_indicator_eq_of_affine_combination_eq affineIndependent_iff_indicator_eq_of_affineCombination_eqₓ'. -/
 /-- A family is affinely independent if and only if any affine
 combinations (with sum of weights 1) that evaluate to the same point
@@ -285,7 +285,7 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
 lean 3 declaration is
   forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w1 : ι -> k) (w2 : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w1 i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w2 i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => 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(Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w1) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w2)) -> (Eq.{max (succ u4) (succ u1)} (ι -> k) w1 w2))
 but is expected to have type
-  forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w1 : ι -> k) (w2 : ι -> k), (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w1 i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) -> (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k 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(Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w2)) -> (Eq.{max (succ u3) (succ u4)} (ι -> k) w1 w2))
+  forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w1 : ι -> k) (w2 : ι -> k), (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w1 i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) -> (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w2 i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_1))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w1) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u2)) (succ u1), succ (max u3 u4), succ u1} (AffineMap.{u3, max u3 u4, max u3 u4, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k 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AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w1) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u2)) (succ u1), succ (max u3 u4), succ u1} (AffineMap.{u3, max u3 u4, max u3 u4, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k 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AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w2)) -> (Eq.{max (succ u3) (succ u4)} (ι -> k) w1 w2))
 Case conversion may be inaccurate. Consider using '#align affine_independent_iff_eq_of_fintype_affine_combination_eq affineIndependent_iff_eq_of_fintype_affineCombination_eqₓ'. -/
 /-- A finite family is affinely independent if and only if any affine
 combinations (with sum of weights 1) that evaluate to the same point are equal. -/
@@ -335,7 +335,7 @@ theorem AffineIndependent.units_lineMap {p : ι → P} (hp : AffineIndependent k
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall (s₁ : Finset.{u4} ι) (s₂ : Finset.{u4} ι) (w₁ : ι -> k) (w₂ : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s₁ (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s₂ (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k 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(NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s₁ p) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => 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_inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s₂ p) w₂)) -> (Eq.{max (succ u4) (succ u1)} (ι -> k) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₁) w₁) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₂) w₂)))
 but is expected to have type
-  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall (s₁ : Finset.{u1} ι) (s₂ : Finset.{u1} ι) (w₁ : ι -> k) (w₂ : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s₁ (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s₂ (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s₁ p) w₁) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s₂ p) w₂)) -> (Eq.{max (succ u4) (succ u1)} (ι -> k) (Set.indicator.{u1, u4} ι k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.toSet.{u1} ι s₁) w₁) (Set.indicator.{u1, u4} ι k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.toSet.{u1} ι s₂) w₂)))
+  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall (s₁ : Finset.{u1} ι) (s₂ : Finset.{u1} ι) (w₁ : ι -> k) (w₂ : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s₁ (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s₂ (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (Ring.toSemiring.{u4} k _inst_1))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s₁ p) w₁) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s₂ p) w₂)) -> (Eq.{max (succ u4) (succ u1)} (ι -> k) (Set.indicator.{u1, u4} ι k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.toSet.{u1} ι s₁) w₁) (Set.indicator.{u1, u4} ι k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.toSet.{u1} ι s₂) w₂)))
 Case conversion may be inaccurate. Consider using '#align affine_independent.indicator_eq_of_affine_combination_eq AffineIndependent.indicator_eq_of_affineCombination_eqₓ'. -/
 theorem AffineIndependent.indicator_eq_of_affineCombination_eq {p : ι → P}
     (ha : AffineIndependent k p) (s₁ s₂ : Finset ι) (w₁ w₂ : ι → k) (hw₁ : (∑ i in s₁, w₁ i) = 1)
@@ -691,7 +691,7 @@ theorem affineIndependent_iff {ι} {p : ι → V} :
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u4} ι}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k 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 but is expected to have type
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(Ring.toNonAssocRing.{u4} k _inst_1)))) r (HSub.hSub.{u4, u4, u4} k k k (instHSub.{u4} k (Ring.toSub.{u4} k _inst_1)) (w₁ i) (w₂ i))))))))
+  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k 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V (Submodule.setLike.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3)) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u4), max (succ u1) (succ u4), succ u3} (LinearMap.{u4, u4, max u4 u1, u3} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u1 u4, u3} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u1, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u4, u3, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (Set.{u2} P) (Set.instInsertSet.{u2} P) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w₁) (Singleton.singleton.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (Set.{u2} P) (Set.instSingletonSet.{u2} P) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w₂))))) (Exists.{succ u4} k (fun (r : k) => forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u4} k (w i) (HMul.hMul.{u4, u4, u4} k k k (instHMul.{u4} k (NonUnitalNonAssocRing.toMul.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) r (HSub.hSub.{u4, u4, u4} k k k (instHSub.{u4} k (Ring.toSub.{u4} k _inst_1)) (w₁ i) (w₂ i))))))))
 Case conversion may be inaccurate. Consider using '#align weighted_vsub_mem_vector_span_pair weightedVSub_mem_vectorSpan_pairₓ'. -/
 /-- Given an affinely independent family of points, a weighted subtraction lies in the
 `vector_span` of two points given as affine combinations if and only if it is a weighted
@@ -727,7 +727,7 @@ theorem weightedVSub_mem_vectorSpan_pair {p : ι → P} (h : AffineIndependent k
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u4} ι}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι 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 but is expected to have type
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(Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w₂))))) (Exists.{succ u4} k (fun (r : k) => forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u4} k (w i) (HAdd.hAdd.{u4, u4, u4} k k k (instHAdd.{u4} k (Distrib.toAdd.{u4} k (NonUnitalNonAssocSemiring.toDistrib.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))))) (HMul.hMul.{u4, u4, u4} k k k (instHMul.{u4} k (NonUnitalNonAssocRing.toMul.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) r (HSub.hSub.{u4, u4, u4} k k k (instHSub.{u4} k (Ring.toSub.{u4} k _inst_1)) (w₂ i) (w₁ i))) (w₁ i)))))))
 Case conversion may be inaccurate. Consider using '#align affine_combination_mem_affine_span_pair affineCombination_mem_affineSpan_pairₓ'. -/
 /-- Given an affinely independent family of points, an affine combination lies in the
 span of two points given as affine combinations if and only if it is an affine combination
@@ -994,7 +994,7 @@ attribute [local instance] LinearOrderedRing.decidableLt
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u4} ι}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) s (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) s (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k 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(fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k 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(LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₁) (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k 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(StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₂))))) -> (forall {i : ι} {j : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) j s) -> (Eq.{succ u1} k (w₁ i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))))))) -> (Eq.{succ u1} k (w₁ j) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))))))) -> (Eq.{1} SignType (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w₂ i)) (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w₂ j))) -> (Eq.{1} SignType (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k 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(PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w i)) (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w j)))))
 but is expected to have type
-  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : LinearOrderedRing.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k 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(fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 (Insert.insert.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (Set.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (Set.instInsertSet.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₁) (Singleton.singleton.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (Set.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (Set.instSingletonSet.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₂))))) -> (forall {i : ι} {j : ι}, (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) j s) -> (Eq.{succ u4} k (w₁ i) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1)))))))) -> (Eq.{succ u4} k (w₁ j) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1)))))))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w₂ i)) (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w₂ j))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w i)) (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w j)))))
+  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : LinearOrderedRing.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (Semiring.toOne.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k 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_inst_1)) _inst_2 _inst_3 _inst_4) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (AffineSubspace.instSetLikeAffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k 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AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₁) (Singleton.singleton.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (Set.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (Set.instSingletonSet.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) 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(LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₂))))) -> (forall {i : ι} {j : ι}, (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) j s) -> (Eq.{succ u4} k (w₁ i) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1)))))))) -> (Eq.{succ u4} k (w₁ j) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1)))))))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w₂ i)) (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w₂ j))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w i)) (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w j)))))
 Case conversion may be inaccurate. Consider using '#align sign_eq_of_affine_combination_mem_affine_span_pair sign_eq_of_affineCombination_mem_affineSpan_pairₓ'. -/
 /-- Given an affinely independent family of points, suppose that an affine combination lies in
 the span of two points given as affine combinations, and suppose that, for two indices, the
@@ -1020,7 +1020,7 @@ theorem sign_eq_of_affineCombination_mem_affineSpan_pair {p : ι → P} (h : Aff
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {s : Finset.{u4} ι}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (forall {i₁ : ι} {i₂ : ι} {i₃ : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i₁ s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i₂ s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i₃ s) -> (Ne.{succ u4} ι i₁ i₂) -> (Ne.{succ u4} ι i₁ i₃) -> (Ne.{succ u4} ι i₂ i₃) -> (forall {c : k}, (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) c) -> (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) c (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4)) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) (p i₁) (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} k k k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} k k k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) => k -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} k k k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 (p i₂) (p i₃)) c))))) -> (Eq.{1} SignType (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w i₂)) (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w i₃))))))
 but is expected to have type
-  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : LinearOrderedRing.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))))) -> (forall {i₁ : ι} {i₂ : ι} {i₃ : ι}, (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i₁ s) -> (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i₂ s) -> (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i₃ s) -> (Ne.{succ u1} ι i₁ i₂) -> (Ne.{succ u1} ι i₁ i₃) -> (Ne.{succ u1} ι i₂ i₃) -> (forall {c : k}, (LT.lt.{u4} k (Preorder.toLT.{u4} k (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) c) -> (LT.lt.{u4} k (Preorder.toLT.{u4} k (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) c (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))))) -> (Membership.mem.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k 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(LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 (Insert.insert.{u2, u2} P (Set.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c)) (Set.instInsertSet.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c)) (p i₁) (Singleton.singleton.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c) (Set.{u2} ((fun 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(a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) _x) (AffineMap.funLike.{u4, u4, u4, u3, u2} k k k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u4, u3, u2} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 (p i₂) (p i₃)) c))))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w i₂)) (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w i₃))))))
 Case conversion may be inaccurate. Consider using '#align sign_eq_of_affine_combination_mem_affine_span_single_line_map sign_eq_of_affineCombination_mem_affineSpan_single_lineMapₓ'. -/
 /-- Given an affinely independent family of points, suppose that an affine combination lies in
 the span of one point of that family and a combination of another two points of that family given

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

@@ -69,7 +69,7 @@ def AffineIndependent (p : ι → P) : Prop :=
 lean 3 declaration is
   forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (p : ι -> P), Iff (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (s : Finset.{u4} ι) (w : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Eq.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))))))))))
 but is expected to have type
-  forall (k : Type.{u4}) {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} (p : ι -> P), Iff (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (s : Finset.{u1} ι) (w : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u4), max (succ u1) (succ u4), succ u3} (LinearMap.{u4, u4, max u4 u1, u3} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u1 u4, u3} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u1, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (OfNat.ofNat.{u3} V 0 (Zero.toOfNat0.{u3} V (NegZeroClass.toZero.{u3} V (SubNegZeroMonoid.toNegZeroClass.{u3} V (SubtractionMonoid.toSubNegZeroMonoid.{u3} V (SubtractionCommMonoid.toSubtractionMonoid.{u3} V (AddCommGroup.toDivisionAddCommMonoid.{u3} V _inst_2)))))))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u4} k (w i) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))))))))
+  forall (k : Type.{u4}) {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} (p : ι -> P), Iff (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (s : Finset.{u1} ι) (w : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u4), max (succ u1) (succ u4), succ u3} (LinearMap.{u4, u4, max u4 u1, u3} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u1 u4, u3} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u1, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (OfNat.ofNat.{u3} V 0 (Zero.toOfNat0.{u3} V (NegZeroClass.toZero.{u3} V (SubNegZeroMonoid.toNegZeroClass.{u3} V (SubtractionMonoid.toSubNegZeroMonoid.{u3} V (SubtractionCommMonoid.toSubtractionMonoid.{u3} V (AddCommGroup.toDivisionAddCommMonoid.{u3} V _inst_2)))))))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u4} k (w i) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))))))))
 Case conversion may be inaccurate. Consider using '#align affine_independent_def affineIndependent_defₓ'. -/
 /-- The definition of `affine_independent`. -/
 theorem affineIndependent_def (p : ι → P) :
@@ -94,7 +94,7 @@ theorem affineIndependent_of_subsingleton [Subsingleton ι] (p : ι → P) : Aff
 lean 3 declaration is
   forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))) -> (Eq.{succ u2} V (coeFn.{max (succ (max u4 u1)) (succ u2), max (succ (max u4 u1)) (succ u2)} (LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u4 u1, u2} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3) => (ι -> k) -> V) (LinearMap.hasCoeToFun.{u1, u1, max u4 u1, u2} k k (ι -> k) V (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (Pi.addCommMonoid.{u4, u1} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.Function.module.{u4, u1, u1} ι k k (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) _inst_3 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (Finset.weightedVSub.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w) (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (forall (i : ι), Eq.{succ u1} k (w i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))))))))
 but is expected to have type
-  forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w : ι -> k), (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2400 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w) (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (forall (i : ι), Eq.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))))
+  forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w : ι -> k), (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w i)) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) w) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), max (succ u4) (succ u3), succ u2} (LinearMap.{u3, u3, max u3 u4, u2} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u4 u3, u2} k k (ι -> k) V (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (Pi.addCommMonoid.{u4, u3} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) _inst_3 (RingHom.id.{u3} k (NonAssocRing.toNonAssocSemiring.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.weightedVSub.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w) (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (forall (i : ι), Eq.{succ u3} k (w i) (OfNat.ofNat.{u3} k 0 (Zero.toOfNat0.{u3} k (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align affine_independent_iff_of_fintype affineIndependent_iff_of_fintypeₓ'. -/
 /-- A family indexed by a `fintype` is affinely independent if and
 only if no nontrivial weighted subtractions over `finset.univ` (where
@@ -234,7 +234,7 @@ theorem linearIndependent_set_iff_affineIndependent_vadd_union_singleton {s : Se
 lean 3 declaration is
   forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (p : ι -> P), Iff (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (s1 : Finset.{u4} ι) (s2 : Finset.{u4} ι) (w1 : ι -> k) (w2 : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s1 (fun (i : ι) => w1 i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s2 (fun (i : ι) => w2 i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k 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 but is expected to have type
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(NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s1 p) w1) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s2 p) w2)) -> (Eq.{max (succ u4) (succ u1)} (ι -> k) (Set.indicator.{u1, u4} ι k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.toSet.{u1} ι s1) w1) (Set.indicator.{u1, u4} ι k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.toSet.{u1} ι s2) w2)))
 Case conversion may be inaccurate. Consider using '#align affine_independent_iff_indicator_eq_of_affine_combination_eq affineIndependent_iff_indicator_eq_of_affineCombination_eqₓ'. -/
 /-- A family is affinely independent if and only if any affine
 combinations (with sum of weights 1) that evaluate to the same point
@@ -285,7 +285,7 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
 lean 3 declaration is
   forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w1 : ι -> k) (w2 : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w1 i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w2 i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => 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(Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w1) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w2)) -> (Eq.{max (succ u4) (succ u1)} (ι -> k) w1 w2))
 but is expected to have type
-  forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w1 : ι -> k) (w2 : ι -> k), (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w1 i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) -> (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k 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(Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w2)) -> (Eq.{max (succ u3) (succ u4)} (ι -> k) w1 w2))
+  forall (k : Type.{u3}) {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Fintype.{u4} ι] (p : ι -> P), Iff (AffineIndependent.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) (forall (w1 : ι -> k) (w2 : ι -> k), (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w1 i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) -> (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => w2 i)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1))))) -> (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w1) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u2)) (succ u1), succ (max u3 u4), succ u1} (AffineMap.{u3, max u3 u4, max u3 u4, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u3 u4, max u3 u4, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w1) (FunLike.coe.{max (max (succ (max u3 u4)) (succ u2)) (succ u1), succ (max u3 u4), succ u1} (AffineMap.{u3, max u3 u4, max u3 u4, u2, u1} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_1)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k 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AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι (Finset.univ.{u4} ι _inst_5) p) w2)) -> (Eq.{max (succ u3) (succ u4)} (ι -> k) w1 w2))
 Case conversion may be inaccurate. Consider using '#align affine_independent_iff_eq_of_fintype_affine_combination_eq affineIndependent_iff_eq_of_fintype_affineCombination_eqₓ'. -/
 /-- A finite family is affinely independent if and only if any affine
 combinations (with sum of weights 1) that evaluate to the same point are equal. -/
@@ -335,7 +335,7 @@ theorem AffineIndependent.units_lineMap {p : ι → P} (hp : AffineIndependent k
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall (s₁ : Finset.{u4} ι) (s₂ : Finset.{u4} ι) (w₁ : ι -> k) (w₂ : ι -> k), (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s₁ (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s₂ (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u3} P (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k 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(NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s₁ p) w₁) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => 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_inst_1 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_1) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s₂ p) w₂)) -> (Eq.{max (succ u4) (succ u1)} (ι -> k) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₁) w₁) (Set.indicator.{u4, u1} ι k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Finset.{u4} ι) (Set.{u4} ι) (HasLiftT.mk.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (CoeTCₓ.coe.{succ u4, succ u4} (Finset.{u4} ι) (Set.{u4} ι) (Finset.Set.hasCoeT.{u4} ι))) s₂) w₂)))
 but is expected to have type
-  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall (s₁ : Finset.{u1} ι) (s₂ : Finset.{u1} ι) (w₁ : ι -> k) (w₂ : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s₁ (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s₂ (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s₁ p) w₁) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s₂ p) w₂)) -> (Eq.{max (succ u4) (succ u1)} (ι -> k) (Set.indicator.{u1, u4} ι k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.toSet.{u1} ι s₁) w₁) (Set.indicator.{u1, u4} ι k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.toSet.{u1} ι s₂) w₂)))
+  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall (s₁ : Finset.{u1} ι) (s₂ : Finset.{u1} ι) (w₁ : ι -> k) (w₂ : ι -> k), (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s₁ (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s₂ (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) -> (Eq.{succ u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s₁ p) w₁) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s₂ p) w₂)) -> (Eq.{max (succ u4) (succ u1)} (ι -> k) (Set.indicator.{u1, u4} ι k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.toSet.{u1} ι s₁) w₁) (Set.indicator.{u1, u4} ι k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1))) (Finset.toSet.{u1} ι s₂) w₂)))
 Case conversion may be inaccurate. Consider using '#align affine_independent.indicator_eq_of_affine_combination_eq AffineIndependent.indicator_eq_of_affineCombination_eqₓ'. -/
 theorem AffineIndependent.indicator_eq_of_affineCombination_eq {p : ι → P}
     (ha : AffineIndependent k p) (s₁ s₂ : Finset ι) (w₁ w₂ : ι → k) (hw₁ : (∑ i in s₁, w₁ i) = 1)
@@ -691,7 +691,7 @@ theorem affineIndependent_iff {ι} {p : ι → V} :
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u4} ι}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k 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 but is expected to have type
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+  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k 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_inst_2) _inst_3) V (Submodule.setLike.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3)) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u4), max (succ u1) (succ u4), succ u3} (LinearMap.{u4, u4, max u4 u1, u3} k k (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))) (ι -> k) V (Pi.addCommMonoid.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => V) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max u1 u4, u3} k k (ι -> k) V (Ring.toSemiring.{u4} k _inst_1) (Ring.toSemiring.{u4} k _inst_1) (Pi.addCommMonoid.{u1, u4} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.2390 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) _inst_3 (RingHom.id.{u4} k (NonAssocRing.toNonAssocSemiring.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (Finset.weightedVSub.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w) (vectorSpan.{u4, u3, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (Set.{u2} P) (Set.instInsertSet.{u2} P) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w₁) (Singleton.singleton.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (Set.{u2} P) (Set.instSingletonSet.{u2} P) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w₂))))) (Exists.{succ u4} k (fun (r : k) => forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u4} k (w i) (HMul.hMul.{u4, u4, u4} k k k (instHMul.{u4} k (NonUnitalNonAssocRing.toMul.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) r (HSub.hSub.{u4, u4, u4} k k k (instHSub.{u4} k (Ring.toSub.{u4} k _inst_1)) (w₁ i) (w₂ i))))))))
 Case conversion may be inaccurate. Consider using '#align weighted_vsub_mem_vector_span_pair weightedVSub_mem_vectorSpan_pairₓ'. -/
 /-- Given an affinely independent family of points, a weighted subtraction lies in the
 `vector_span` of two points given as affine combinations if and only if it is a weighted
@@ -727,7 +727,7 @@ theorem weightedVSub_mem_vectorSpan_pair {p : ι → P} (h : AffineIndependent k
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u4} ι}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι 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 but is expected to have type
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(a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P _inst_1 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_1)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_1)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_1 ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι s p) w₂))))) (Exists.{succ u4} k (fun (r : k) => forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Eq.{succ u4} k (w i) (HAdd.hAdd.{u4, u4, u4} k k k (instHAdd.{u4} k (Distrib.toAdd.{u4} k (NonUnitalNonAssocSemiring.toDistrib.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))))) (HMul.hMul.{u4, u4, u4} k k k (instHMul.{u4} k (NonUnitalNonAssocRing.toMul.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) r (HSub.hSub.{u4, u4, u4} k k k (instHSub.{u4} k (Ring.toSub.{u4} k _inst_1)) (w₂ i) (w₁ i))) (w₁ i)))))))
 Case conversion may be inaccurate. Consider using '#align affine_combination_mem_affine_span_pair affineCombination_mem_affineSpan_pairₓ'. -/
 /-- Given an affinely independent family of points, an affine combination lies in the
 span of two points given as affine combinations if and only if it is an affine combination
@@ -994,7 +994,7 @@ attribute [local instance] LinearOrderedRing.decidableLt
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u4} ι}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 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(LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₁) (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k 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(StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₂))))) -> (forall {i : ι} {j : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) j s) -> (Eq.{succ u1} k (w₁ i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))))))) -> (Eq.{succ u1} k (w₁ j) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))))))) -> (Eq.{1} SignType (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w₂ i)) (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w₂ j))) -> (Eq.{1} SignType (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k 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(PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w i)) (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w j)))))
 but is expected to have type
-  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : LinearOrderedRing.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k 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(fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 (Insert.insert.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (Set.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (Set.instInsertSet.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₁) (Singleton.singleton.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (Set.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (Set.instSingletonSet.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₂))))) -> (forall {i : ι} {j : ι}, (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) j s) -> (Eq.{succ u4} k (w₁ i) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1)))))))) -> (Eq.{succ u4} k (w₁ j) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1)))))))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w₂ i)) (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w₂ j))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w i)) (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w j)))))
+  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : LinearOrderedRing.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))))) -> (Membership.mem.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => 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(fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 (Insert.insert.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₁) (Set.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (Set.instInsertSet.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) 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(Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₁) (Singleton.singleton.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (Set.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (Set.instSingletonSet.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₂))))) -> (forall {i : ι} {j : ι}, (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) j s) -> (Eq.{succ u4} k (w₁ i) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1)))))))) -> (Eq.{succ u4} k (w₁ j) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1)))))))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w₂ i)) (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w₂ j))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) 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(LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w j)))))
 Case conversion may be inaccurate. Consider using '#align sign_eq_of_affine_combination_mem_affine_span_pair sign_eq_of_affineCombination_mem_affineSpan_pairₓ'. -/
 /-- Given an affinely independent family of points, suppose that an affine combination lies in
 the span of two points given as affine combinations, and suppose that, for two indices, the
@@ -1020,7 +1020,7 @@ theorem sign_eq_of_affineCombination_mem_affineSpan_pair {p : ι → P} (h : Aff
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {s : Finset.{u4} ι}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (forall {i₁ : ι} {i₂ : ι} {i₃ : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i₁ s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i₂ s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i₃ s) -> (Ne.{succ u4} ι i₁ i₂) -> (Ne.{succ u4} ι i₁ i₃) -> (Ne.{succ u4} ι i₂ i₃) -> (forall {c : k}, (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) c) -> (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) c (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4)) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) (p i₁) (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} k k k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} k k k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) => k -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} k k k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 (p i₂) (p i₃)) c))))) -> (Eq.{1} SignType (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w i₂)) (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w i₃))))))
 but is expected to have type
-  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : LinearOrderedRing.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))))) -> (forall {i₁ : ι} {i₂ : ι} {i₃ : ι}, (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i₁ s) -> (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i₂ s) -> (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i₃ s) -> (Ne.{succ u1} ι i₁ i₂) -> (Ne.{succ u1} ι i₁ i₃) -> (Ne.{succ u1} ι i₂ i₃) -> (forall {c : k}, (LT.lt.{u4} k (Preorder.toLT.{u4} k (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) c) -> (LT.lt.{u4} k (Preorder.toLT.{u4} k (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) c (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))))) -> (Membership.mem.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k 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(Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) ι) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w) (affineSpan.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 (Insert.insert.{u2, u2} P (Set.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c)) (Set.instInsertSet.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c)) (p i₁) (Singleton.singleton.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c) (Set.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 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u2} k k k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u4, u3, u2} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 (p i₂) (p i₃)) c))))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w i₂)) (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w i₃))))))
 Case conversion may be inaccurate. Consider using '#align sign_eq_of_affine_combination_mem_affine_span_single_line_map sign_eq_of_affineCombination_mem_affineSpan_single_lineMapₓ'. -/
 /-- Given an affinely independent family of points, suppose that an affine combination lies in
 the span of one point of that family and a combination of another two points of that family given

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b8ba04e2f326f3f7cf24ad129beda58531ada61

@@ -1146,7 +1146,7 @@ def face {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ} (h
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {n : Nat} (s : Affine.Simplex.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 n) {fs : Finset.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))} {m : Nat} (h : Eq.{1} Nat (Finset.card.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) fs) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), Eq.{succ u3} P (Affine.Simplex.points.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 m (Affine.Simplex.face.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s fs m h) i) (Affine.Simplex.points.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LinearOrder.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LinearOrder.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LinearOrder.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))))))) (Finset.orderEmbOfFin.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) fs (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) h) i))
 but is expected to have type
-  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {n : Nat} (s : Affine.Simplex.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 n) {fs : Finset.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))} {m : Nat} (h : Eq.{1} Nat (Finset.card.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) fs) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{succ u1} P (Affine.Simplex.points.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 m (Affine.Simplex.face.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s fs m h) i) (Affine.Simplex.points.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 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=> LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instDistribLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))))) (Finset.orderEmbOfFin.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) fs (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) h) i))
 Case conversion may be inaccurate. Consider using '#align affine.simplex.face_points Affine.Simplex.face_pointsₓ'. -/
 /-- The points of a face of a simplex are given by `mono_of_fin`. -/
 theorem face_points {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ}
@@ -1159,7 +1159,7 @@ theorem face_points {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {n : Nat} (s : Affine.Simplex.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 n) {fs : Finset.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))} {m : Nat} (h : Eq.{1} Nat (Finset.card.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) fs) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), Eq.{succ u3} ((Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> P) (Affine.Simplex.points.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 m (Affine.Simplex.face.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s fs m h)) (Function.comp.{1, 1, succ u3} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) P (Affine.Simplex.points.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s) (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LinearOrder.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))))) (fun (_x : RelEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LinearOrder.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))))))) => (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (SemilatticeInf.toPartialOrder.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Lattice.toSemilatticeInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LinearOrder.toLattice.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))))))) (Finset.orderEmbOfFin.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.linearOrder (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) fs (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) m (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) h)))
 but is expected to have type
-  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {n : Nat} (s : Affine.Simplex.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 n) {fs : Finset.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))} {m : Nat} (h : Eq.{1} Nat (Finset.card.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) fs) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{succ u1} ((Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) -> P) (Affine.Simplex.points.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 m (Affine.Simplex.face.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s fs m h)) (Function.comp.{1, 1, succ u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) P (Affine.Simplex.points.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 n s) (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Preorder.toLE.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (PartialOrder.toPreorder.{0} (Fin (HAdd.hAdd.{0, 0, 0} 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1)))))))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))))) (Finset.orderEmbOfFin.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) fs (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) m (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) h)))
 Case conversion may be inaccurate. Consider using '#align affine.simplex.face_points' Affine.Simplex.face_points'ₓ'. -/
 /-- The points of a face of a simplex are given by `mono_of_fin`. -/
 theorem face_points' {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ}

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e281deff072232a3c5b3e90034bd65dde396312

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
 
 ! This file was ported from Lean 3 source module linear_algebra.affine_space.independent
-! leanprover-community/mathlib commit 2de9c37fa71dde2f1c6feff19876dd6a7b1519f0
+! leanprover-community/mathlib commit 4f81bc21e32048db7344b7867946e992cf5f68cc
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,6 +18,9 @@ import Mathbin.LinearAlgebra.Basis
 /-!
 # Affine independence
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines affinely independent families of points.
 
 ## Main definitions

mathlib commit https://github.com/leanprover-community/mathlib/commit/246f6f7989ff86bd07e1b014846f11304f33cf9e

@@ -52,6 +52,7 @@ variable [affine_space V P] {ι : Type _}
 
 include V
 
+#print AffineIndependent /-
 /-- An indexed family is said to be affinely independent if no
 nontrivial weighted subtractions (where the sum of weights is 0) are
 0. -/
@@ -59,7 +60,14 @@ def AffineIndependent (p : ι → P) : Prop :=
   ∀ (s : Finset ι) (w : ι → k),
     (∑ i in s, w i) = 0 → s.weightedVSub p w = (0 : V) → ∀ i ∈ s, w i = 0
 #align affine_independent AffineIndependent
+-/
 
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+Case conversion may be inaccurate. Consider using '#align affine_independent_def affineIndependent_defₓ'. -/
 /-- The definition of `affine_independent`. -/
 theorem affineIndependent_def (p : ι → P) :
     AffineIndependent k p ↔
@@ -68,11 +76,23 @@ theorem affineIndependent_def (p : ι → P) :
   Iff.rfl
 #align affine_independent_def affineIndependent_def
 
+/- warning: affine_independent_of_subsingleton -> affineIndependent_of_subsingleton is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_independent_of_subsingleton affineIndependent_of_subsingletonₓ'. -/
 /-- A family with at most one point is affinely independent. -/
 theorem affineIndependent_of_subsingleton [Subsingleton ι] (p : ι → P) : AffineIndependent k p :=
   fun s w h hs i hi => Fintype.eq_of_subsingleton_of_sum_eq h i hi
 #align affine_independent_of_subsingleton affineIndependent_of_subsingleton
 
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+Case conversion may be inaccurate. Consider using '#align affine_independent_iff_of_fintype affineIndependent_iff_of_fintypeₓ'. -/
 /-- A family indexed by a `fintype` is affinely independent if and
 only if no nontrivial weighted subtractions over `finset.univ` (where
 the sum of the weights is 0) are 0. -/
@@ -89,6 +109,12 @@ theorem affineIndependent_iff_of_fintype [Fintype ι] (p : ι → P) :
     simpa [hi] using h
 #align affine_independent_iff_of_fintype affineIndependent_iff_of_fintype
 
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+Case conversion may be inaccurate. Consider using '#align affine_independent_iff_linear_independent_vsub affineIndependent_iff_linearIndependent_vsubₓ'. -/
 /-- A family is affinely independent if and only if the differences
 from a base point in that family are linearly independent. -/
 theorem affineIndependent_iff_linearIndependent_vsub (p : ι → P) (i1 : ι) :
@@ -146,6 +172,12 @@ theorem affineIndependent_iff_linearIndependent_vsub (p : ι → P) (i1 : ι) :
       exact Finset.eq_zero_of_sum_eq_zero hw h2b i hi
 #align affine_independent_iff_linear_independent_vsub affineIndependent_iff_linearIndependent_vsub
 
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+Case conversion may be inaccurate. Consider using '#align affine_independent_set_iff_linear_independent_vsub affineIndependent_set_iff_linearIndependent_vsubₓ'. -/
 /-- A set is affinely independent if and only if the differences from
 a base point in that set are linearly independent. -/
 theorem affineIndependent_set_iff_linearIndependent_vsub {s : Set P} {p₁ : P} (hp₁ : p₁ ∈ s) :
@@ -171,6 +203,12 @@ theorem affineIndependent_set_iff_linearIndependent_vsub {s : Set P} {p₁ : P}
         Subtype.ext (Subtype.ext (vsub_left_cancel (Subtype.ext_iff.1 hx)))
 #align affine_independent_set_iff_linear_independent_vsub affineIndependent_set_iff_linearIndependent_vsub
 
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+Case conversion may be inaccurate. Consider using '#align linear_independent_set_iff_affine_independent_vadd_union_singleton linearIndependent_set_iff_affineIndependent_vadd_union_singletonₓ'. -/
 /-- A set of nonzero vectors is linearly independent if and only if,
 given a point `p₁`, the vectors added to `p₁` and `p₁` itself are
 affinely independent. -/
@@ -189,6 +227,12 @@ theorem linearIndependent_set_iff_affineIndependent_vadd_union_singleton {s : Se
   rw [h]
 #align linear_independent_set_iff_affine_independent_vadd_union_singleton linearIndependent_set_iff_affineIndependent_vadd_union_singleton
 
+/- warning: affine_independent_iff_indicator_eq_of_affine_combination_eq -> affineIndependent_iff_indicator_eq_of_affineCombination_eq is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align affine_independent_iff_indicator_eq_of_affine_combination_eq affineIndependent_iff_indicator_eq_of_affineCombination_eqₓ'. -/
 /-- A family is affinely independent if and only if any affine
 combinations (with sum of weights 1) that evaluate to the same point
 have equal `set.indicator`. -/
@@ -234,6 +278,12 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
       simpa [w2] using hws
 #align affine_independent_iff_indicator_eq_of_affine_combination_eq affineIndependent_iff_indicator_eq_of_affineCombination_eq
 
+/- warning: affine_independent_iff_eq_of_fintype_affine_combination_eq -> affineIndependent_iff_eq_of_fintype_affineCombination_eq is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_independent_iff_eq_of_fintype_affine_combination_eq affineIndependent_iff_eq_of_fintype_affineCombination_eqₓ'. -/
 /-- A finite family is affinely independent if and only if any affine
 combinations (with sum of weights 1) that evaluate to the same point are equal. -/
 theorem affineIndependent_iff_eq_of_fintype_affineCombination_eq [Fintype ι] (p : ι → P) :
@@ -259,6 +309,12 @@ theorem affineIndependent_iff_eq_of_fintype_affineCombination_eq [Fintype ι] (p
 
 variable {k}
 
+/- warning: affine_independent.units_line_map -> AffineIndependent.units_lineMap is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_independent.units_line_map AffineIndependent.units_lineMapₓ'. -/
 /-- If we single out one member of an affine-independent family of points and affinely transport
 all others along the line joining them to this member, the resulting new family of points is affine-
 independent.
@@ -272,6 +328,12 @@ theorem AffineIndependent.units_lineMap {p : ι → P} (hp : AffineIndependent k
   exact hp.units_smul fun i => w i
 #align affine_independent.units_line_map AffineIndependent.units_lineMap
 
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+Case conversion may be inaccurate. Consider using '#align affine_independent.indicator_eq_of_affine_combination_eq AffineIndependent.indicator_eq_of_affineCombination_eqₓ'. -/
 theorem AffineIndependent.indicator_eq_of_affineCombination_eq {p : ι → P}
     (ha : AffineIndependent k p) (s₁ s₂ : Finset ι) (w₁ w₂ : ι → k) (hw₁ : (∑ i in s₁, w₁ i) = 1)
     (hw₂ : (∑ i in s₂, w₂ i) = 1) (h : s₁.affineCombination k p w₁ = s₂.affineCombination k p w₂) :
@@ -279,6 +341,12 @@ theorem AffineIndependent.indicator_eq_of_affineCombination_eq {p : ι → P}
   (affineIndependent_iff_indicator_eq_of_affineCombination_eq k p).1 ha s₁ s₂ w₁ w₂ hw₁ hw₂ h
 #align affine_independent.indicator_eq_of_affine_combination_eq AffineIndependent.indicator_eq_of_affineCombination_eq
 
+/- warning: affine_independent.injective -> AffineIndependent.injective is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_independent.injective AffineIndependent.injectiveₓ'. -/
 /-- An affinely independent family is injective, if the underlying
 ring is nontrivial. -/
 protected theorem AffineIndependent.injective [Nontrivial k] {p : ι → P}
@@ -290,6 +358,12 @@ protected theorem AffineIndependent.injective [Nontrivial k] {p : ι → P}
   exact ha.ne_zero ⟨i, hij'⟩ (vsub_eq_zero_iff_eq.mpr hij)
 #align affine_independent.injective AffineIndependent.injective
 
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+Case conversion may be inaccurate. Consider using '#align affine_independent.comp_embedding AffineIndependent.comp_embeddingₓ'. -/
 /-- If a family is affinely independent, so is any subfamily given by
 composition of an embedding into index type with the original
 family. -/
@@ -316,6 +390,12 @@ theorem AffineIndependent.comp_embedding {ι2 : Type _} (f : ι2 ↪ ι) {p : ι
     rw [← ha fs' w' hw's hs' (f i0) ((Finset.mem_map' _).2 hi0), hw']
 #align affine_independent.comp_embedding AffineIndependent.comp_embedding
 
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+Case conversion may be inaccurate. Consider using '#align affine_independent.subtype AffineIndependent.subtypeₓ'. -/
 /-- If a family is affinely independent, so is any subfamily indexed
 by a subtype of the index type. -/
 protected theorem AffineIndependent.subtype {p : ι → P} (ha : AffineIndependent k p) (s : Set ι) :
@@ -323,6 +403,12 @@ protected theorem AffineIndependent.subtype {p : ι → P} (ha : AffineIndepende
   ha.comp_embedding (Embedding.subtype _)
 #align affine_independent.subtype AffineIndependent.subtype
 
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+Case conversion may be inaccurate. Consider using '#align affine_independent.range AffineIndependent.rangeₓ'. -/
 /-- If an indexed family of points is affinely independent, so is the
 corresponding set of points. -/
 protected theorem AffineIndependent.range {p : ι → P} (ha : AffineIndependent k p) :
@@ -336,6 +422,12 @@ protected theorem AffineIndependent.range {p : ι → P} (ha : AffineIndependent
   simp [hf]
 #align affine_independent.range AffineIndependent.range
 
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 theorem affineIndependent_equiv {ι' : Type _} (e : ι ≃ ι') {p : ι' → P} :
     AffineIndependent k (p ∘ e) ↔ AffineIndependent k p :=
   by
@@ -348,6 +440,12 @@ theorem affineIndependent_equiv {ι' : Type _} (e : ι ≃ ι') {p : ι' → P}
   exact h.comp_embedding e.symm.to_embedding
 #align affine_independent_equiv affineIndependent_equiv
 
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 /-- If a set of points is affinely independent, so is any subset. -/
 protected theorem AffineIndependent.mono {s t : Set P}
     (ha : AffineIndependent k (fun x => x : t → P)) (hs : s ⊆ t) :
@@ -355,6 +453,12 @@ protected theorem AffineIndependent.mono {s t : Set P}
   ha.comp_embedding (s.embeddingOfSubset t hs)
 #align affine_independent.mono AffineIndependent.mono
 
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 /-- If the range of an injective indexed family of points is affinely
 independent, so is that family. -/
 theorem AffineIndependent.of_set_of_injective {p : ι → P}
@@ -371,6 +475,12 @@ variable {V₂ P₂ : Type _} [AddCommGroup V₂] [Module k V₂] [affine_space
 
 include V₂
 
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 /-- If the image of a family of points in affine space under an affine transformation is affine-
 independent, then the original family of points is also affine-independent. -/
 theorem AffineIndependent.of_comp {p : ι → P} (f : P →ᵃ[k] P₂) (hai : AffineIndependent k (f ∘ p)) :
@@ -385,6 +495,12 @@ theorem AffineIndependent.of_comp {p : ι → P} (f : P →ᵃ[k] P₂) (hai : A
   exact LinearIndependent.of_comp f.linear hai
 #align affine_independent.of_comp AffineIndependent.of_comp
 
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 /-- The image of a family of points in affine space, under an injective affine transformation, is
 affine-independent. -/
 theorem AffineIndependent.map' {p : ι → P} (hai : AffineIndependent k p) (f : P →ᵃ[k] P₂)
@@ -401,18 +517,36 @@ theorem AffineIndependent.map' {p : ι → P} (hai : AffineIndependent k p) (f :
   exact LinearIndependent.map' hai f.linear hf'
 #align affine_independent.map' AffineIndependent.map'
 
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 /-- Injective affine maps preserve affine independence. -/
 theorem AffineMap.affineIndependent_iff {p : ι → P} (f : P →ᵃ[k] P₂) (hf : Function.Injective f) :
     AffineIndependent k (f ∘ p) ↔ AffineIndependent k p :=
   ⟨AffineIndependent.of_comp f, fun hai => AffineIndependent.map' hai f hf⟩
 #align affine_map.affine_independent_iff AffineMap.affineIndependent_iff
 
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 /-- Affine equivalences preserve affine independence of families of points. -/
 theorem AffineEquiv.affineIndependent_iff {p : ι → P} (e : P ≃ᵃ[k] P₂) :
     AffineIndependent k (e ∘ p) ↔ AffineIndependent k p :=
   e.toAffineMap.affineIndependent_iff e.toEquiv.Injective
 #align affine_equiv.affine_independent_iff AffineEquiv.affineIndependent_iff
 
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+Case conversion may be inaccurate. Consider using '#align affine_equiv.affine_independent_set_of_eq_iff AffineEquiv.affineIndependent_set_of_eq_iffₓ'. -/
 /-- Affine equivalences preserve affine independence of subsets. -/
 theorem AffineEquiv.affineIndependent_set_of_eq_iff {s : Set P} (e : P ≃ᵃ[k] P₂) :
     AffineIndependent k (coe : e '' s → P₂) ↔ AffineIndependent k (coe : s → P) :=
@@ -423,6 +557,12 @@ theorem AffineEquiv.affineIndependent_set_of_eq_iff {s : Set P} (e : P ≃ᵃ[k]
 
 end Composition
 
+/- warning: affine_independent.exists_mem_inter_of_exists_mem_inter_affine_span -> AffineIndependent.exists_mem_inter_of_exists_mem_inter_affineSpan is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align affine_independent.exists_mem_inter_of_exists_mem_inter_affine_span AffineIndependent.exists_mem_inter_of_exists_mem_inter_affineSpanₓ'. -/
 /-- If a family is affinely independent, and the spans of points
 indexed by two subsets of the index type have a point in common, those
 subsets of the index type have an element in common, if the underlying
@@ -444,6 +584,12 @@ theorem AffineIndependent.exists_mem_inter_of_exists_mem_inter_affineSpan [Nontr
   use i, hfs1 hifs1, hfs2 (Set.mem_of_indicator_ne_zero hinz)
 #align affine_independent.exists_mem_inter_of_exists_mem_inter_affine_span AffineIndependent.exists_mem_inter_of_exists_mem_inter_affineSpan
 
+/- warning: affine_independent.affine_span_disjoint_of_disjoint -> AffineIndependent.affineSpan_disjoint_of_disjoint is a dubious translation:
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+but is expected to have type
+  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} [_inst_5 : Nontrivial.{u4} k] {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall {s1 : Set.{u1} ι} {s2 : Set.{u1} ι}, (Disjoint.{u1} (Set.{u1} ι) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} ι) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} ι) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} ι) (Set.instCompleteBooleanAlgebraSet.{u1} ι)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} ι) (Preorder.toLE.{u1} (Set.{u1} ι) (PartialOrder.toPreorder.{u1} (Set.{u1} ι) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} ι) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} ι) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} ι) (Set.instCompleteBooleanAlgebraSet.{u1} ι)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} ι) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} ι) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} ι) (Set.instCompleteBooleanAlgebraSet.{u1} ι)))))) s1 s2) -> (Disjoint.{u2} (Set.{u2} P) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} P) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} P) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} P) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} P) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} P) (Set.instCompleteBooleanAlgebraSet.{u2} P)))))) (BoundedOrder.toOrderBot.{u2} (Set.{u2} P) (Preorder.toLE.{u2} (Set.{u2} P) (PartialOrder.toPreorder.{u2} (Set.{u2} P) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} P) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} P) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} P) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} P) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} P) (Set.instCompleteBooleanAlgebraSet.{u2} P)))))))) (CompleteLattice.toBoundedOrder.{u2} (Set.{u2} P) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} P) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} P) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} P) (Set.instCompleteBooleanAlgebraSet.{u2} P)))))) (SetLike.coe.{u2, u2} (AffineSubspace.{u4, u3, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u4, u3, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (affineSpan.{u4, u3, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.image.{u1, u2} ι P p s1))) (SetLike.coe.{u2, u2} (AffineSubspace.{u4, u3, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u4, u3, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (affineSpan.{u4, u3, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.image.{u1, u2} ι P p s2)))))
+Case conversion may be inaccurate. Consider using '#align affine_independent.affine_span_disjoint_of_disjoint AffineIndependent.affineSpan_disjoint_of_disjointₓ'. -/
 /-- If a family is affinely independent, the spans of points indexed
 by disjoint subsets of the index type are disjoint, if the underlying
 ring is nontrivial. -/
@@ -456,6 +602,12 @@ theorem AffineIndependent.affineSpan_disjoint_of_disjoint [Nontrivial k] {p : ι
   exact Set.disjoint_iff.1 hd hi
 #align affine_independent.affine_span_disjoint_of_disjoint AffineIndependent.affineSpan_disjoint_of_disjoint
 
+/- warning: affine_independent.mem_affine_span_iff -> AffineIndependent.mem_affineSpan_iff is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} [_inst_5 : Nontrivial.{u1} k] {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall (i : ι) (s : Set.{u4} ι), Iff (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (p i) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.image.{u4, u3} ι P p s))) (Membership.Mem.{u4, u4} ι (Set.{u4} ι) (Set.hasMem.{u4} ι) i s))
+but is expected to have type
+  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} [_inst_5 : Nontrivial.{u4} k] {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall (i : ι) (s : Set.{u1} ι), Iff (Membership.mem.{u2, u2} P (AffineSubspace.{u4, u3, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u4, u3, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u4, u3, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (p i) (affineSpan.{u4, u3, u2} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.image.{u1, u2} ι P p s))) (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) i s))
+Case conversion may be inaccurate. Consider using '#align affine_independent.mem_affine_span_iff AffineIndependent.mem_affineSpan_iffₓ'. -/
 /-- If a family is affinely independent, a point in the family is in
 the span of some of the points given by a subset of the index type if
 and only if that point's index is in the subset, if the underlying
@@ -473,6 +625,12 @@ protected theorem AffineIndependent.mem_affineSpan_iff [Nontrivial k] {p : ι 
   · exact fun h => mem_affineSpan k (Set.mem_image_of_mem p h)
 #align affine_independent.mem_affine_span_iff AffineIndependent.mem_affineSpan_iff
 
+/- warning: affine_independent.not_mem_affine_span_diff -> AffineIndependent.not_mem_affineSpan_diff is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align affine_independent.not_mem_affine_span_diff AffineIndependent.not_mem_affineSpan_diffₓ'. -/
 /-- If a family is affinely independent, a point in the family is not
 in the affine span of the other points, if the underlying ring is
 nontrivial. -/
@@ -481,6 +639,12 @@ theorem AffineIndependent.not_mem_affineSpan_diff [Nontrivial k] {p : ι → P}
   simp [ha]
 #align affine_independent.not_mem_affine_span_diff AffineIndependent.not_mem_affineSpan_diff
 
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+Case conversion may be inaccurate. Consider using '#align exists_nontrivial_relation_sum_zero_of_not_affine_ind exists_nontrivial_relation_sum_zero_of_not_affine_indₓ'. -/
 theorem exists_nontrivial_relation_sum_zero_of_not_affine_ind {t : Finset V}
     (h : ¬AffineIndependent k (coe : t → V)) :
     ∃ f : V → k, (∑ e in t, f e • e) = 0 ∧ (∑ e in t, f e) = 0 ∧ ∃ x ∈ t, f x ≠ 0 := by
@@ -506,6 +670,12 @@ theorem exists_nontrivial_relation_sum_zero_of_not_affine_ind {t : Finset V}
         hw]
 #align exists_nontrivial_relation_sum_zero_of_not_affine_ind exists_nontrivial_relation_sum_zero_of_not_affine_ind
 
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+Case conversion may be inaccurate. Consider using '#align affine_independent_iff affineIndependent_iffₓ'. -/
 /-- Viewing a module as an affine space modelled on itself, we can characterise affine independence
 in terms of linear combinations. -/
 theorem affineIndependent_iff {ι} {p : ι → V} :
@@ -514,6 +684,12 @@ theorem affineIndependent_iff {ι} {p : ι → V} :
   forall₃_congr fun s w hw => by simp [s.weighted_vsub_eq_linear_combination hw]
 #align affine_independent_iff affineIndependent_iff
 
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+but is expected to have type
+  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_1)))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (Ring.toSemiring.{u4} k _inst_1)))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k 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+Case conversion may be inaccurate. Consider using '#align weighted_vsub_mem_vector_span_pair weightedVSub_mem_vectorSpan_pairₓ'. -/
 /-- Given an affinely independent family of points, a weighted subtraction lies in the
 `vector_span` of two points given as affine combinations if and only if it is a weighted
 subtraction with weights a multiple of the difference between the weights of the two points. -/
@@ -544,6 +720,12 @@ theorem weightedVSub_mem_vectorSpan_pair {p : ι → P} (h : AffineIndependent k
     congr
 #align weighted_vsub_mem_vector_span_pair weightedVSub_mem_vectorSpan_pair
 
+/- warning: affine_combination_mem_affine_span_pair -> affineCombination_mem_affineSpan_pair is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align affine_combination_mem_affine_span_pair affineCombination_mem_affineSpan_pairₓ'. -/
 /-- Given an affinely independent family of points, an affine combination lies in the
 span of two points given as affine combinations if and only if it is an affine combination
 with weights those of one point plus a multiple of the difference between the weights of the
@@ -572,6 +754,12 @@ variable [affine_space V P] {ι : Type _}
 
 include V
 
+/- warning: exists_subset_affine_independent_affine_span_eq_top -> exists_subset_affineIndependent_affineSpan_eq_top is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align exists_subset_affine_independent_affine_span_eq_top exists_subset_affineIndependent_affineSpan_eq_topₓ'. -/
 /-- An affinely independent set of points can be extended to such a
 set that spans the whole space. -/
 theorem exists_subset_affineIndependent_affineSpan_eq_top {s : Set P}
@@ -611,6 +799,12 @@ theorem exists_subset_affineIndependent_affineSpan_eq_top {s : Set P}
 
 variable (k V)
 
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+Case conversion may be inaccurate. Consider using '#align exists_affine_independent exists_affineIndependentₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem exists_affineIndependent (s : Set P) :
     ∃ (t : _)(_ : t ⊆ s), affineSpan k t = affineSpan k s ∧ AffineIndependent k (coe : t → P) :=
@@ -639,6 +833,12 @@ theorem exists_affineIndependent (s : Set P) :
 
 variable (k) {V P}
 
+/- warning: affine_independent_of_ne -> affineIndependent_of_ne is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_independent_of_ne affineIndependent_of_neₓ'. -/
 /-- Two different points are affinely independent. -/
 theorem affineIndependent_of_ne {p₁ p₂ : P} (h : p₁ ≠ p₂) : AffineIndependent k ![p₁, p₂] :=
   by
@@ -659,6 +859,12 @@ theorem affineIndependent_of_ne {p₁ p₂ : P} (h : p₁ ≠ p₂) : AffineInde
 
 variable {k V P}
 
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+Case conversion may be inaccurate. Consider using '#align affine_independent.affine_independent_of_not_mem_span AffineIndependent.affineIndependent_of_not_mem_spanₓ'. -/
 /-- If all but one point of a family are affinely independent, and that point does not lie in
 the affine span of that family, the family is affinely independent. -/
 theorem AffineIndependent.affineIndependent_of_not_mem_span {p : ι → P} {i : ι}
@@ -707,6 +913,12 @@ theorem AffineIndependent.affineIndependent_of_not_mem_span {p : ι → P} {i :
       · exact ha s' w' hw' hs' ⟨j, hji⟩ (Finset.mem_subtype.2 hj)
 #align affine_independent.affine_independent_of_not_mem_span AffineIndependent.affineIndependent_of_not_mem_span
 
+/- warning: affine_independent_of_ne_of_mem_of_mem_of_not_mem -> affineIndependent_of_ne_of_mem_of_mem_of_not_mem is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : AffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4} {p₁ : P} {p₂ : P} {p₃ : P}, (Ne.{succ u1} P p₁ p₂) -> (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4)) p₁ s) -> (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4)) p₂ s) -> (Not (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4)) p₃ s)) -> (AffineIndependent.{u3, u2, u1, 0} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4 (Fin (Nat.succ (Nat.succ (Nat.succ (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Matrix.vecCons.{u1} P (Nat.succ (Nat.succ (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) p₁ (Matrix.vecCons.{u1} P (Nat.succ (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) p₂ (Matrix.vecCons.{u1} P (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) p₃ (Matrix.vecEmpty.{u1} P)))))
+Case conversion may be inaccurate. Consider using '#align affine_independent_of_ne_of_mem_of_mem_of_not_mem affineIndependent_of_ne_of_mem_of_mem_of_not_memₓ'. -/
 /-- If distinct points `p₁` and `p₂` lie in `s` but `p₃` does not, the three points are affinely
 independent. -/
 theorem affineIndependent_of_ne_of_mem_of_mem_of_not_mem {s : AffineSubspace k P} {p₁ p₂ p₃ : P}
@@ -727,6 +939,12 @@ theorem affineIndependent_of_ne_of_mem_of_mem_of_not_mem {s : AffineSubspace k P
   fin_cases x <;> simp [hp₁, hp₂]
 #align affine_independent_of_ne_of_mem_of_mem_of_not_mem affineIndependent_of_ne_of_mem_of_mem_of_not_mem
 
+/- warning: affine_independent_of_ne_of_mem_of_not_mem_of_mem -> affineIndependent_of_ne_of_mem_of_not_mem_of_mem is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4} {p₁ : P} {p₂ : P} {p₃ : P}, (Ne.{succ u3} P p₁ p₃) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4)) p₁ s) -> (Not (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4)) p₂ s)) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4)) p₃ s) -> (AffineIndependent.{u1, u2, u3, 0} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 (Fin (Nat.succ (Nat.succ (Nat.succ (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))))) (Matrix.vecCons.{u3} P (Nat.succ (Nat.succ (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) p₁ (Matrix.vecCons.{u3} P (Nat.succ (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) p₂ (Matrix.vecCons.{u3} P (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) p₃ (Matrix.vecEmpty.{u3} P)))))
+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : AffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4} {p₁ : P} {p₂ : P} {p₃ : P}, (Ne.{succ u1} P p₁ p₃) -> (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4)) p₁ s) -> (Not (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4)) p₂ s)) -> (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4)) p₃ s) -> (AffineIndependent.{u3, u2, u1, 0} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4 (Fin (Nat.succ (Nat.succ (Nat.succ (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Matrix.vecCons.{u1} P (Nat.succ (Nat.succ (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) p₁ (Matrix.vecCons.{u1} P (Nat.succ (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) p₂ (Matrix.vecCons.{u1} P (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) p₃ (Matrix.vecEmpty.{u1} P)))))
+Case conversion may be inaccurate. Consider using '#align affine_independent_of_ne_of_mem_of_not_mem_of_mem affineIndependent_of_ne_of_mem_of_not_mem_of_memₓ'. -/
 /-- If distinct points `p₁` and `p₃` lie in `s` but `p₂` does not, the three points are affinely
 independent. -/
 theorem affineIndependent_of_ne_of_mem_of_not_mem_of_mem {s : AffineSubspace k P} {p₁ p₂ p₃ : P}
@@ -739,6 +957,12 @@ theorem affineIndependent_of_ne_of_mem_of_not_mem_of_mem {s : AffineSubspace k P
   fin_cases x <;> rfl
 #align affine_independent_of_ne_of_mem_of_not_mem_of_mem affineIndependent_of_ne_of_mem_of_not_mem_of_mem
 
+/- warning: affine_independent_of_ne_of_not_mem_of_mem_of_mem -> affineIndependent_of_ne_of_not_mem_of_mem_of_mem is a dubious translation:
+lean 3 declaration is
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+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : AffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4} {p₁ : P} {p₂ : P} {p₃ : P}, (Ne.{succ u1} P p₂ p₃) -> (Not (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4)) p₁ s)) -> (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4)) p₂ s) -> (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4)) p₃ s) -> (AffineIndependent.{u3, u2, u1, 0} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4 (Fin (Nat.succ (Nat.succ (Nat.succ (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Matrix.vecCons.{u1} P (Nat.succ (Nat.succ (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) p₁ (Matrix.vecCons.{u1} P (Nat.succ (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) p₂ (Matrix.vecCons.{u1} P (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) p₃ (Matrix.vecEmpty.{u1} P)))))
+Case conversion may be inaccurate. Consider using '#align affine_independent_of_ne_of_not_mem_of_mem_of_mem affineIndependent_of_ne_of_not_mem_of_mem_of_memₓ'. -/
 /-- If distinct points `p₂` and `p₃` lie in `s` but `p₁` does not, the three points are affinely
 independent. -/
 theorem affineIndependent_of_ne_of_not_mem_of_mem_of_mem {s : AffineSubspace k P} {p₁ p₂ p₃ : P}
@@ -763,6 +987,12 @@ include V
 
 attribute [local instance] LinearOrderedRing.decidableLt
 
+/- warning: sign_eq_of_affine_combination_mem_affine_span_pair -> sign_eq_of_affineCombination_mem_affineSpan_pair is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u4} ι}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) s (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) s (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k (AddMonoidWithOne.toOne.{u1} k (AddGroupWithOne.toAddMonoidWithOne.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))))))) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4)) (coeFn.{max (succ (max u4 u1)) (succ u2) (succ u3), max (succ (max u4 u1)) (succ u3)} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k 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: ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Pi.addTorsor.{u4, u1, u1} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) _inst_2 _inst_3 _inst_4) (Finset.affineCombination.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι s p) w₂))))) -> (forall {i : ι} {j : ι}, (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i s) -> (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) j s) -> (Eq.{succ u1} k (w₁ i) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))))))) -> (Eq.{succ u1} k (w₁ j) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))))))) -> (Eq.{1} SignType (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k 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(PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w₂ j))) -> (Eq.{1} SignType (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k 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(PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (fun (a : k) (b : k) => LinearOrderedRing.decidableLt.{u1} k _inst_1 a b)) (w i)) (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => k -> SignType) (OrderHom.hasCoeToFun.{u1, 0} k SignType (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))))) (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k 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+but is expected to have type
+  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : LinearOrderedRing.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {w₁ : ι -> k} {w₂ : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w₁ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))))) -> (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : ι) => w₂ i)) (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))))) -> (Membership.mem.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (AffineSubspace.instSetLikeAffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w₂) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u3)) (succ u2), succ (max u4 u1), succ u2} (AffineMap.{u4, max u4 u1, max u4 u1, u3, u2} k (ι -> k) (ι -> k) V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (i : ι) => 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_inst_4 ι s p) w₂))))) -> (forall {i : ι} {j : ι}, (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) j s) -> (Eq.{succ u4} k (w₁ i) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1)))))))) -> (Eq.{succ u4} k (w₁ j) (OfNat.ofNat.{u4} k 0 (Zero.toOfNat0.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1)))))))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w₂ i)) (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u4} k (MonoidWithZero.toZero.{u4} k (Semiring.toMonoidWithZero.{u4} k (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w₂ j))) -> (Eq.{1} SignType (OrderHom.toFun.{u4, 0} k SignType (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) 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(LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))) (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))) (fun (a : k) (b : k) => LinearOrderedRing.decidable_lt.{u4} k _inst_1 a b)) (w j)))))
+Case conversion may be inaccurate. Consider using '#align sign_eq_of_affine_combination_mem_affine_span_pair sign_eq_of_affineCombination_mem_affineSpan_pairₓ'. -/
 /-- Given an affinely independent family of points, suppose that an affine combination lies in
 the span of two points given as affine combinations, and suppose that, for two indices, the
 coefficients in the first point in the span are zero and those in the second point in the span
@@ -783,6 +1013,12 @@ theorem sign_eq_of_affineCombination_mem_affineSpan_pair {p : ι → P} (h : Aff
   rw [hr i hi, hr j hj, hi0, hj0, add_zero, add_zero, sub_zero, sub_zero, sign_mul, sign_mul, hij]
 #align sign_eq_of_affine_combination_mem_affine_span_pair sign_eq_of_affineCombination_mem_affineSpan_pair
 
+/- warning: sign_eq_of_affine_combination_mem_affine_span_single_line_map -> sign_eq_of_affineCombination_mem_affineSpan_single_lineMap is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} {p : ι -> P}, (AffineIndependent.{u1, u2, u3, u4} k V P (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {s : Finset.{u4} ι}, (Eq.{succ u1} k (Finset.sum.{u1, u4} k ι (AddCommGroup.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))))) s (fun (i : ι) => w i)) (OfNat.ofNat.{u1} k 1 (OfNat.mk.{u1} k 1 (One.one.{u1} k 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+but is expected to have type
+  forall {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : LinearOrderedRing.{u4} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u4, u3} k V (StrictOrderedSemiring.toSemiring.{u4} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} k (LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u1}} {p : ι -> P}, (AffineIndependent.{u4, u3, u2, u1} k V P (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4 ι p) -> (forall {w : ι -> k} {s : Finset.{u1} ι}, (Eq.{succ u4} k (Finset.sum.{u4, u1} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))))) s (fun (i : 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(LinearOrderedRing.toLinearOrderedSemiring.{u4} k _inst_1))))))) c) -> (LT.lt.{u4} k (Preorder.toLT.{u4} k (PartialOrder.toPreorder.{u4} k (StrictOrderedRing.toPartialOrder.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)))) c (OfNat.ofNat.{u4} k 1 (One.toOfNat1.{u4} k (NonAssocRing.toOne.{u4} k (Ring.toNonAssocRing.{u4} k (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1))))))) -> (Membership.mem.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) w) (AffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k _inst_1)) _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u4, u3, u2} k V ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c) (StrictOrderedRing.toRing.{u4} k (LinearOrderedRing.toStrictOrderedRing.{u4} k 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+Case conversion may be inaccurate. Consider using '#align sign_eq_of_affine_combination_mem_affine_span_single_line_map sign_eq_of_affineCombination_mem_affineSpan_single_lineMapₓ'. -/
 /-- Given an affinely independent family of points, suppose that an affine combination lies in
 the span of one point of that family and a combination of another two points of that family given
 by `line_map` with coefficient between 0 and 1. Then the coefficients of those two points in the
@@ -817,27 +1053,39 @@ variable [affine_space V P]
 
 include V
 
+#print Affine.Simplex /-
 /-- A `simplex k P n` is a collection of `n + 1` affinely
 independent points. -/
 structure Simplex (n : ℕ) where
   points : Fin (n + 1) → P
   Independent : AffineIndependent k points
 #align affine.simplex Affine.Simplex
+-/
 
+#print Affine.Triangle /-
 /-- A `triangle k P` is a collection of three affinely independent points. -/
 abbrev Triangle :=
   Simplex k P 2
 #align affine.triangle Affine.Triangle
+-/
 
 namespace Simplex
 
 variable {P}
 
+#print Affine.Simplex.mkOfPoint /-
 /-- Construct a 0-simplex from a point. -/
 def mkOfPoint (p : P) : Simplex k P 0 :=
   ⟨fun _ => p, affineIndependent_of_subsingleton k _⟩
 #align affine.simplex.mk_of_point Affine.Simplex.mkOfPoint
+-/
 
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+Case conversion may be inaccurate. Consider using '#align affine.simplex.mk_of_point_points Affine.Simplex.mkOfPoint_pointsₓ'. -/
 /-- The point in a simplex constructed with `mk_of_point`. -/
 @[simp]
 theorem mkOfPoint_points (p : P) (i : Fin 1) : (mkOfPoint k p).points i = p :=
@@ -847,12 +1095,20 @@ theorem mkOfPoint_points (p : P) (i : Fin 1) : (mkOfPoint k p).points i = p :=
 instance [Inhabited P] : Inhabited (Simplex k P 0) :=
   ⟨mkOfPoint k default⟩
 
+#print Affine.Simplex.nonempty /-
 instance nonempty : Nonempty (Simplex k P 0) :=
   ⟨mkOfPoint k <| AddTorsor.nonempty.some⟩
 #align affine.simplex.nonempty Affine.Simplex.nonempty
+-/
 
 variable {k V}
 
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 /-- Two simplices are equal if they have the same points. -/
 @[ext]
 theorem ext {n : ℕ} {s1 s2 : Simplex k P n} (h : ∀ i, s1.points i = s2.points i) : s1 = s2 :=
@@ -863,18 +1119,32 @@ theorem ext {n : ℕ} {s1 s2 : Simplex k P n} (h : ∀ i, s1.points i = s2.point
   exact h i
 #align affine.simplex.ext Affine.Simplex.ext
 
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 /-- Two simplices are equal if and only if they have the same points. -/
 theorem ext_iff {n : ℕ} (s1 s2 : Simplex k P n) : s1 = s2 ↔ ∀ i, s1.points i = s2.points i :=
   ⟨fun h _ => h ▸ rfl, ext⟩
 #align affine.simplex.ext_iff Affine.Simplex.ext_iff
 
+#print Affine.Simplex.face /-
 /-- A face of a simplex is a simplex with the given subset of
 points. -/
 def face {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ} (h : fs.card = m + 1) :
     Simplex k P m :=
   ⟨s.points ∘ fs.orderEmbOfFin h, s.Independent.comp_embedding (fs.orderEmbOfFin h).toEmbedding⟩
 #align affine.simplex.face Affine.Simplex.face
+-/
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align affine.simplex.face_points Affine.Simplex.face_pointsₓ'. -/
 /-- The points of a face of a simplex are given by `mono_of_fin`. -/
 theorem face_points {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ}
     (h : fs.card = m + 1) (i : Fin (m + 1)) :
@@ -882,12 +1152,24 @@ theorem face_points {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m
   rfl
 #align affine.simplex.face_points Affine.Simplex.face_points
 
+/- warning: affine.simplex.face_points' -> Affine.Simplex.face_points' is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align affine.simplex.face_points' Affine.Simplex.face_points'ₓ'. -/
 /-- The points of a face of a simplex are given by `mono_of_fin`. -/
 theorem face_points' {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ}
     (h : fs.card = m + 1) : (s.face h).points = s.points ∘ fs.orderEmbOfFin h :=
   rfl
 #align affine.simplex.face_points' Affine.Simplex.face_points'
 
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+Case conversion may be inaccurate. Consider using '#align affine.simplex.face_eq_mk_of_point Affine.Simplex.face_eq_mkOfPointₓ'. -/
 /-- A single-point face equals the 0-simplex constructed with
 `mk_of_point`. -/
 @[simp]
@@ -898,6 +1180,12 @@ theorem face_eq_mkOfPoint {n : ℕ} (s : Simplex k P n) (i : Fin (n + 1)) :
   simp [face_points]
 #align affine.simplex.face_eq_mk_of_point Affine.Simplex.face_eq_mkOfPoint
 
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+Case conversion may be inaccurate. Consider using '#align affine.simplex.range_face_points Affine.Simplex.range_face_pointsₓ'. -/
 /-- The set of points of a face. -/
 @[simp]
 theorem range_face_points {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ}
@@ -905,18 +1193,32 @@ theorem range_face_points {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1
   rw [face_points', Set.range_comp, Finset.range_orderEmbOfFin]
 #align affine.simplex.range_face_points Affine.Simplex.range_face_points
 
+#print Affine.Simplex.reindex /-
 /-- Remap a simplex along an `equiv` of index types. -/
 @[simps]
 def reindex {m n : ℕ} (s : Simplex k P m) (e : Fin (m + 1) ≃ Fin (n + 1)) : Simplex k P n :=
   ⟨s.points ∘ e.symm, (affineIndependent_equiv e.symm).2 s.Independent⟩
 #align affine.simplex.reindex Affine.Simplex.reindex
+-/
 
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 /-- Reindexing by `equiv.refl` yields the original simplex. -/
 @[simp]
 theorem reindex_refl {n : ℕ} (s : Simplex k P n) : s.reindex (Equiv.refl (Fin (n + 1))) = s :=
   ext fun _ => rfl
 #align affine.simplex.reindex_refl Affine.Simplex.reindex_refl
 
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+Case conversion may be inaccurate. Consider using '#align affine.simplex.reindex_trans Affine.Simplex.reindex_transₓ'. -/
 /-- Reindexing by the composition of two equivalences is the same as reindexing twice. -/
 @[simp]
 theorem reindex_trans {n₁ n₂ n₃ : ℕ} (e₁₂ : Fin (n₁ + 1) ≃ Fin (n₂ + 1))
@@ -925,18 +1227,36 @@ theorem reindex_trans {n₁ n₂ n₃ : ℕ} (e₁₂ : Fin (n₁ + 1) ≃ Fin (
   rfl
 #align affine.simplex.reindex_trans Affine.Simplex.reindex_trans
 
+/- warning: affine.simplex.reindex_reindex_symm -> Affine.Simplex.reindex_reindex_symm is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine.simplex.reindex_reindex_symm Affine.Simplex.reindex_reindex_symmₓ'. -/
 /-- Reindexing by an equivalence and its inverse yields the original simplex. -/
 @[simp]
 theorem reindex_reindex_symm {m n : ℕ} (s : Simplex k P m) (e : Fin (m + 1) ≃ Fin (n + 1)) :
     (s.reindex e).reindex e.symm = s := by rw [← reindex_trans, Equiv.self_trans_symm, reindex_refl]
 #align affine.simplex.reindex_reindex_symm Affine.Simplex.reindex_reindex_symm
 
+/- warning: affine.simplex.reindex_symm_reindex -> Affine.Simplex.reindex_symm_reindex is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine.simplex.reindex_symm_reindex Affine.Simplex.reindex_symm_reindexₓ'. -/
 /-- Reindexing by the inverse of an equivalence and that equivalence yields the original simplex. -/
 @[simp]
 theorem reindex_symm_reindex {m n : ℕ} (s : Simplex k P m) (e : Fin (n + 1) ≃ Fin (m + 1)) :
     (s.reindex e.symm).reindex e = s := by rw [← reindex_trans, Equiv.symm_trans_self, reindex_refl]
 #align affine.simplex.reindex_symm_reindex Affine.Simplex.reindex_symm_reindex
 
+/- warning: affine.simplex.reindex_range_points -> Affine.Simplex.reindex_range_points is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine.simplex.reindex_range_points Affine.Simplex.reindex_range_pointsₓ'. -/
 /-- Reindexing a simplex produces one with the same set of points. -/
 @[simp]
 theorem reindex_range_points {m n : ℕ} (s : Simplex k P m) (e : Fin (m + 1) ≃ Fin (n + 1)) :
@@ -957,6 +1277,12 @@ variable {k : Type _} {V : Type _} {P : Type _} [DivisionRing k] [AddCommGroup V
 
 include V
 
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+Case conversion may be inaccurate. Consider using '#align affine.simplex.face_centroid_eq_centroid Affine.Simplex.face_centroid_eq_centroidₓ'. -/
 /-- The centroid of a face of a simplex as the centroid of a subset of
 the points. -/
 @[simp]
@@ -968,6 +1294,12 @@ theorem face_centroid_eq_centroid {n : ℕ} (s : Simplex k P n) {fs : Finset (Fi
   simp
 #align affine.simplex.face_centroid_eq_centroid Affine.Simplex.face_centroid_eq_centroid
 
+/- warning: affine.simplex.centroid_eq_iff -> Affine.Simplex.centroid_eq_iff is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align affine.simplex.centroid_eq_iff Affine.Simplex.centroid_eq_iffₓ'. -/
 /-- Over a characteristic-zero division ring, the centroids given by
 two subsets of the points of a simplex are equal if and only if those
 faces are given by the same subset of points. -/
@@ -997,6 +1329,12 @@ theorem centroid_eq_iff [CharZero k] {n : ℕ} (s : Simplex k P n) {fs₁ fs₂
   · simpa [hni, hi, key] using ha.symm
 #align affine.simplex.centroid_eq_iff Affine.Simplex.centroid_eq_iff
 
+/- warning: affine.simplex.face_centroid_eq_iff -> Affine.Simplex.face_centroid_eq_iff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine.simplex.face_centroid_eq_iff Affine.Simplex.face_centroid_eq_iffₓ'. -/
 /-- Over a characteristic-zero division ring, the centroids of two
 faces of a simplex are equal if and only if those faces are given by
 the same subset of points. -/
@@ -1009,6 +1347,12 @@ theorem face_centroid_eq_iff [CharZero k] {n : ℕ} (s : Simplex k P n)
   exact s.centroid_eq_iff h₁ h₂
 #align affine.simplex.face_centroid_eq_iff Affine.Simplex.face_centroid_eq_iff
 
+/- warning: affine.simplex.centroid_eq_of_range_eq -> Affine.Simplex.centroid_eq_of_range_eq is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : DivisionRing.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k (DivisionRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {n : Nat} {s₁ : Affine.Simplex.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 n} {s₂ : Affine.Simplex.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 n}, (Eq.{succ u3} (Set.{u3} P) (Set.range.{u3, 1} P (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Affine.Simplex.points.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 n s₁)) (Set.range.{u3, 1} P (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Affine.Simplex.points.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 n s₂))) -> (Eq.{succ u3} P (Finset.centroid.{u1, u2, u3, 0} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Finset.univ.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.fintype (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Affine.Simplex.points.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 n s₁)) (Finset.centroid.{u1, u2, u3, 0} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Finset.univ.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.fintype (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Affine.Simplex.points.{u1, u2, u3} k V P (DivisionRing.toRing.{u1} k _inst_1) _inst_2 _inst_3 _inst_4 n s₂)))
+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : DivisionRing.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (DivisionSemiring.toSemiring.{u3} k (DivisionRing.toDivisionSemiring.{u3} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {n : Nat} {s₁ : Affine.Simplex.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4 n} {s₂ : Affine.Simplex.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4 n}, (Eq.{succ u1} (Set.{u1} P) (Set.range.{u1, 1} P (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Affine.Simplex.points.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4 n s₁)) (Set.range.{u1, 1} P (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Affine.Simplex.points.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4 n s₂))) -> (Eq.{succ u1} P (Finset.centroid.{u3, u2, u1, 0} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Finset.univ.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.fintype (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Affine.Simplex.points.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4 n s₁)) (Finset.centroid.{u3, u2, u1, 0} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Finset.univ.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.fintype (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Affine.Simplex.points.{u3, u2, u1} k V P (DivisionRing.toRing.{u3} k _inst_1) _inst_2 _inst_3 _inst_4 n s₂)))
+Case conversion may be inaccurate. Consider using '#align affine.simplex.centroid_eq_of_range_eq Affine.Simplex.centroid_eq_of_range_eqₓ'. -/
 /-- Two simplices with the same points have the same centroid. -/
 theorem centroid_eq_of_range_eq {n : ℕ} {s₁ s₂ : Simplex k P n}
     (h : Set.range s₁.points = Set.range s₂.points) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/5ec62c8106221a3f9160e4e4fcc3eed79fe213e9

@@ -57,14 +57,14 @@ nontrivial weighted subtractions (where the sum of weights is 0) are
 0. -/
 def AffineIndependent (p : ι → P) : Prop :=
   ∀ (s : Finset ι) (w : ι → k),
-    (∑ i in s, w i) = 0 → s.weightedVsub p w = (0 : V) → ∀ i ∈ s, w i = 0
+    (∑ i in s, w i) = 0 → s.weightedVSub p w = (0 : V) → ∀ i ∈ s, w i = 0
 #align affine_independent AffineIndependent
 
 /-- The definition of `affine_independent`. -/
 theorem affineIndependent_def (p : ι → P) :
     AffineIndependent k p ↔
       ∀ (s : Finset ι) (w : ι → k),
-        (∑ i in s, w i) = 0 → s.weightedVsub p w = (0 : V) → ∀ i ∈ s, w i = 0 :=
+        (∑ i in s, w i) = 0 → s.weightedVSub p w = (0 : V) → ∀ i ∈ s, w i = 0 :=
   Iff.rfl
 #align affine_independent_def affineIndependent_def
 
@@ -78,12 +78,12 @@ only if no nontrivial weighted subtractions over `finset.univ` (where
 the sum of the weights is 0) are 0. -/
 theorem affineIndependent_iff_of_fintype [Fintype ι] (p : ι → P) :
     AffineIndependent k p ↔
-      ∀ w : ι → k, (∑ i, w i) = 0 → Finset.univ.weightedVsub p w = (0 : V) → ∀ i, w i = 0 :=
+      ∀ w : ι → k, (∑ i, w i) = 0 → Finset.univ.weightedVSub p w = (0 : V) → ∀ i, w i = 0 :=
   by
   constructor
   · exact fun h w hw hs i => h Finset.univ w hw hs i (Finset.mem_univ _)
   · intro h s w hw hs i hi
-    rw [Finset.weightedVsub_indicator_subset _ _ (Finset.subset_univ s)] at hs
+    rw [Finset.weightedVSub_indicator_subset _ _ (Finset.subset_univ s)] at hs
     rw [Set.sum_indicator_subset _ (Finset.subset_univ s)] at hw
     replace h := h ((↑s : Set ι).indicator w) hw hs i
     simpa [hi] using h
@@ -124,16 +124,16 @@ theorem affineIndependent_iff_linearIndependent_vsub (p : ι → P) (i1 : ι) :
           by
           simp_rw [hf2def, hg2def, hfg]
           exact fun x => rfl
-        rw [Finset.weightedVsub_eq_weightedVsubOfPoint_of_sum_eq_zero s2 f p hf (p i1),
-          Finset.weightedVsubOfPoint_insert, Finset.weightedVsubOfPoint_apply,
+        rw [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero s2 f p hf (p i1),
+          Finset.weightedVSubOfPoint_insert, Finset.weightedVSubOfPoint_apply,
           Finset.sum_subtype_map_embedding fun x hx => hf2g2 x]
         exact hg
       exact h s2 f hf hs2 i (Finset.mem_insert_of_mem (Finset.mem_map.2 ⟨i, hi, rfl⟩))
     · intro h
       rw [linearIndependent_iff'] at h
       intro s w hw hs i hi
-      rw [Finset.weightedVsub_eq_weightedVsubOfPoint_of_sum_eq_zero s w p hw (p i1), ←
-        s.weighted_vsub_of_point_erase w p i1, Finset.weightedVsubOfPoint_apply] at hs
+      rw [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero s w p hw (p i1), ←
+        s.weighted_vsub_of_point_erase w p i1, Finset.weightedVSubOfPoint_apply] at hs
       let f : ι → V := fun i => w i • (p i -ᵥ p i1)
       have hs2 : (∑ i in (s.erase i1).Subtype fun i => i ≠ i1, f i) = 0 :=
         by
@@ -226,7 +226,7 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
       let w2 := w + w1
       have hw2 : (∑ i in s, w2 i) = 1 := by simp [w2, Finset.sum_add_distrib, hw, hw1]
       have hw2s : s.affine_combination k p w2 = p i0 := by
-        simp [w2, ← Finset.weightedVsub_vadd_affineCombination, hs, hw1s]
+        simp [w2, ← Finset.weightedVSub_vadd_affineCombination, hs, hw1s]
       replace ha := ha s s w2 w1 hw2 hw1 (hw1s.symm ▸ hw2s)
       have hws : w2 i0 - w1 i0 = 0 := by
         rw [← Finset.mem_coe] at hi0
@@ -310,7 +310,7 @@ theorem AffineIndependent.comp_embedding {ι2 : Type _} (f : ι2 ↪ ι) {p : ι
       simp [hw']
     have hs' : fs'.weighted_vsub p w' = (0 : V) :=
       by
-      rw [← hs, Finset.weightedVsub_map]
+      rw [← hs, Finset.weightedVSub_map]
       congr with i
       simp [hw']
     rw [← ha fs' w' hw's hs' (f i0) ((Finset.mem_map' _).2 hi0), hw']
@@ -488,8 +488,8 @@ theorem exists_nontrivial_relation_sum_zero_of_not_affine_ind {t : Finset V}
     rw [affineIndependent_iff_of_fintype] at h
     simp only [exists_prop, not_forall] at h
     obtain ⟨w, hw, hwt, i, hi⟩ := h
-    simp only [Finset.weightedVsub_eq_weightedVsubOfPoint_of_sum_eq_zero _ w (coe : t → V) hw 0,
-      vsub_eq_sub, Finset.weightedVsubOfPoint_apply, sub_zero] at hwt
+    simp only [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero _ w (coe : t → V) hw 0,
+      vsub_eq_sub, Finset.weightedVSubOfPoint_apply, sub_zero] at hwt
     let f : ∀ x : V, x ∈ t → k := fun x hx => w ⟨x, hx⟩
     refine'
       ⟨fun x => if hx : x ∈ t then f x hx else (0 : k), _, _,
@@ -517,10 +517,10 @@ theorem affineIndependent_iff {ι} {p : ι → V} :
 /-- Given an affinely independent family of points, a weighted subtraction lies in the
 `vector_span` of two points given as affine combinations if and only if it is a weighted
 subtraction with weights a multiple of the difference between the weights of the two points. -/
-theorem weightedVsub_mem_vectorSpan_pair {p : ι → P} (h : AffineIndependent k p) {w w₁ w₂ : ι → k}
+theorem weightedVSub_mem_vectorSpan_pair {p : ι → P} (h : AffineIndependent k p) {w w₁ w₂ : ι → k}
     {s : Finset ι} (hw : (∑ i in s, w i) = 0) (hw₁ : (∑ i in s, w₁ i) = 1)
     (hw₂ : (∑ i in s, w₂ i) = 1) :
-    s.weightedVsub p w ∈
+    s.weightedVSub p w ∈
         vectorSpan k ({s.affineCombination k p w₁, s.affineCombination k p w₂} : Set P) ↔
       ∃ r : k, ∀ i ∈ s, w i = r * (w₁ i - w₂ i) :=
   by
@@ -542,7 +542,7 @@ theorem weightedVsub_mem_vectorSpan_pair {p : ι → P} (h : AffineIndependent k
     rw [s.weighted_vsub_congr hr fun _ _ => rfl, s.affine_combination_vsub, ←
       s.weighted_vsub_const_smul]
     congr
-#align weighted_vsub_mem_vector_span_pair weightedVsub_mem_vectorSpan_pair
+#align weighted_vsub_mem_vector_span_pair weightedVSub_mem_vectorSpan_pair
 
 /-- Given an affinely independent family of points, an affine combination lies in the
 span of two points given as affine combinations if and only if it is an affine combination
@@ -557,7 +557,7 @@ theorem affineCombination_mem_affineSpan_pair {p : ι → P} (h : AffineIndepend
   rw [← vsub_vadd (s.affine_combination k p w) (s.affine_combination k p w₁),
     AffineSubspace.vadd_mem_iff_mem_direction _ (left_mem_affineSpan_pair _ _ _),
     direction_affineSpan, s.affine_combination_vsub, Set.pair_comm,
-    weightedVsub_mem_vectorSpan_pair h _ hw₂ hw₁]
+    weightedVSub_mem_vectorSpan_pair h _ hw₂ hw₁]
   · simp only [Pi.sub_apply, sub_eq_iff_eq_add]
   · simp_rw [Pi.sub_apply, Finset.sum_sub_distrib, hw, hw₁, sub_self]
 #align affine_combination_mem_affine_span_pair affineCombination_mem_affineSpan_pair
@@ -696,8 +696,8 @@ theorem AffineIndependent.affineIndependent_of_not_mem_span {p : ι → P} {i :
         exact hwx (his.neg_resolve_left hxs)
       have hs' : s'.weighted_vsub p' w' = (0 : V) :=
         by
-        simp_rw [Finset.weightedVsub_subtype_eq_filter]
-        rw [Finset.weightedVsub_filter_of_ne, hs]
+        simp_rw [Finset.weightedVSub_subtype_eq_filter]
+        rw [Finset.weightedVSub_filter_of_ne, hs]
         rintro x hxs hwx rfl
         exact hwx (his.neg_resolve_left hxs)
       intro j hj

mathlib commit https://github.com/leanprover-community/mathlib/commit/b685f506164f8d17a6404048bc4d696739c5d976

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
 
 ! This file was ported from Lean 3 source module linear_algebra.affine_space.independent
-! leanprover-community/mathlib commit 09258fb7f75d741b7eda9fa18d5c869e2135d9f1
+! leanprover-community/mathlib commit 2de9c37fa71dde2f1c6feff19876dd6a7b1519f0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -197,7 +197,7 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
       ∀ (s1 s2 : Finset ι) (w1 w2 : ι → k),
         (∑ i in s1, w1 i) = 1 →
           (∑ i in s2, w2 i) = 1 →
-            s1.affineCombination p w1 = s2.affineCombination p w2 →
+            s1.affineCombination k p w1 = s2.affineCombination k p w2 →
               Set.indicator (↑s1) w1 = Set.indicator (↑s2) w2 :=
   by
   classical
@@ -220,12 +220,12 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
       let w1 : ι → k := Function.update (Function.const ι 0) i0 1
       have hw1 : (∑ i in s, w1 i) = 1 := by
         rw [Finset.sum_update_of_mem hi0, Finset.sum_const_zero, add_zero]
-      have hw1s : s.affine_combination p w1 = p i0 :=
+      have hw1s : s.affine_combination k p w1 = p i0 :=
         s.affine_combination_of_eq_one_of_eq_zero w1 p hi0 (Function.update_same _ _ _)
           fun _ _ hne => Function.update_noteq hne _ _
       let w2 := w + w1
       have hw2 : (∑ i in s, w2 i) = 1 := by simp [w2, Finset.sum_add_distrib, hw, hw1]
-      have hw2s : s.affine_combination p w2 = p i0 := by
+      have hw2s : s.affine_combination k p w2 = p i0 := by
         simp [w2, ← Finset.weightedVsub_vadd_affineCombination, hs, hw1s]
       replace ha := ha s s w2 w1 hw2 hw1 (hw1s.symm ▸ hw2s)
       have hws : w2 i0 - w1 i0 = 0 := by
@@ -241,7 +241,7 @@ theorem affineIndependent_iff_eq_of_fintype_affineCombination_eq [Fintype ι] (p
       ∀ w1 w2 : ι → k,
         (∑ i, w1 i) = 1 →
           (∑ i, w2 i) = 1 →
-            Finset.univ.affineCombination p w1 = Finset.univ.affineCombination p w2 → w1 = w2 :=
+            Finset.univ.affineCombination k p w1 = Finset.univ.affineCombination k p w2 → w1 = w2 :=
   by
   rw [affineIndependent_iff_indicator_eq_of_affineCombination_eq]
   constructor
@@ -274,7 +274,7 @@ theorem AffineIndependent.units_lineMap {p : ι → P} (hp : AffineIndependent k
 
 theorem AffineIndependent.indicator_eq_of_affineCombination_eq {p : ι → P}
     (ha : AffineIndependent k p) (s₁ s₂ : Finset ι) (w₁ w₂ : ι → k) (hw₁ : (∑ i in s₁, w₁ i) = 1)
-    (hw₂ : (∑ i in s₂, w₂ i) = 1) (h : s₁.affineCombination p w₁ = s₂.affineCombination p w₂) :
+    (hw₂ : (∑ i in s₂, w₂ i) = 1) (h : s₁.affineCombination k p w₁ = s₂.affineCombination k p w₂) :
     Set.indicator (↑s₁) w₁ = Set.indicator (↑s₂) w₂ :=
   (affineIndependent_iff_indicator_eq_of_affineCombination_eq k p).1 ha s₁ s₂ w₁ w₂ hw₁ hw₂ h
 #align affine_independent.indicator_eq_of_affine_combination_eq AffineIndependent.indicator_eq_of_affineCombination_eq
@@ -521,7 +521,7 @@ theorem weightedVsub_mem_vectorSpan_pair {p : ι → P} (h : AffineIndependent k
     {s : Finset ι} (hw : (∑ i in s, w i) = 0) (hw₁ : (∑ i in s, w₁ i) = 1)
     (hw₂ : (∑ i in s, w₂ i) = 1) :
     s.weightedVsub p w ∈
-        vectorSpan k ({s.affineCombination p w₁, s.affineCombination p w₂} : Set P) ↔
+        vectorSpan k ({s.affineCombination k p w₁, s.affineCombination k p w₂} : Set P) ↔
       ∃ r : k, ∀ i ∈ s, w i = r * (w₁ i - w₂ i) :=
   by
   rw [mem_vectorSpan_pair]
@@ -551,10 +551,10 @@ two points. -/
 theorem affineCombination_mem_affineSpan_pair {p : ι → P} (h : AffineIndependent k p)
     {w w₁ w₂ : ι → k} {s : Finset ι} (hw : (∑ i in s, w i) = 1) (hw₁ : (∑ i in s, w₁ i) = 1)
     (hw₂ : (∑ i in s, w₂ i) = 1) :
-    s.affineCombination p w ∈ line[k, s.affineCombination p w₁, s.affineCombination p w₂] ↔
+    s.affineCombination k p w ∈ line[k, s.affineCombination k p w₁, s.affineCombination k p w₂] ↔
       ∃ r : k, ∀ i ∈ s, w i = r * (w₂ i - w₁ i) + w₁ i :=
   by
-  rw [← vsub_vadd (s.affine_combination p w) (s.affine_combination p w₁),
+  rw [← vsub_vadd (s.affine_combination k p w) (s.affine_combination k p w₁),
     AffineSubspace.vadd_mem_iff_mem_direction _ (left_mem_affineSpan_pair _ _ _),
     direction_affineSpan, s.affine_combination_vsub, Set.pair_comm,
     weightedVsub_mem_vectorSpan_pair h _ hw₂ hw₁]
@@ -771,7 +771,8 @@ sign. -/
 theorem sign_eq_of_affineCombination_mem_affineSpan_pair {p : ι → P} (h : AffineIndependent k p)
     {w w₁ w₂ : ι → k} {s : Finset ι} (hw : (∑ i in s, w i) = 1) (hw₁ : (∑ i in s, w₁ i) = 1)
     (hw₂ : (∑ i in s, w₂ i) = 1)
-    (hs : s.affineCombination p w ∈ line[k, s.affineCombination p w₁, s.affineCombination p w₂])
+    (hs :
+      s.affineCombination k p w ∈ line[k, s.affineCombination k p w₁, s.affineCombination k p w₂])
     {i j : ι} (hi : i ∈ s) (hj : j ∈ s) (hi0 : w₁ i = 0) (hj0 : w₁ j = 0)
     (hij : SignType.sign (w₂ i) = SignType.sign (w₂ j)) :
     SignType.sign (w i) = SignType.sign (w j) :=
@@ -790,7 +791,7 @@ theorem sign_eq_of_affineCombination_mem_affineSpan_single_lineMap {p : ι → P
     (h : AffineIndependent k p) {w : ι → k} {s : Finset ι} (hw : (∑ i in s, w i) = 1) {i₁ i₂ i₃ : ι}
     (h₁ : i₁ ∈ s) (h₂ : i₂ ∈ s) (h₃ : i₃ ∈ s) (h₁₂ : i₁ ≠ i₂) (h₁₃ : i₁ ≠ i₃) (h₂₃ : i₂ ≠ i₃)
     {c : k} (hc0 : 0 < c) (hc1 : c < 1)
-    (hs : s.affineCombination p w ∈ line[k, p i₁, AffineMap.lineMap (p i₂) (p i₃) c]) :
+    (hs : s.affineCombination k p w ∈ line[k, p i₁, AffineMap.lineMap (p i₂) (p i₃) c]) :
     SignType.sign (w i₂) = SignType.sign (w i₃) := by
   classical
     rw [← s.affine_combination_affine_combination_single_weights k p h₁, ←

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -160,16 +160,15 @@ theorem affineIndependent_set_iff_linearIndependent_vsub {s : Set P} {p₁ : P}
     let f : (fun p : P => (p -ᵥ p₁ : V)) '' (s \ {p₁}) → { x : s // x ≠ ⟨p₁, hp₁⟩ } := fun x =>
       ⟨⟨(x : V) +ᵥ p₁, Set.mem_of_mem_diff (hv x)⟩, fun hx =>
         Set.not_mem_of_mem_diff (hv x) (Subtype.ext_iff.1 hx)⟩
-    convert
-      h.comp f fun x1 x2 hx =>
+    convert h.comp f fun x1 x2 hx =>
         Subtype.ext (vadd_right_cancel p₁ (Subtype.ext_iff.1 (Subtype.ext_iff.1 hx)))
     ext v
     exact (vadd_vsub (v : V) p₁).symm
   · intro h
     let f : { x : s // x ≠ ⟨p₁, hp₁⟩ } → (fun p : P => (p -ᵥ p₁ : V)) '' (s \ {p₁}) := fun x =>
       ⟨((x : s) : P) -ᵥ p₁, ⟨x, ⟨⟨(x : s).property, fun hx => x.property (Subtype.ext hx)⟩, rfl⟩⟩⟩
-    convert
-      h.comp f fun x1 x2 hx => Subtype.ext (Subtype.ext (vsub_left_cancel (Subtype.ext_iff.1 hx)))
+    convert h.comp f fun x1 x2 hx =>
+        Subtype.ext (Subtype.ext (vsub_left_cancel (Subtype.ext_iff.1 hx)))
 #align affine_independent_set_iff_linear_independent_vsub affineIndependent_set_iff_linearIndependent_vsub
 
 /-- A set of nonzero vectors is linearly independent if and only if,
@@ -963,7 +962,7 @@ the points. -/
 theorem face_centroid_eq_centroid {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ}
     (h : fs.card = m + 1) : Finset.univ.centroid k (s.face h).points = fs.centroid k s.points :=
   by
-  convert (finset.univ.centroid_map k (fs.order_emb_of_fin h).toEmbedding s.points).symm
+  convert(finset.univ.centroid_map k (fs.order_emb_of_fin h).toEmbedding s.points).symm
   rw [← Finset.coe_inj, Finset.coe_map, Finset.coe_univ, Set.image_univ]
   simp
 #align affine.simplex.face_centroid_eq_centroid Affine.Simplex.face_centroid_eq_centroid

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -612,7 +612,7 @@ theorem exists_subset_affineIndependent_affineSpan_eq_top {s : Set P}
 
 variable (k V)
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem exists_affineIndependent (s : Set P) :
     ∃ (t : _)(_ : t ⊆ s), affineSpan k t = affineSpan k s ∧ AffineIndependent k (coe : t → P) :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

A PR analogous to #12338 and #12361: reformatting proofs following the multiple goals linter of #12339.

@@ -473,10 +473,11 @@ theorem exists_nontrivial_relation_sum_zero_of_not_affine_ind {t : Finset V}
       vsub_eq_sub, Finset.weightedVSubOfPoint_apply, sub_zero] at hwt
     let f : ∀ x : V, x ∈ t → k := fun x hx => w ⟨x, hx⟩
     refine' ⟨fun x => if hx : x ∈ t then f x hx else (0 : k), _, _, by use i; simp [hi]⟩
-    suffices (∑ e : V in t, dite (e ∈ t) (fun hx => f e hx • e) fun _ => 0) = 0 by
-      convert this
-      rename V => x
-      by_cases hx : x ∈ t <;> simp [hx]
+    on_goal 1 =>
+      suffices (∑ e : V in t, dite (e ∈ t) (fun hx => f e hx • e) fun _ => 0) = 0 by
+        convert this
+        rename V => x
+        by_cases hx : x ∈ t <;> simp [hx]
     all_goals
       simp only [Finset.sum_dite_of_true fun _ h => h, Finset.mk_coe, hwt, hw]
 #align exists_nontrivial_relation_sum_zero_of_not_affine_ind exists_nontrivial_relation_sum_zero_of_not_affine_ind

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -43,7 +43,6 @@ open scoped BigOperators Affine
 section AffineIndependent
 
 variable (k : Type*) {V : Type*} {P : Type*} [Ring k] [AddCommGroup V] [Module k V]
-
 variable [AffineSpace V P] {ι : Type*}
 
 /-- An indexed family is said to be affinely independent if no
@@ -565,7 +564,6 @@ end AffineIndependent
 section DivisionRing
 
 variable {k : Type*} {V : Type*} {P : Type*} [DivisionRing k] [AddCommGroup V] [Module k V]
-
 variable [AffineSpace V P] {ι : Type*}
 
 /-- An affinely independent set of points can be extended to such a
@@ -741,7 +739,6 @@ end DivisionRing
 section Ordered
 
 variable {k : Type*} {V : Type*} {P : Type*} [LinearOrderedRing k] [AddCommGroup V]
-
 variable [Module k V] [AffineSpace V P] {ι : Type*}
 
 attribute [local instance] LinearOrderedRing.decidableLT
@@ -793,7 +790,6 @@ end Ordered
 namespace Affine
 
 variable (k : Type*) {V : Type*} (P : Type*) [Ring k] [AddCommGroup V] [Module k V]
-
 variable [AffineSpace V P]
 
 /-- A `Simplex k P n` is a collection of `n + 1` affinely

Per the style guidelines, λ is disallowed in mathlib. This is close to exhaustive; I left some tactic code alone when it seemed to me that tactic could be upstreamed soon.

Notes

• In lines I was modifying anyway, I also converted => to ↦.
• Also contains some mild in-passing indentation fixes in Mathlib/Order/SupClosed.
• Some doc comments still contained Lean 3 syntax λ x, , which I also replaced.

@@ -965,7 +965,7 @@ theorem centroid_eq_iff [CharZero k] {n : ℕ} (s : Simplex k P n) {fs₁ fs₂
   specialize ha i
   have key : ∀ n : ℕ, (n : k) + 1 ≠ 0 := fun n h => by norm_cast at h
   -- we should be able to golf this to
-  -- `refine ⟨fun hi => decidable.by_contradiction (λ hni, _), ...⟩`,
+  -- `refine ⟨fun hi ↦ decidable.by_contradiction (fun hni ↦ ?_), ...⟩`,
   -- but for some unknown reason it doesn't work.
   constructor <;> intro hi <;> by_contra hni
   · simp [hni, hi, key] at ha

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

@@ -294,7 +294,7 @@ theorem AffineIndependent.comp_embedding {ι2 : Type*} (f : ι2 ↪ ι) {p : ι
       intro i2
       have h : ∃ i : ι2, f i = f i2 := ⟨i2, rfl⟩
       have hs : h.choose = i2 := f.injective h.choose_spec
-      simp_rw [dif_pos h, hs]
+      simp_rw [w', dif_pos h, hs]
     have hw's : ∑ i in fs', w' i = 0 := by
       rw [← hw, Finset.sum_map]
       simp [hw']
@@ -666,7 +666,7 @@ theorem AffineIndependent.affineIndependent_of_not_mem_span {p : ι → P} {i :
       have hwmi : wm i = -1 := by simp [wm, his.2]
       let w' : { y // y ≠ i } → k := fun x => wm x
       have hw' : ∑ x in s', w' x = 1 := by
-        simp_rw [Finset.sum_subtype_eq_sum_filter]
+        simp_rw [w', s', Finset.sum_subtype_eq_sum_filter]
         rw [← s.sum_filter_add_sum_filter_not (· ≠ i)] at hwm
         simp_rw [Classical.not_not] at hwm
         -- Porting note: this `erw` used to be part of the `simp_rw`
@@ -680,12 +680,12 @@ theorem AffineIndependent.affineIndependent_of_not_mem_span {p : ι → P} {i :
     · rw [not_and_or, Classical.not_not] at his
       let w' : { y // y ≠ i } → k := fun x => w x
       have hw' : ∑ x in s', w' x = 0 := by
-        simp_rw [Finset.sum_subtype_eq_sum_filter]
+        simp_rw [w', s', Finset.sum_subtype_eq_sum_filter]
         rw [Finset.sum_filter_of_ne, hw]
         rintro x hxs hwx rfl
         exact hwx (his.neg_resolve_left hxs)
       have hs' : s'.weightedVSub p' w' = (0 : V) := by
-        simp_rw [Finset.weightedVSub_subtype_eq_filter]
+        simp_rw [w', s', p', Finset.weightedVSub_subtype_eq_filter]
         rw [Finset.weightedVSub_filter_of_ne, hs]
         rintro x hxs hwx rfl
         exact hwx (his.neg_resolve_left hxs)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -111,7 +111,7 @@ theorem affineIndependent_iff_linearIndependent_vsub (p : ι → P) (i1 : ι) :
         set f2 : ι → V := fun x => f x • (p x -ᵥ p i1) with hf2def
         set g2 : { x // x ≠ i1 } → V := fun x => g x • (p x -ᵥ p i1)
         have hf2g2 : ∀ x : { x // x ≠ i1 }, f2 x = g2 x := by
-          simp only [hf2def]
+          simp only [g2, hf2def]
           refine' fun x => _
           rw [hfg]
         rw [Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero s2 f p hf (p i1),
@@ -220,14 +220,14 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
           fun _ _ hne => Function.update_noteq hne _ _
       let w2 := w + w1
       have hw2 : ∑ i in s, w2 i = 1 := by
-        simp_all only [Pi.add_apply, Finset.sum_add_distrib, zero_add]
+        simp_all only [w2, Pi.add_apply, Finset.sum_add_distrib, zero_add]
       have hw2s : s.affineCombination k p w2 = p i0 := by
-        simp_all only [← Finset.weightedVSub_vadd_affineCombination, zero_vadd]
+        simp_all only [w2, ← Finset.weightedVSub_vadd_affineCombination, zero_vadd]
       replace ha := ha s s w2 w1 hw2 hw1 (hw1s.symm ▸ hw2s)
       have hws : w2 i0 - w1 i0 = 0 := by
         rw [← Finset.mem_coe] at hi0
         rw [← Set.indicator_of_mem hi0 w2, ← Set.indicator_of_mem hi0 w1, ha, sub_self]
-      simpa using hws
+      simpa [w2] using hws
 #align affine_independent_iff_indicator_eq_of_affine_combination_eq affineIndependent_iff_indicator_eq_of_affineCombination_eq
 
 /-- A finite family is affinely independent if and only if any affine
@@ -321,7 +321,7 @@ protected theorem AffineIndependent.range {p : ι → P} (ha : AffineIndependent
   let fe : Set.range p ↪ ι := ⟨f, fun x₁ x₂ he => Subtype.ext (hf x₁ ▸ hf x₂ ▸ he ▸ rfl)⟩
   convert ha.comp_embedding fe
   ext
-  simp [hf]
+  simp [fe, hf]
 #align affine_independent.range AffineIndependent.range
 
 theorem affineIndependent_equiv {ι' : Type*} (e : ι ≃ ι') {p : ι' → P} :
@@ -581,7 +581,7 @@ theorem exists_subset_affineIndependent_affineSpan_eq_top {s : Set P}
     rw [Basis.coe_ofVectorSpace] at hsvi hsvt
     have h0 : ∀ v : V, v ∈ Basis.ofVectorSpaceIndex _ _ → v ≠ 0 := by
       intro v hv
-      simpa using hsv.ne_zero ⟨v, hv⟩
+      simpa [hsv] using hsv.ne_zero ⟨v, hv⟩
     rw [linearIndependent_set_iff_affineIndependent_vadd_union_singleton k h0 p₁] at hsvi
     exact
       ⟨{p₁} ∪ (fun v => v +ᵥ p₁) '' _, Set.empty_subset _, hsvi,
@@ -594,7 +594,7 @@ theorem exists_subset_affineIndependent_affineSpan_eq_top {s : Set P}
     have hsv := h.subset_extend (Set.subset_univ _)
     have h0 : ∀ v : V, v ∈ h.extend _ → v ≠ 0 := by
       intro v hv
-      simpa using bsv.ne_zero ⟨v, hv⟩
+      simpa [bsv] using bsv.ne_zero ⟨v, hv⟩
     rw [linearIndependent_set_iff_affineIndependent_vadd_union_singleton k h0 p₁] at hsvi
     refine' ⟨{p₁} ∪ (fun v => v +ᵥ p₁) '' h.extend (Set.subset_univ _), _, _⟩
     · refine' Set.Subset.trans _ (Set.union_subset_union_right _ (Set.image_subset _ hsv))
@@ -661,9 +661,9 @@ theorem AffineIndependent.affineIndependent_of_not_mem_span {p : ι → P} {i :
     by_cases his : i ∈ s ∧ w i ≠ 0
     · refine' False.elim (hi _)
       let wm : ι → k := -(w i)⁻¹ • w
-      have hms : s.weightedVSub p wm = (0 : V) := by simp [hs]
-      have hwm : ∑ i in s, wm i = 0 := by simp [← Finset.mul_sum, hw]
-      have hwmi : wm i = -1 := by simp [his.2]
+      have hms : s.weightedVSub p wm = (0 : V) := by simp [wm, hs]
+      have hwm : ∑ i in s, wm i = 0 := by simp [wm, ← Finset.mul_sum, hw]
+      have hwmi : wm i = -1 := by simp [wm, his.2]
       let w' : { y // y ≠ i } → k := fun x => wm x
       have hw' : ∑ x in s', w' x = 1 := by
         simp_rw [Finset.sum_subtype_eq_sum_filter]

Finset versions of the renamed lemmas are also added.

@@ -614,7 +614,7 @@ theorem exists_affineIndependent (s : Set P) :
   rw [linearIndependent_set_iff_affineIndependent_vadd_union_singleton k hb₀ p] at hb₃
   refine' ⟨{p} ∪ Equiv.vaddConst p '' b, _, _, hb₃⟩
   · apply Set.union_subset (Set.singleton_subset_iff.mpr hp)
-    rwa [← (Equiv.vaddConst p).subset_image' b s]
+    rwa [← (Equiv.vaddConst p).subset_symm_image b s]
   · rw [Equiv.coe_vaddConst_symm, ← vectorSpan_eq_span_vsub_set_right k hp] at hb₂
     apply AffineSubspace.ext_of_direction_eq
     · have : Submodule.span k b = Submodule.span k (insert 0 b) := by simp

This is a follow-up to #9215. It changes the following theorems and definitions:

• IsOpen.exists_subset_affineIndependent_span_eq_top
• IsConformalMap
• SimpleGraph.induce_connected_of_patches
• Submonoid.exists_list_of_mem_closure
• AddSubmonoid.exists_list_of_mem_closure
• AffineSubspace.mem_affineSpan_insert_iff
• AffineBasis.exists_affine_subbasis
• exists_affineIndependent
• LinearMap.mem_submoduleImage
• Basis.basis_singleton_iff
• atom_iff_nonzero_span
• finrank_eq_one_iff'
• Submodule.basis_of_pid_aux
• exists_linearIndependent_extension
• exists_linearIndependent
• countable_cover_nhdsWithin_of_sigma_compact
• mem_residual

Also deprecate ENNReal.exists_ne_top'.

@@ -606,7 +606,7 @@ theorem exists_subset_affineIndependent_affineSpan_eq_top {s : Set P}
 variable (k V)
 
 theorem exists_affineIndependent (s : Set P) :
-    ∃ (t : _) (_ : t ⊆ s), affineSpan k t = affineSpan k s ∧ AffineIndependent k ((↑) : t → P) := by
+    ∃ t ⊆ s, affineSpan k t = affineSpan k s ∧ AffineIndependent k ((↑) : t → P) := by
   rcases s.eq_empty_or_nonempty with (rfl | ⟨p, hp⟩)
   · exact ⟨∅, Set.empty_subset ∅, rfl, affineIndependent_of_subsingleton k _⟩
   obtain ⟨b, hb₁, hb₂, hb₃⟩ := exists_linearIndependent k ((Equiv.vaddConst p).symm '' s)

@@ -37,9 +37,8 @@ This file defines affinely independent families of points.
 
 noncomputable section
 
-open BigOperators Affine
-
-open Function
+open Finset Function
+open scoped BigOperators Affine
 
 section AffineIndependent
 
@@ -483,6 +482,8 @@ theorem exists_nontrivial_relation_sum_zero_of_not_affine_ind {t : Finset V}
       simp only [Finset.sum_dite_of_true fun _ h => h, Finset.mk_coe, hwt, hw]
 #align exists_nontrivial_relation_sum_zero_of_not_affine_ind exists_nontrivial_relation_sum_zero_of_not_affine_ind
 
+variable {s : Finset ι} {w w₁ w₂ : ι → k} {p : ι → V}
+
 /-- Viewing a module as an affine space modelled on itself, we can characterise affine independence
 in terms of linear combinations. -/
 theorem affineIndependent_iff {ι} {p : ι → V} :
@@ -491,6 +492,28 @@ theorem affineIndependent_iff {ι} {p : ι → V} :
   forall₃_congr fun s w hw => by simp [s.weightedVSub_eq_linear_combination hw]
 #align affine_independent_iff affineIndependent_iff
 
+lemma AffineIndependent.eq_zero_of_sum_eq_zero (hp : AffineIndependent k p)
+    (hw₀ : ∑ i in s, w i = 0) (hw₁ : ∑ i in s, w i • p i = 0) : ∀ i ∈ s, w i = 0 :=
+  affineIndependent_iff.1 hp _ _ hw₀ hw₁
+
+lemma AffineIndependent.eq_of_sum_eq_sum (hp : AffineIndependent k p)
+    (hw : ∑ i in s, w₁ i = ∑ i in s, w₂ i) (hwp : ∑ i in s, w₁ i • p i = ∑ i in s, w₂ i • p i) :
+    ∀ i ∈ s, w₁ i = w₂ i := by
+  refine fun i hi ↦ sub_eq_zero.1 (hp.eq_zero_of_sum_eq_zero (w := w₁ - w₂) ?_ ?_ _ hi) <;>
+    simpa [sub_mul, sub_smul, sub_eq_zero]
+
+lemma AffineIndependent.eq_zero_of_sum_eq_zero_subtype {s : Finset V}
+    (hp : AffineIndependent k ((↑) : s → V)) {w : V → k} (hw₀ : ∑ x in s, w x = 0)
+    (hw₁ : ∑ x in s, w x • x = 0) : ∀ x ∈ s, w x = 0 := by
+  rw [← sum_attach] at hw₀ hw₁
+  exact fun x hx ↦ hp.eq_zero_of_sum_eq_zero hw₀ hw₁ ⟨x, hx⟩ (mem_univ _)
+
+lemma AffineIndependent.eq_of_sum_eq_sum_subtype {s : Finset V}
+    (hp : AffineIndependent k ((↑) : s → V)) {w₁ w₂ : V → k} (hw : ∑ i in s, w₁ i = ∑ i in s, w₂ i)
+    (hwp : ∑ i in s, w₁ i • i = ∑ i in s, w₂ i • i) : ∀ i ∈ s, w₁ i = w₂ i := by
+  refine fun i hi => sub_eq_zero.1 (hp.eq_zero_of_sum_eq_zero_subtype (w := w₁ - w₂) ?_ ?_ _ hi) <;>
+    simpa [sub_mul, sub_smul, sub_eq_zero]
+
 /-- Given an affinely independent family of points, a weighted subtraction lies in the
 `vectorSpan` of two points given as affine combinations if and only if it is a weighted
 subtraction with weights a multiple of the difference between the weights of the two points. -/

Function.support is a very basic definition. Nevertheless, it is a pretty heavy import because it imports most objects a support lemma can be written about.

This PR reverses the dependencies between those objects and Function.support, so that the latter can become a much more lightweight import.

Only two import could not easily be reversed, namely the ones to Data.Set.Finite and Order.ConditionallyCompleteLattice.Basic, so I created two new files instead.

I credit:

• Yury for https://github.com/leanprover-community/mathlib/pull/6791
• Oliver for https://github.com/leanprover-community/mathlib/pull/7439

@@ -78,7 +78,7 @@ theorem affineIndependent_iff_of_fintype [Fintype ι] (p : ι → P) :
   · exact fun h w hw hs i => h Finset.univ w hw hs i (Finset.mem_univ _)
   · intro h s w hw hs i hi
     rw [Finset.weightedVSub_indicator_subset _ _ (Finset.subset_univ s)] at hs
-    rw [Set.sum_indicator_subset _ (Finset.subset_univ s)] at hw
+    rw [← Finset.sum_indicator_subset _ (Finset.subset_univ s)] at hw
     replace h := h ((↑s : Set ι).indicator w) hw hs i
     simpa [hi] using h
 #align affine_independent_iff_of_fintype affineIndependent_iff_of_fintype
@@ -191,8 +191,8 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
       ext i
       by_cases hi : i ∈ s1 ∪ s2
       · rw [← sub_eq_zero]
-        rw [Set.sum_indicator_subset _ (Finset.subset_union_left s1 s2)] at hw1
-        rw [Set.sum_indicator_subset _ (Finset.subset_union_right s1 s2)] at hw2
+        rw [← Finset.sum_indicator_subset _ (Finset.subset_union_left s1 s2)] at hw1
+        rw [← Finset.sum_indicator_subset _ (Finset.subset_union_right s1 s2)] at hw2
         have hws : (∑ i in s1 ∪ s2, (Set.indicator (↑s1) w1 - Set.indicator (↑s2) w2) i) = 0 := by
           simp [hw1, hw2]
         rw [Finset.affineCombination_indicator_subset _ _ (Finset.subset_union_left s1 s2),
@@ -242,9 +242,9 @@ theorem affineIndependent_iff_eq_of_fintype_affineCombination_eq [Fintype ι] (p
     simpa only [Set.indicator_univ, Finset.coe_univ] using h _ _ w1 w2 hw1 hw2 hweq
   · intro h s1 s2 w1 w2 hw1 hw2 hweq
     have hw1' : (∑ i, (s1 : Set ι).indicator w1 i) = 1 := by
-      rwa [Set.sum_indicator_subset _ (Finset.subset_univ s1)] at hw1
+      rwa [Finset.sum_indicator_subset _ (Finset.subset_univ s1)]
     have hw2' : (∑ i, (s2 : Set ι).indicator w2 i) = 1 := by
-      rwa [Set.sum_indicator_subset _ (Finset.subset_univ s2)] at hw2
+      rwa [Finset.sum_indicator_subset _ (Finset.subset_univ s2)]
     rw [Finset.affineCombination_indicator_subset w1 p (Finset.subset_univ s1),
       Finset.affineCombination_indicator_subset w2 p (Finset.subset_univ s2)] at hweq
     exact h _ _ hw1' hw2' hweq

Only Prop-values fields should be capitalized, not P-valued fields where P is Prop-valued.

Rather than fixing Nonempty := in constructors, I just deleted the line as the instance can almost always be found automatically.

@@ -551,7 +551,7 @@ theorem exists_subset_affineIndependent_affineSpan_eq_top {s : Set P}
     (h : AffineIndependent k (fun p => p : s → P)) :
     ∃ t : Set P, s ⊆ t ∧ AffineIndependent k (fun p => p : t → P) ∧ affineSpan k t = ⊤ := by
   rcases s.eq_empty_or_nonempty with (rfl | ⟨p₁, hp₁⟩)
-  · have p₁ : P := AddTorsor.Nonempty.some
+  · have p₁ : P := AddTorsor.nonempty.some
     let hsv := Basis.ofVectorSpace k V
     have hsvi := hsv.linearIndependent
     have hsvt := hsv.span_eq
@@ -805,7 +805,7 @@ instance [Inhabited P] : Inhabited (Simplex k P 0) :=
   ⟨mkOfPoint k default⟩
 
 instance nonempty : Nonempty (Simplex k P 0) :=
-  ⟨mkOfPoint k <| AddTorsor.Nonempty.some⟩
+  ⟨mkOfPoint k <| AddTorsor.nonempty.some⟩
 #align affine.simplex.nonempty Affine.Simplex.nonempty
 
 variable {k}

This holds a proof not a Prop, so should be lowercase.

@@ -777,7 +777,7 @@ variable [AffineSpace V P]
 independent points. -/
 structure Simplex (n : ℕ) where
   points : Fin (n + 1) → P
-  Independent : AffineIndependent k points
+  independent : AffineIndependent k points
 #align affine.simplex Affine.Simplex
 
 /-- A `Triangle k P` is a collection of three affinely independent points. -/
@@ -828,7 +828,7 @@ theorem ext_iff {n : ℕ} (s1 s2 : Simplex k P n) : s1 = s2 ↔ ∀ i, s1.points
 points. -/
 def face {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ} (h : fs.card = m + 1) :
     Simplex k P m :=
-  ⟨s.points ∘ fs.orderEmbOfFin h, s.Independent.comp_embedding (fs.orderEmbOfFin h).toEmbedding⟩
+  ⟨s.points ∘ fs.orderEmbOfFin h, s.independent.comp_embedding (fs.orderEmbOfFin h).toEmbedding⟩
 #align affine.simplex.face Affine.Simplex.face
 
 /-- The points of a face of a simplex are given by `mono_of_fin`. -/
@@ -865,7 +865,7 @@ theorem range_face_points {n : ℕ} (s : Simplex k P n) {fs : Finset (Fin (n + 1
 /-- Remap a simplex along an `Equiv` of index types. -/
 @[simps]
 def reindex {m n : ℕ} (s : Simplex k P m) (e : Fin (m + 1) ≃ Fin (n + 1)) : Simplex k P n :=
-  ⟨s.points ∘ e.symm, (affineIndependent_equiv e.symm).2 s.Independent⟩
+  ⟨s.points ∘ e.symm, (affineIndependent_equiv e.symm).2 s.independent⟩
 #align affine.simplex.reindex Affine.Simplex.reindex
 
 /-- Reindexing by `Equiv.refl` yields the original simplex. -/
@@ -933,7 +933,7 @@ theorem centroid_eq_iff [CharZero k] {n : ℕ} (s : Simplex k P n) {fs₁ fs₂
   rw [Finset.centroid_eq_affineCombination_fintype,
     Finset.centroid_eq_affineCombination_fintype] at h
   have ha :=
-    (affineIndependent_iff_indicator_eq_of_affineCombination_eq k s.points).1 s.Independent _ _ _ _
+    (affineIndependent_iff_indicator_eq_of_affineCombination_eq k s.points).1 s.independent _ _ _ _
       (fs₁.sum_centroidWeightsIndicator_eq_one_of_card_eq_add_one k h₁)
       (fs₂.sum_centroidWeightsIndicator_eq_one_of_card_eq_add_one k h₂) h
   simp_rw [Finset.coe_univ, Set.indicator_univ, Function.funext_iff,
@@ -967,8 +967,8 @@ theorem centroid_eq_of_range_eq {n : ℕ} {s₁ s₂ : Simplex k P n}
   rw [← Set.image_univ, ← Set.image_univ, ← Finset.coe_univ] at h
   exact
     Finset.univ.centroid_eq_of_inj_on_of_image_eq k _
-      (fun _ _ _ _ he => AffineIndependent.injective s₁.Independent he)
-      (fun _ _ _ _ he => AffineIndependent.injective s₂.Independent he) h
+      (fun _ _ _ _ he => AffineIndependent.injective s₁.independent he)
+      (fun _ _ _ _ he => AffineIndependent.injective s₂.independent he) h
 #align affine.simplex.centroid_eq_of_range_eq Affine.Simplex.centroid_eq_of_range_eq
 
 end Simplex

PR contents

This is the supremum of

• #8284
• #8056
• #8023
• #8332
• #8226 (already approved)
• #7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -688,7 +688,7 @@ theorem affineIndependent_of_ne_of_mem_of_mem_of_not_mem {s : AffineSubspace k P
   refine' hp₃ ((AffineSubspace.le_def' _ s).1 _ p₃ h)
   simp_rw [affineSpan_le, Set.image_subset_iff, Set.subset_def, Set.mem_preimage]
   intro x
-  fin_cases x <;> simp [hp₁, hp₂]
+  fin_cases x <;> simp (config := {decide := true}) [hp₁, hp₂]
 #align affine_independent_of_ne_of_mem_of_mem_of_not_mem affineIndependent_of_ne_of_mem_of_mem_of_not_mem
 
 /-- If distinct points `p₁` and `p₃` lie in `s` but `p₂` does not, the three points are affinely

This reverts commit f3695eb2.

@@ -402,7 +402,8 @@ theorem AffineEquiv.affineIndependent_iff {p : ι → P} (e : P ≃ᵃ[k] P₂)
 theorem AffineEquiv.affineIndependent_set_of_eq_iff {s : Set P} (e : P ≃ᵃ[k] P₂) :
     AffineIndependent k ((↑) : e '' s → P₂) ↔ AffineIndependent k ((↑) : s → P) := by
   have : e ∘ ((↑) : s → P) = ((↑) : e '' s → P₂) ∘ (e : P ≃ P₂).image s := rfl
-  rw [← e.affineIndependent_iff, this, affineIndependent_equiv]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [← e.affineIndependent_iff, this, affineIndependent_equiv]
 #align affine_equiv.affine_independent_set_of_eq_iff AffineEquiv.affineIndependent_set_of_eq_iff
 
 end Composition

This reverts commit 26eb2b0a.

@@ -402,8 +402,7 @@ theorem AffineEquiv.affineIndependent_iff {p : ι → P} (e : P ≃ᵃ[k] P₂)
 theorem AffineEquiv.affineIndependent_set_of_eq_iff {s : Set P} (e : P ≃ᵃ[k] P₂) :
     AffineIndependent k ((↑) : e '' s → P₂) ↔ AffineIndependent k ((↑) : s → P) := by
   have : e ∘ ((↑) : s → P) = ((↑) : e '' s → P₂) ∘ (e : P ≃ P₂).image s := rfl
-  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [← e.affineIndependent_iff, this, affineIndependent_equiv]
+  rw [← e.affineIndependent_iff, this, affineIndependent_equiv]
 #align affine_equiv.affine_independent_set_of_eq_iff AffineEquiv.affineIndependent_set_of_eq_iff
 
 end Composition

This includes all the changes from #7606.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -402,7 +402,8 @@ theorem AffineEquiv.affineIndependent_iff {p : ι → P} (e : P ≃ᵃ[k] P₂)
 theorem AffineEquiv.affineIndependent_set_of_eq_iff {s : Set P} (e : P ≃ᵃ[k] P₂) :
     AffineIndependent k ((↑) : e '' s → P₂) ↔ AffineIndependent k ((↑) : s → P) := by
   have : e ∘ ((↑) : s → P) = ((↑) : e '' s → P₂) ∘ (e : P ≃ P₂).image s := rfl
-  rw [← e.affineIndependent_iff, this, affineIndependent_equiv]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [← e.affineIndependent_iff, this, affineIndependent_equiv]
 #align affine_equiv.affine_independent_set_of_eq_iff AffineEquiv.affineIndependent_set_of_eq_iff
 
 end Composition

Purely cosmetic PR.

@@ -209,7 +209,7 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
           simp only [Set.indicator, Finset.mem_coe, ite_eq_right_iff]
           intro h
           by_contra
-          exact ( mt (@Set.mem_union_right _ i ↑s2 ↑s1) hi) h
+          exact (mt (@Set.mem_union_right _ i ↑s2 ↑s1) hi) h
         simp [h₁, h₂]
     · intro ha s w hw hs i0 hi0
       let w1 : ι → k := Function.update (Function.const ι 0) i0 1

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -737,7 +737,6 @@ theorem sign_eq_of_affineCombination_mem_affineSpan_pair {p : ι → P} (h : Aff
     SignType.sign (w i) = SignType.sign (w j) := by
   rw [affineCombination_mem_affineSpan_pair h hw hw₁ hw₂] at hs
   rcases hs with ⟨r, hr⟩
-  dsimp only at hr
   rw [hr i hi, hr j hj, hi0, hj0, add_zero, add_zero, sub_zero, sub_zero, sign_mul, sign_mul, hij]
 #align sign_eq_of_affine_combination_mem_affine_span_pair sign_eq_of_affineCombination_mem_affineSpan_pair
 

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -43,9 +43,9 @@ open Function
 
 section AffineIndependent
 
-variable (k : Type _) {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Module k V]
+variable (k : Type*) {V : Type*} {P : Type*} [Ring k] [AddCommGroup V] [Module k V]
 
-variable [AffineSpace V P] {ι : Type _}
+variable [AffineSpace V P] {ι : Type*}
 
 /-- An indexed family is said to be affinely independent if no
 nontrivial weighted subtractions (where the sum of weights is 0) are
@@ -285,7 +285,7 @@ protected theorem AffineIndependent.injective [Nontrivial k] {p : ι → P}
 /-- If a family is affinely independent, so is any subfamily given by
 composition of an embedding into index type with the original
 family. -/
-theorem AffineIndependent.comp_embedding {ι2 : Type _} (f : ι2 ↪ ι) {p : ι → P}
+theorem AffineIndependent.comp_embedding {ι2 : Type*} (f : ι2 ↪ ι) {p : ι → P}
     (ha : AffineIndependent k p) : AffineIndependent k (p ∘ f) := by
   classical
     intro fs w hw hs i0 hi0
@@ -325,7 +325,7 @@ protected theorem AffineIndependent.range {p : ι → P} (ha : AffineIndependent
   simp [hf]
 #align affine_independent.range AffineIndependent.range
 
-theorem affineIndependent_equiv {ι' : Type _} (e : ι ≃ ι') {p : ι' → P} :
+theorem affineIndependent_equiv {ι' : Type*} (e : ι ≃ ι') {p : ι' → P} :
     AffineIndependent k (p ∘ e) ↔ AffineIndependent k p := by
   refine' ⟨_, AffineIndependent.comp_embedding e.toEmbedding⟩
   intro h
@@ -355,7 +355,7 @@ theorem AffineIndependent.of_set_of_injective {p : ι → P}
 
 section Composition
 
-variable {V₂ P₂ : Type _} [AddCommGroup V₂] [Module k V₂] [AffineSpace V₂ P₂]
+variable {V₂ P₂ : Type*} [AddCommGroup V₂] [Module k V₂] [AffineSpace V₂ P₂]
 
 /-- If the image of a family of points in affine space under an affine transformation is affine-
 independent, then the original family of points is also affine-independent. -/
@@ -540,9 +540,9 @@ end AffineIndependent
 
 section DivisionRing
 
-variable {k : Type _} {V : Type _} {P : Type _} [DivisionRing k] [AddCommGroup V] [Module k V]
+variable {k : Type*} {V : Type*} {P : Type*} [DivisionRing k] [AddCommGroup V] [Module k V]
 
-variable [AffineSpace V P] {ι : Type _}
+variable [AffineSpace V P] {ι : Type*}
 
 /-- An affinely independent set of points can be extended to such a
 set that spans the whole space. -/
@@ -716,9 +716,9 @@ end DivisionRing
 
 section Ordered
 
-variable {k : Type _} {V : Type _} {P : Type _} [LinearOrderedRing k] [AddCommGroup V]
+variable {k : Type*} {V : Type*} {P : Type*} [LinearOrderedRing k] [AddCommGroup V]
 
-variable [Module k V] [AffineSpace V P] {ι : Type _}
+variable [Module k V] [AffineSpace V P] {ι : Type*}
 
 attribute [local instance] LinearOrderedRing.decidableLT
 
@@ -769,7 +769,7 @@ end Ordered
 
 namespace Affine
 
-variable (k : Type _) {V : Type _} (P : Type _) [Ring k] [AddCommGroup V] [Module k V]
+variable (k : Type*) {V : Type*} (P : Type*) [Ring k] [AddCommGroup V] [Module k V]
 
 variable [AffineSpace V P]
 
@@ -909,7 +909,7 @@ namespace Affine
 
 namespace Simplex
 
-variable {k : Type _} {V : Type _} {P : Type _} [DivisionRing k] [AddCommGroup V] [Module k V]
+variable {k : Type*} {V : Type*} {P : Type*} [DivisionRing k] [AddCommGroup V] [Module k V]
   [AffineSpace V P]
 
 /-- The centroid of a face of a simplex as the centroid of a subset of

This breaks a dependency cycle with Module.Free, which means we can immediately show that all vector spaces are free modules.

The lemmas are moved without modification in this PR. A subsequent PR can use the Module.Free results to golf the vector space ones, and deduplicate the API.

Co-authored-by: Oliver Nash <github@olivernash.org>

@@ -8,7 +8,7 @@ import Mathlib.Data.Fin.VecNotation
 import Mathlib.Data.Sign
 import Mathlib.LinearAlgebra.AffineSpace.Combination
 import Mathlib.LinearAlgebra.AffineSpace.AffineEquiv
-import Mathlib.LinearAlgebra.Basis
+import Mathlib.LinearAlgebra.Basis.VectorSpace
 
 #align_import linear_algebra.affine_space.independent from "leanprover-community/mathlib"@"2de9c37fa71dde2f1c6feff19876dd6a7b1519f0"
 

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Joseph Myers. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
-
-! This file was ported from Lean 3 source module linear_algebra.affine_space.independent
-! leanprover-community/mathlib commit 2de9c37fa71dde2f1c6feff19876dd6a7b1519f0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Finset.Sort
 import Mathlib.Data.Fin.VecNotation
@@ -15,6 +10,8 @@ import Mathlib.LinearAlgebra.AffineSpace.Combination
 import Mathlib.LinearAlgebra.AffineSpace.AffineEquiv
 import Mathlib.LinearAlgebra.Basis
 
+#align_import linear_algebra.affine_space.independent from "leanprover-community/mathlib"@"2de9c37fa71dde2f1c6feff19876dd6a7b1519f0"
+
 /-!
 # Affine independence
 

• Also remove most superfluous parentheses around big operators (∑, ∏ and variants).
• roughly the used regex: ([^a-zA-Zα-ωΑ-Ω'𝓝ℳ₀𝕂ₛ)]) \(([∑∏][^()∑∏]*,[^()∑∏:]*)\) ([⊂⊆=<≤]) replaced by $1 $2 $3

@@ -55,14 +55,14 @@ nontrivial weighted subtractions (where the sum of weights is 0) are
 0. -/
 def AffineIndependent (p : ι → P) : Prop :=
   ∀ (s : Finset ι) (w : ι → k),
-    (∑ i in s, w i) = 0 → s.weightedVSub p w = (0 : V) → ∀ i ∈ s, w i = 0
+    ∑ i in s, w i = 0 → s.weightedVSub p w = (0 : V) → ∀ i ∈ s, w i = 0
 #align affine_independent AffineIndependent
 
 /-- The definition of `AffineIndependent`. -/
 theorem affineIndependent_def (p : ι → P) :
     AffineIndependent k p ↔
       ∀ (s : Finset ι) (w : ι → k),
-        (∑ i in s, w i) = 0 → s.weightedVSub p w = (0 : V) → ∀ i ∈ s, w i = 0 :=
+        ∑ i in s, w i = 0 → s.weightedVSub p w = (0 : V) → ∀ i ∈ s, w i = 0 :=
   Iff.rfl
 #align affine_independent_def affineIndependent_def
 
@@ -76,7 +76,7 @@ only if no nontrivial weighted subtractions over `Finset.univ` (where
 the sum of the weights is 0) are 0. -/
 theorem affineIndependent_iff_of_fintype [Fintype ι] (p : ι → P) :
     AffineIndependent k p ↔
-      ∀ w : ι → k, (∑ i, w i) = 0 → Finset.univ.weightedVSub p w = (0 : V) → ∀ i, w i = 0 := by
+      ∀ w : ι → k, ∑ i, w i = 0 → Finset.univ.weightedVSub p w = (0 : V) → ∀ i, w i = 0 := by
   constructor
   · exact fun h w hw hs i => h Finset.univ w hw hs i (Finset.mem_univ _)
   · intro h s w hw hs i hi
@@ -103,7 +103,7 @@ theorem affineIndependent_iff_linearIndependent_vsub (p : ι → P) (i1 : ι) :
         dsimp only
         erw [dif_neg x.property, Subtype.coe_eta]
       rw [hfg]
-      have hf : (∑ ι in s2, f ι) = 0 := by
+      have hf : ∑ ι in s2, f ι = 0 := by
         rw [Finset.sum_insert
             (Finset.not_mem_map_subtype_of_not_property s (Classical.not_not.2 rfl)),
           Finset.sum_subtype_map_embedding fun x _ => (hfg x).symm]
@@ -184,8 +184,8 @@ have equal `Set.indicator`. -/
 theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P) :
     AffineIndependent k p ↔
       ∀ (s1 s2 : Finset ι) (w1 w2 : ι → k),
-        (∑ i in s1, w1 i) = 1 →
-          (∑ i in s2, w2 i) = 1 →
+        ∑ i in s1, w1 i = 1 →
+          ∑ i in s2, w2 i = 1 →
             s1.affineCombination k p w1 = s2.affineCombination k p w2 →
               Set.indicator (↑s1) w1 = Set.indicator (↑s2) w2 := by
   classical
@@ -216,14 +216,14 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
         simp [h₁, h₂]
     · intro ha s w hw hs i0 hi0
       let w1 : ι → k := Function.update (Function.const ι 0) i0 1
-      have hw1 : (∑ i in s, w1 i) = 1 := by
+      have hw1 : ∑ i in s, w1 i = 1 := by
         rw [Finset.sum_update_of_mem hi0]
         simp only [Finset.sum_const_zero, add_zero, const_apply]
       have hw1s : s.affineCombination k p w1 = p i0 :=
         s.affineCombination_of_eq_one_of_eq_zero w1 p hi0 (Function.update_same _ _ _)
           fun _ _ hne => Function.update_noteq hne _ _
       let w2 := w + w1
-      have hw2 : (∑ i in s, w2 i) = 1 := by
+      have hw2 : ∑ i in s, w2 i = 1 := by
         simp_all only [Pi.add_apply, Finset.sum_add_distrib, zero_add]
       have hw2s : s.affineCombination k p w2 = p i0 := by
         simp_all only [← Finset.weightedVSub_vadd_affineCombination, zero_vadd]
@@ -237,7 +237,7 @@ theorem affineIndependent_iff_indicator_eq_of_affineCombination_eq (p : ι → P
 /-- A finite family is affinely independent if and only if any affine
 combinations (with sum of weights 1) that evaluate to the same point are equal. -/
 theorem affineIndependent_iff_eq_of_fintype_affineCombination_eq [Fintype ι] (p : ι → P) :
-    AffineIndependent k p ↔ ∀ w1 w2 : ι → k, (∑ i, w1 i) = 1 → (∑ i, w2 i) = 1 →
+    AffineIndependent k p ↔ ∀ w1 w2 : ι → k, ∑ i, w1 i = 1 → ∑ i, w2 i = 1 →
     Finset.univ.affineCombination k p w1 = Finset.univ.affineCombination k p w2 → w1 = w2 := by
   rw [affineIndependent_iff_indicator_eq_of_affineCombination_eq]
   constructor
@@ -268,8 +268,8 @@ theorem AffineIndependent.units_lineMap {p : ι → P} (hp : AffineIndependent k
 #align affine_independent.units_line_map AffineIndependent.units_lineMap
 
 theorem AffineIndependent.indicator_eq_of_affineCombination_eq {p : ι → P}
-    (ha : AffineIndependent k p) (s₁ s₂ : Finset ι) (w₁ w₂ : ι → k) (hw₁ : (∑ i in s₁, w₁ i) = 1)
-    (hw₂ : (∑ i in s₂, w₂ i) = 1) (h : s₁.affineCombination k p w₁ = s₂.affineCombination k p w₂) :
+    (ha : AffineIndependent k p) (s₁ s₂ : Finset ι) (w₁ w₂ : ι → k) (hw₁ : ∑ i in s₁, w₁ i = 1)
+    (hw₂ : ∑ i in s₂, w₂ i = 1) (h : s₁.affineCombination k p w₁ = s₂.affineCombination k p w₂) :
     Set.indicator (↑s₁) w₁ = Set.indicator (↑s₂) w₂ :=
   (affineIndependent_iff_indicator_eq_of_affineCombination_eq k p).1 ha s₁ s₂ w₁ w₂ hw₁ hw₂ h
 #align affine_independent.indicator_eq_of_affine_combination_eq AffineIndependent.indicator_eq_of_affineCombination_eq
@@ -299,7 +299,7 @@ theorem AffineIndependent.comp_embedding {ι2 : Type _} (f : ι2 ↪ ι) {p : ι
       have h : ∃ i : ι2, f i = f i2 := ⟨i2, rfl⟩
       have hs : h.choose = i2 := f.injective h.choose_spec
       simp_rw [dif_pos h, hs]
-    have hw's : (∑ i in fs', w' i) = 0 := by
+    have hw's : ∑ i in fs', w' i = 0 := by
       rw [← hw, Finset.sum_map]
       simp [hw']
     have hs' : fs'.weightedVSub p w' = (0 : V) := by
@@ -424,7 +424,7 @@ theorem AffineIndependent.exists_mem_inter_of_exists_mem_inter_affineSpan [Nontr
   rcases hp0s2 with ⟨fs2, hfs2, w2, hw2, hp0s2⟩
   rw [affineIndependent_iff_indicator_eq_of_affineCombination_eq] at ha
   replace ha := ha fs1 fs2 w1 w2 hw1 hw2 (hp0s1 ▸ hp0s2)
-  have hnz : (∑ i in fs1, w1 i) ≠ 0 := hw1.symm ▸ one_ne_zero
+  have hnz : ∑ i in fs1, w1 i ≠ 0 := hw1.symm ▸ one_ne_zero
   rcases Finset.exists_ne_zero_of_sum_ne_zero hnz with ⟨i, hifs1, hinz⟩
   simp_rw [← Set.indicator_of_mem (Finset.mem_coe.2 hifs1) w1, ha] at hinz
   use i, hfs1 hifs1
@@ -468,7 +468,7 @@ theorem AffineIndependent.not_mem_affineSpan_diff [Nontrivial k] {p : ι → P}
 
 theorem exists_nontrivial_relation_sum_zero_of_not_affine_ind {t : Finset V}
     (h : ¬AffineIndependent k ((↑) : t → V)) :
-    ∃ f : V → k, (∑ e in t, f e • e) = 0 ∧ (∑ e in t, f e) = 0 ∧ ∃ x ∈ t, f x ≠ 0 := by
+    ∃ f : V → k, ∑ e in t, f e • e = 0 ∧ ∑ e in t, f e = 0 ∧ ∃ x ∈ t, f x ≠ 0 := by
   classical
     rw [affineIndependent_iff_of_fintype] at h
     simp only [exists_prop, not_forall] at h
@@ -489,7 +489,7 @@ theorem exists_nontrivial_relation_sum_zero_of_not_affine_ind {t : Finset V}
 in terms of linear combinations. -/
 theorem affineIndependent_iff {ι} {p : ι → V} :
     AffineIndependent k p ↔
-      ∀ (s : Finset ι) (w : ι → k), s.sum w = 0 → (∑ e in s, w e • p e) = 0 → ∀ e ∈ s, w e = 0 :=
+      ∀ (s : Finset ι) (w : ι → k), s.sum w = 0 → ∑ e in s, w e • p e = 0 → ∀ e ∈ s, w e = 0 :=
   forall₃_congr fun s w hw => by simp [s.weightedVSub_eq_linear_combination hw]
 #align affine_independent_iff affineIndependent_iff
 
@@ -497,8 +497,8 @@ theorem affineIndependent_iff {ι} {p : ι → V} :
 `vectorSpan` of two points given as affine combinations if and only if it is a weighted
 subtraction with weights a multiple of the difference between the weights of the two points. -/
 theorem weightedVSub_mem_vectorSpan_pair {p : ι → P} (h : AffineIndependent k p) {w w₁ w₂ : ι → k}
-    {s : Finset ι} (hw : (∑ i in s, w i) = 0) (hw₁ : (∑ i in s, w₁ i) = 1)
-    (hw₂ : (∑ i in s, w₂ i) = 1) :
+    {s : Finset ι} (hw : ∑ i in s, w i = 0) (hw₁ : ∑ i in s, w₁ i = 1)
+    (hw₂ : ∑ i in s, w₂ i = 1) :
     s.weightedVSub p w ∈
         vectorSpan k ({s.affineCombination k p w₁, s.affineCombination k p w₂} : Set P) ↔
       ∃ r : k, ∀ i ∈ s, w i = r * (w₁ i - w₂ i) := by
@@ -527,8 +527,8 @@ span of two points given as affine combinations if and only if it is an affine c
 with weights those of one point plus a multiple of the difference between the weights of the
 two points. -/
 theorem affineCombination_mem_affineSpan_pair {p : ι → P} (h : AffineIndependent k p)
-    {w w₁ w₂ : ι → k} {s : Finset ι} (_ : (∑ i in s, w i) = 1) (hw₁ : (∑ i in s, w₁ i) = 1)
-    (hw₂ : (∑ i in s, w₂ i) = 1) :
+    {w w₁ w₂ : ι → k} {s : Finset ι} (_ : ∑ i in s, w i = 1) (hw₁ : ∑ i in s, w₁ i = 1)
+    (hw₂ : ∑ i in s, w₂ i = 1) :
     s.affineCombination k p w ∈ line[k, s.affineCombination k p w₁, s.affineCombination k p w₂] ↔
       ∃ r : k, ∀ i ∈ s, w i = r * (w₂ i - w₁ i) + w₁ i := by
   rw [← vsub_vadd (s.affineCombination k p w) (s.affineCombination k p w₁),
@@ -641,10 +641,10 @@ theorem AffineIndependent.affineIndependent_of_not_mem_span {p : ι → P} {i :
     · refine' False.elim (hi _)
       let wm : ι → k := -(w i)⁻¹ • w
       have hms : s.weightedVSub p wm = (0 : V) := by simp [hs]
-      have hwm : (∑ i in s, wm i) = 0 := by simp [← Finset.mul_sum, hw]
+      have hwm : ∑ i in s, wm i = 0 := by simp [← Finset.mul_sum, hw]
       have hwmi : wm i = -1 := by simp [his.2]
       let w' : { y // y ≠ i } → k := fun x => wm x
-      have hw' : (∑ x in s', w' x) = 1 := by
+      have hw' : ∑ x in s', w' x = 1 := by
         simp_rw [Finset.sum_subtype_eq_sum_filter]
         rw [← s.sum_filter_add_sum_filter_not (· ≠ i)] at hwm
         simp_rw [Classical.not_not] at hwm
@@ -658,7 +658,7 @@ theorem AffineIndependent.affineIndependent_of_not_mem_span {p : ι → P} {i :
       exact affineCombination_mem_affineSpan hw' p'
     · rw [not_and_or, Classical.not_not] at his
       let w' : { y // y ≠ i } → k := fun x => w x
-      have hw' : (∑ x in s', w' x) = 0 := by
+      have hw' : ∑ x in s', w' x = 0 := by
         simp_rw [Finset.sum_subtype_eq_sum_filter]
         rw [Finset.sum_filter_of_ne, hw]
         rintro x hxs hwx rfl
@@ -731,8 +731,8 @@ coefficients in the first point in the span are zero and those in the second poi
 have the same sign. Then the coefficients in the combination lying in the span have the same
 sign. -/
 theorem sign_eq_of_affineCombination_mem_affineSpan_pair {p : ι → P} (h : AffineIndependent k p)
-    {w w₁ w₂ : ι → k} {s : Finset ι} (hw : (∑ i in s, w i) = 1) (hw₁ : (∑ i in s, w₁ i) = 1)
-    (hw₂ : (∑ i in s, w₂ i) = 1)
+    {w w₁ w₂ : ι → k} {s : Finset ι} (hw : ∑ i in s, w i = 1) (hw₁ : ∑ i in s, w₁ i = 1)
+    (hw₂ : ∑ i in s, w₂ i = 1)
     (hs :
       s.affineCombination k p w ∈ line[k, s.affineCombination k p w₁, s.affineCombination k p w₂])
     {i j : ι} (hi : i ∈ s) (hj : j ∈ s) (hi0 : w₁ i = 0) (hj0 : w₁ j = 0)
@@ -749,7 +749,7 @@ the span of one point of that family and a combination of another two points of
 by `lineMap` with coefficient between 0 and 1. Then the coefficients of those two points in the
 combination lying in the span have the same sign. -/
 theorem sign_eq_of_affineCombination_mem_affineSpan_single_lineMap {p : ι → P}
-    (h : AffineIndependent k p) {w : ι → k} {s : Finset ι} (hw : (∑ i in s, w i) = 1) {i₁ i₂ i₃ : ι}
+    (h : AffineIndependent k p) {w : ι → k} {s : Finset ι} (hw : ∑ i in s, w i = 1) {i₁ i₂ i₃ : ι}
     (h₁ : i₁ ∈ s) (h₂ : i₂ ∈ s) (h₃ : i₃ ∈ s) (h₁₂ : i₁ ≠ i₂) (h₁₃ : i₁ ≠ i₃) (h₂₃ : i₂ ≠ i₃)
     {c : k} (hc0 : 0 < c) (hc1 : c < 1)
     (hs : s.affineCombination k p w ∈ line[k, p i₁, AffineMap.lineMap (p i₂) (p i₃) c]) :

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -262,7 +262,7 @@ independent.
 This is the affine version of `LinearIndependent.units_smul`. -/
 theorem AffineIndependent.units_lineMap {p : ι → P} (hp : AffineIndependent k p) (j : ι)
     (w : ι → Units k) : AffineIndependent k fun i => AffineMap.lineMap (p j) (p i) (w i : k) := by
-  rw [affineIndependent_iff_linearIndependent_vsub k _ j] at hp⊢
+  rw [affineIndependent_iff_linearIndependent_vsub k _ j] at hp ⊢
   simp only [AffineMap.lineMap_vsub_left, AffineMap.coe_const, AffineMap.lineMap_same, const_apply]
   exact hp.units_smul fun i => w i
 #align affine_independent.units_line_map AffineIndependent.units_lineMap

This renames

• decidable_eq to decidableEq
• decidable_lt to decidableLT
• decidable_le to decidableLE
• decidableLT_of_decidableLE to decidableLTOfDecidableLE
• decidableEq_of_decidableLE to decidableEqOfDecidableLE

These fields are data not proofs, so they should be lowerCamelCased.

@@ -723,7 +723,7 @@ variable {k : Type _} {V : Type _} {P : Type _} [LinearOrderedRing k] [AddCommGr
 
 variable [Module k V] [AffineSpace V P] {ι : Type _}
 
-attribute [local instance] LinearOrderedRing.decidable_lt
+attribute [local instance] LinearOrderedRing.decidableLT
 
 /-- Given an affinely independent family of points, suppose that an affine combination lies in
 the span of two points given as affine combinations, and suppose that, for two indices, the

We make sure that the canonical path from NonAssocSemiring to Ring passes through Semiring, as this is a path which is followed all the time in linear algebra where the defining semilinear map σ : R →+* S depends on the NonAssocSemiring structure of R and S while the module definition depends on the Semiring structure.

Tt is not currently possible to adjust priorities by hand (see lean4#2115). Instead, the last declared instance is used, so we make sure that Semiring is declared after NonAssocRing, so that Semiring -> NonAssocSemiring is tried before NonAssocRing -> NonAssocSemiring.

@@ -50,7 +50,6 @@ variable (k : Type _) {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Modul
 
 variable [AffineSpace V P] {ι : Type _}
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- An indexed family is said to be affinely independent if no
 nontrivial weighted subtractions (where the sum of weights is 0) are
 0. -/
@@ -59,7 +58,6 @@ def AffineIndependent (p : ι → P) : Prop :=
     (∑ i in s, w i) = 0 → s.weightedVSub p w = (0 : V) → ∀ i ∈ s, w i = 0
 #align affine_independent AffineIndependent
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- The definition of `AffineIndependent`. -/
 theorem affineIndependent_def (p : ι → P) :
     AffineIndependent k p ↔
@@ -73,7 +71,6 @@ theorem affineIndependent_of_subsingleton [Subsingleton ι] (p : ι → P) : Aff
   fun _ _ h _ i hi => Fintype.eq_of_subsingleton_of_sum_eq h i hi
 #align affine_independent_of_subsingleton affineIndependent_of_subsingleton
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- A family indexed by a `Fintype` is affinely independent if and
 only if no nontrivial weighted subtractions over `Finset.univ` (where
 the sum of the weights is 0) are 0. -/
@@ -89,7 +86,6 @@ theorem affineIndependent_iff_of_fintype [Fintype ι] (p : ι → P) :
     simpa [hi] using h
 #align affine_independent_iff_of_fintype affineIndependent_iff_of_fintype
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- A family is affinely independent if and only if the differences
 from a base point in that family are linearly independent. -/
 theorem affineIndependent_iff_linearIndependent_vsub (p : ι → P) (i1 : ι) :
@@ -289,7 +285,6 @@ protected theorem AffineIndependent.injective [Nontrivial k] {p : ι → P}
   simp_all only [ne_eq]
 #align affine_independent.injective AffineIndependent.injective
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- If a family is affinely independent, so is any subfamily given by
 composition of an embedding into index type with the original
 family. -/
@@ -498,7 +493,6 @@ theorem affineIndependent_iff {ι} {p : ι → V} :
   forall₃_congr fun s w hw => by simp [s.weightedVSub_eq_linear_combination hw]
 #align affine_independent_iff affineIndependent_iff
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- Given an affinely independent family of points, a weighted subtraction lies in the
 `vectorSpan` of two points given as affine combinations if and only if it is a weighted
 subtraction with weights a multiple of the difference between the weights of the two points. -/
@@ -634,7 +628,6 @@ theorem affineIndependent_of_ne {p₁ p₂ : P} (h : p₁ ≠ p₂) : AffineInde
 
 variable {k}
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- If all but one point of a family are affinely independent, and that point does not lie in
 the affine span of that family, the family is affinely independent. -/
 theorem AffineIndependent.affineIndependent_of_not_mem_span {p : ι → P} {i : ι}

Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>