topology.algebra.module.basic
⟷
Mathlib.Topology.Algebra.Module.Basic
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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(last sync)
to_span_singleton
to topological spaces (#19116)
This should be straightforward to forward-port, as it involves deleting one hunk and pasting in another.
@@ -1003,6 +1003,37 @@ lemma smul_right_comp [has_continuous_mul R₁] {x : M₂} {c : R₁} :
smul_right (1 : R₁ →L[R₁] R₁) (c • x) :=
by { ext, simp [mul_smul] }
+section to_span_singleton
+variables (R₁)
+variables [has_continuous_smul R₁ M₁]
+
+/-- Given an element `x` of a topological space `M` over a semiring `R`, the natural continuous
+linear map from `R` to `M` by taking multiples of `x`.-/
+def to_span_singleton (x : M₁) : R₁ →L[R₁] M₁ :=
+{ to_linear_map := linear_map.to_span_singleton R₁ M₁ x,
+ cont := continuous_id.smul continuous_const }
+
+lemma to_span_singleton_apply (x : M₁) (r : R₁) : to_span_singleton R₁ x r = r • x :=
+rfl
+
+lemma to_span_singleton_add [has_continuous_add M₁] (x y : M₁) :
+ to_span_singleton R₁ (x + y) = to_span_singleton R₁ x + to_span_singleton R₁ y :=
+by { ext1, simp [to_span_singleton_apply], }
+
+lemma to_span_singleton_smul' {α} [monoid α] [distrib_mul_action α M₁]
+ [has_continuous_const_smul α M₁]
+ [smul_comm_class R₁ α M₁] (c : α) (x : M₁) :
+ to_span_singleton R₁ (c • x) = c • to_span_singleton R₁ x :=
+by { ext1, rw [to_span_singleton_apply, smul_apply, to_span_singleton_apply, smul_comm], }
+
+/-- A special case of `to_span_singleton_smul'` for when `R` is commutative. -/
+lemma to_span_singleton_smul (R) {M₁} [comm_semiring R] [add_comm_monoid M₁] [module R M₁]
+ [topological_space R] [topological_space M₁] [has_continuous_smul R M₁] (c : R) (x : M₁) :
+ to_span_singleton R (c • x) = c • to_span_singleton R x :=
+to_span_singleton_smul' R c x
+
+end to_span_singleton
+
end semiring
section pi
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comp_of_eq lemmas
about how (I think) we should better formulate composition lemmas of properties of functions.comp_of_eq lemmas
: exactly the same problems happen in Lean 4.smooth_iff_proj_smooth -> smooth_prod_iff
differentiable_at.fderiv_within_prod -> differentiable_within_at.fderiv_within_prod
path_connected_space
instance of the tangent space. This instance is sufficient to compile sphere-eversion, without any normed_space
instances on the tangent space (which are not the canonical structure on the tangent space).@@ -955,6 +955,19 @@ lemma range_coprod [module R₁ M₂] [module R₁ M₃] [has_continuous_add M
range (f₁.coprod f₂) = range f₁ ⊔ range f₂ :=
linear_map.range_coprod _ _
+lemma comp_fst_add_comp_snd [module R₁ M₂] [module R₁ M₃] [has_continuous_add M₃]
+ (f : M₁ →L[R₁] M₃) (g : M₂ →L[R₁] M₃) :
+ f.comp (continuous_linear_map.fst R₁ M₁ M₂) +
+ g.comp (continuous_linear_map.snd R₁ M₁ M₂) =
+ f.coprod g :=
+rfl
+
+
+lemma coprod_inl_inr [has_continuous_add M₁] [has_continuous_add M'₁] :
+ (continuous_linear_map.inl R₁ M₁ M'₁).coprod (continuous_linear_map.inr R₁ M₁ M'₁) =
+ continuous_linear_map.id R₁ (M₁ × M'₁) :=
+by { apply coe_injective, apply linear_map.coprod_inl_inr }
+
section
variables {R S : Type*} [semiring R] [semiring S] [module R M₁] [module R M₂] [module R S]
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(first ported)
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -1828,7 +1828,7 @@ theorem smulRight_one_pow [TopologicalSpace R] [TopologicalRing R] (c : R) (n :
by
induction' n with n ihn
· ext; simp
- · rw [pow_succ, ihn, mul_def, smul_right_comp, smul_eq_mul, pow_succ']
+ · rw [pow_succ', ihn, mul_def, smul_right_comp, smul_eq_mul, pow_succ]
#align continuous_linear_map.smul_right_one_pow ContinuousLinearMap.smulRight_one_pow
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -105,14 +105,14 @@ theorem Submodule.eq_top_of_nonempty_interior' [NeBot (𝓝[{x : R | IsUnit x}]
by
rcases hs with ⟨y, hy⟩
refine' Submodule.eq_top_iff'.2 fun x => _
- rw [mem_interior_iff_mem_nhds] at hy
+ rw [mem_interior_iff_mem_nhds] at hy
have : tendsto (fun c : R => y + c • x) (𝓝[{x : R | IsUnit x}] 0) (𝓝 (y + (0 : R) • x)) :=
tendsto_const_nhds.add ((tendsto_nhdsWithin_of_tendsto_nhds tendsto_id).smul tendsto_const_nhds)
- rw [zero_smul, add_zero] at this
+ rw [zero_smul, add_zero] at this
obtain ⟨_, hu : y + _ • _ ∈ s, u, rfl⟩ :=
nonempty_of_mem (inter_mem (mem_map.1 (this hy)) self_mem_nhdsWithin)
have hy' : y ∈ ↑s := mem_of_mem_nhds hy
- rwa [s.add_mem_iff_right hy', ← Units.smul_def, s.smul_mem_iff' u] at hu
+ rwa [s.add_mem_iff_right hy', ← Units.smul_def, s.smul_mem_iff' u] at hu
#align submodule.eq_top_of_nonempty_interior' Submodule.eq_top_of_nonempty_interior'
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -299,11 +299,16 @@ theorem LinearMap.continuous_on_pi {ι : Type _} {R : Type _} {M : Type _} [Fini
by
cases nonempty_fintype ι
classical
+ -- for the proof, write `f` in the standard basis, and use that each coordinate is a continuous
+ -- function.
+ have : (f : (ι → R) → M) = fun x => ∑ i : ι, x i • f fun j => if i = j then 1 else 0 := by ext x;
+ exact f.pi_apply_eq_sum_univ x
+ rw [this]
+ refine' continuous_finset_sum _ fun i hi => _
+ exact (continuous_apply i).smul continuous_const
#align linear_map.continuous_on_pi LinearMap.continuous_on_pi
-/
--- for the proof, write `f` in the standard basis, and use that each coordinate is a continuous
--- function.
end Pi
#print ContinuousLinearMap /-
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -299,16 +299,11 @@ theorem LinearMap.continuous_on_pi {ι : Type _} {R : Type _} {M : Type _} [Fini
by
cases nonempty_fintype ι
classical
- -- for the proof, write `f` in the standard basis, and use that each coordinate is a continuous
- -- function.
- have : (f : (ι → R) → M) = fun x => ∑ i : ι, x i • f fun j => if i = j then 1 else 0 := by ext x;
- exact f.pi_apply_eq_sum_univ x
- rw [this]
- refine' continuous_finset_sum _ fun i hi => _
- exact (continuous_apply i).smul continuous_const
#align linear_map.continuous_on_pi LinearMap.continuous_on_pi
-/
+-- for the proof, write `f` in the standard basis, and use that each coordinate is a continuous
+-- function.
end Pi
#print ContinuousLinearMap /-
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -415,7 +415,7 @@ instance (priority := 100) [s : ContinuousSemilinearEquivClass F σ M M₂] :
ContinuousSemilinearMapClass F σ M M₂ :=
{ s with
coe := (coe : F → M → M₂)
- coe_injective' := @FunLike.coe_injective F _ _ _ }
+ coe_injective' := @DFunLike.coe_injective F _ _ _ }
end ContinuousSemilinearEquivClass
@@ -509,7 +509,7 @@ theorem coe_injective : Function.Injective (coe : (M₁ →SL[σ₁₂] M₂)
instance : ContinuousSemilinearMapClass (M₁ →SL[σ₁₂] M₂) σ₁₂ M₁ M₂
where
coe f := f.toFun
- coe_injective' f g h := coe_injective (FunLike.coe_injective h)
+ coe_injective' f g h := coe_injective (DFunLike.coe_injective h)
map_add f := map_add f.toLinearMap
map_continuous f := f.2
map_smulₛₗ f := f.toLinearMap.map_smul'
@@ -558,7 +558,7 @@ theorem coe_inj {f g : M₁ →SL[σ₁₂] M₂} : (f : M₁ →ₛₗ[σ₁₂
#print ContinuousLinearMap.coeFn_injective /-
theorem coeFn_injective : @Function.Injective (M₁ →SL[σ₁₂] M₂) (M₁ → M₂) coeFn :=
- FunLike.coe_injective
+ DFunLike.coe_injective
#align continuous_linear_map.coe_fn_injective ContinuousLinearMap.coeFn_injective
-/
@@ -582,13 +582,13 @@ initialize_simps_projections ContinuousLinearMap (to_linear_map_to_fun → apply
#print ContinuousLinearMap.ext /-
@[ext]
theorem ext {f g : M₁ →SL[σ₁₂] M₂} (h : ∀ x, f x = g x) : f = g :=
- FunLike.ext f g h
+ DFunLike.ext f g h
#align continuous_linear_map.ext ContinuousLinearMap.ext
-/
#print ContinuousLinearMap.ext_iff /-
theorem ext_iff {f g : M₁ →SL[σ₁₂] M₂} : f = g ↔ ∀ x, f x = g x :=
- FunLike.ext_iff
+ DFunLike.ext_iff
#align continuous_linear_map.ext_iff ContinuousLinearMap.ext_iff
-/
@@ -611,7 +611,7 @@ theorem coe_copy (f : M₁ →SL[σ₁₂] M₂) (f' : M₁ → M₂) (h : f' =
#print ContinuousLinearMap.copy_eq /-
theorem copy_eq (f : M₁ →SL[σ₁₂] M₂) (f' : M₁ → M₂) (h : f' = ⇑f) : f.copy f' h = f :=
- FunLike.ext' h
+ DFunLike.ext' h
#align continuous_linear_map.copy_eq ContinuousLinearMap.copy_eq
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -816,7 +816,7 @@ instance uniqueOfRight [Subsingleton M₂] : Unique (M₁ →SL[σ₁₂] M₂)
-/
#print ContinuousLinearMap.exists_ne_zero /-
-theorem exists_ne_zero {f : M₁ →SL[σ₁₂] M₂} (hf : f ≠ 0) : ∃ x, f x ≠ 0 := by by_contra' h;
+theorem exists_ne_zero {f : M₁ →SL[σ₁₂] M₂} (hf : f ≠ 0) : ∃ x, f x ≠ 0 := by by_contra! h;
exact hf (ContinuousLinearMap.ext h)
#align continuous_linear_map.exists_ne_zero ContinuousLinearMap.exists_ne_zero
-/
@@ -3164,11 +3164,11 @@ def ClosedComplemented (p : Submodule R M) : Prop :=
#align submodule.closed_complemented Submodule.ClosedComplemented
-/
-#print Submodule.ClosedComplemented.has_closed_complement /-
-theorem ClosedComplemented.has_closed_complement {p : Submodule R M} [T1Space p]
+#print Submodule.ClosedComplemented.exists_isClosed_isCompl /-
+theorem ClosedComplemented.exists_isClosed_isCompl {p : Submodule R M} [T1Space p]
(h : ClosedComplemented p) : ∃ (q : Submodule R M) (hq : IsClosed (q : Set M)), IsCompl p q :=
Exists.elim h fun f hf => ⟨ker f, f.isClosed_ker, LinearMap.isCompl_of_proj hf⟩
-#align submodule.closed_complemented.has_closed_complement Submodule.ClosedComplemented.has_closed_complement
+#align submodule.closed_complemented.has_closed_complement Submodule.ClosedComplemented.exists_isClosed_isCompl
-/
#print Submodule.ClosedComplemented.isClosed /-
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -4,14 +4,14 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov, Frédéric Dupuis,
Heather Macbeth
-/
-import Mathbin.Topology.Algebra.Ring.Basic
-import Mathbin.Topology.Algebra.MulAction
-import Mathbin.Topology.Algebra.UniformGroup
-import Mathbin.Topology.ContinuousFunction.Basic
-import Mathbin.Topology.UniformSpace.UniformEmbedding
-import Mathbin.Algebra.Algebra.Basic
-import Mathbin.LinearAlgebra.Projection
-import Mathbin.LinearAlgebra.Pi
+import Topology.Algebra.Ring.Basic
+import Topology.Algebra.MulAction
+import Topology.Algebra.UniformGroup
+import Topology.ContinuousFunction.Basic
+import Topology.UniformSpace.UniformEmbedding
+import Algebra.Algebra.Basic
+import LinearAlgebra.Projection
+import LinearAlgebra.Pi
#align_import topology.algebra.module.basic from "leanprover-community/mathlib"@"6285167a053ad0990fc88e56c48ccd9fae6550eb"
mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504
@@ -735,7 +735,7 @@ instance : MulAction S₂ (M₁ →SL[σ₁₂] M₂)
where
smul c f := ⟨c • f, (f.2.const_smul _ : Continuous fun x => c • f x)⟩
one_smul f := ext fun x => one_smul _ _
- mul_smul a b f := ext fun x => mul_smul _ _ _
+ hMul_smul a b f := ext fun x => hMul_smul _ _ _
#print ContinuousLinearMap.smul_apply /-
theorem smul_apply (c : S₂) (f : M₁ →SL[σ₁₂] M₂) (x : M₁) : (c • f) x = c • f x :=
@@ -2749,7 +2749,7 @@ instance automorphismGroup : Group (M₁ ≃L[R₁] M₁)
mul_assoc f g h := by ext; rfl
mul_one f := by ext; rfl
one_mul f := by ext; rfl
- mul_left_inv f := by ext; exact f.left_inv x
+ hMul_left_inv f := by ext; exact f.left_inv x
#align continuous_linear_equiv.automorphism_group ContinuousLinearEquiv.automorphismGroup
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f
@@ -3132,7 +3132,7 @@ theorem to_ring_inverse (e : M ≃L[R] M₂) (f : M →L[R] M₂) :
· suffices ¬IsUnit ((e.symm : M₂ →L[R] M).comp f) by simp [this, h₁]
contrapose! h₁
rcases h₁ with ⟨F, hF⟩
- use (ContinuousLinearEquiv.unitsEquiv _ _ F).trans e
+ use(ContinuousLinearEquiv.unitsEquiv _ _ F).trans e
ext
dsimp; rw [coeFn_coe_base' F, hF]; simp
#align continuous_linear_map.to_ring_inverse ContinuousLinearMap.to_ring_inverse
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -3,11 +3,6 @@ Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov, Frédéric Dupuis,
Heather Macbeth
-
-! This file was ported from Lean 3 source module topology.algebra.module.basic
-! leanprover-community/mathlib commit 6285167a053ad0990fc88e56c48ccd9fae6550eb
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Topology.Algebra.Ring.Basic
import Mathbin.Topology.Algebra.MulAction
@@ -18,6 +13,8 @@ import Mathbin.Algebra.Algebra.Basic
import Mathbin.LinearAlgebra.Projection
import Mathbin.LinearAlgebra.Pi
+#align_import topology.algebra.module.basic from "leanprover-community/mathlib"@"6285167a053ad0990fc88e56c48ccd9fae6550eb"
+
/-!
# Theory of topological modules and continuous linear maps.
mathlib commit https://github.com/leanprover-community/mathlib/commit/6285167a053ad0990fc88e56c48ccd9fae6550eb
@@ -5,7 +5,7 @@ Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov, Fréd
Heather Macbeth
! This file was ported from Lean 3 source module topology.algebra.module.basic
-! leanprover-community/mathlib commit e354e865255654389cc46e6032160238df2e0f40
+! leanprover-community/mathlib commit 6285167a053ad0990fc88e56c48ccd9fae6550eb
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -1504,6 +1504,54 @@ theorem smulRight_comp [ContinuousMul R₁] {x : M₂} {c : R₁} :
#align continuous_linear_map.smul_right_comp ContinuousLinearMap.smulRight_comp
-/
+section ToSpanSingleton
+
+variable (R₁)
+
+variable [ContinuousSMul R₁ M₁]
+
+#print ContinuousLinearMap.toSpanSingleton /-
+/-- Given an element `x` of a topological space `M` over a semiring `R`, the natural continuous
+linear map from `R` to `M` by taking multiples of `x`.-/
+def toSpanSingleton (x : M₁) : R₁ →L[R₁] M₁
+ where
+ toLinearMap := LinearMap.toSpanSingleton R₁ M₁ x
+ cont := continuous_id.smul continuous_const
+#align continuous_linear_map.to_span_singleton ContinuousLinearMap.toSpanSingleton
+-/
+
+#print ContinuousLinearMap.toSpanSingleton_apply /-
+theorem toSpanSingleton_apply (x : M₁) (r : R₁) : toSpanSingleton R₁ x r = r • x :=
+ rfl
+#align continuous_linear_map.to_span_singleton_apply ContinuousLinearMap.toSpanSingleton_apply
+-/
+
+#print ContinuousLinearMap.toSpanSingleton_add /-
+theorem toSpanSingleton_add [ContinuousAdd M₁] (x y : M₁) :
+ toSpanSingleton R₁ (x + y) = toSpanSingleton R₁ x + toSpanSingleton R₁ y := by ext1;
+ simp [to_span_singleton_apply]
+#align continuous_linear_map.to_span_singleton_add ContinuousLinearMap.toSpanSingleton_add
+-/
+
+#print ContinuousLinearMap.toSpanSingleton_smul' /-
+theorem toSpanSingleton_smul' {α} [Monoid α] [DistribMulAction α M₁] [ContinuousConstSMul α M₁]
+ [SMulCommClass R₁ α M₁] (c : α) (x : M₁) :
+ toSpanSingleton R₁ (c • x) = c • toSpanSingleton R₁ x := by ext1;
+ rw [to_span_singleton_apply, smul_apply, to_span_singleton_apply, smul_comm]
+#align continuous_linear_map.to_span_singleton_smul' ContinuousLinearMap.toSpanSingleton_smul'
+-/
+
+#print ContinuousLinearMap.toSpanSingleton_smul /-
+/-- A special case of `to_span_singleton_smul'` for when `R` is commutative. -/
+theorem toSpanSingleton_smul (R) {M₁} [CommSemiring R] [AddCommMonoid M₁] [Module R M₁]
+ [TopologicalSpace R] [TopologicalSpace M₁] [ContinuousSMul R M₁] (c : R) (x : M₁) :
+ toSpanSingleton R (c • x) = c • toSpanSingleton R x :=
+ toSpanSingleton_smul' R c x
+#align continuous_linear_map.to_span_singleton_smul ContinuousLinearMap.toSpanSingleton_smul
+-/
+
+end ToSpanSingleton
+
end Semiring
section Pi
mathlib commit https://github.com/leanprover-community/mathlib/commit/8efcf8022aac8e01df8d302dcebdbc25d6a886c8
@@ -1438,18 +1438,22 @@ theorem range_coprod [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃]
#align continuous_linear_map.range_coprod ContinuousLinearMap.range_coprod
-/
+#print ContinuousLinearMap.comp_fst_add_comp_snd /-
theorem comp_fst_add_comp_snd [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃] (f : M₁ →L[R₁] M₃)
(g : M₂ →L[R₁] M₃) :
f.comp (ContinuousLinearMap.fst R₁ M₁ M₂) + g.comp (ContinuousLinearMap.snd R₁ M₁ M₂) =
f.coprod g :=
rfl
#align continuous_linear_map.comp_fst_add_comp_snd ContinuousLinearMap.comp_fst_add_comp_snd
+-/
+#print ContinuousLinearMap.coprod_inl_inr /-
theorem coprod_inl_inr [ContinuousAdd M₁] [ContinuousAdd M'₁] :
(ContinuousLinearMap.inl R₁ M₁ M'₁).coprod (ContinuousLinearMap.inr R₁ M₁ M'₁) =
ContinuousLinearMap.id R₁ (M₁ × M'₁) :=
by apply coe_injective; apply LinearMap.coprod_inl_inr
#align continuous_linear_map.coprod_inl_inr ContinuousLinearMap.coprod_inl_inr
+-/
section
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -48,6 +48,7 @@ section
variable {R : Type _} {M : Type _} [Ring R] [TopologicalSpace R] [TopologicalSpace M]
[AddCommGroup M] [Module R M]
+#print ContinuousSMul.of_nhds_zero /-
theorem ContinuousSMul.of_nhds_zero [TopologicalRing R] [TopologicalAddGroup M]
(hmul : Tendsto (fun p : R × M => p.1 • p.2) (𝓝 0 ×ᶠ 𝓝 0) (𝓝 0))
(hmulleft : ∀ m : M, Tendsto (fun a : R => a • m) (𝓝 0) (𝓝 0))
@@ -89,6 +90,7 @@ theorem ContinuousSMul.of_nhds_zero [TopologicalRing R] [TopologicalAddGroup M]
· rw [← sub_self]
exact tendsto_id.sub tendsto_const_nhds⟩
#align has_continuous_smul.of_nhds_zero ContinuousSMul.of_nhds_zero
+-/
end
@@ -97,6 +99,7 @@ section
variable {R : Type _} {M : Type _} [Ring R] [TopologicalSpace R] [TopologicalSpace M]
[AddCommGroup M] [ContinuousAdd M] [Module R M] [ContinuousSMul R M]
+#print Submodule.eq_top_of_nonempty_interior' /-
/-- If `M` is a topological module over `R` and `0` is a limit of invertible elements of `R`, then
`⊤` is the only submodule of `M` with a nonempty interior.
This is the case, e.g., if `R` is a nontrivially normed field. -/
@@ -114,9 +117,11 @@ theorem Submodule.eq_top_of_nonempty_interior' [NeBot (𝓝[{x : R | IsUnit x}]
have hy' : y ∈ ↑s := mem_of_mem_nhds hy
rwa [s.add_mem_iff_right hy', ← Units.smul_def, s.smul_mem_iff' u] at hu
#align submodule.eq_top_of_nonempty_interior' Submodule.eq_top_of_nonempty_interior'
+-/
variable (R M)
+#print Module.punctured_nhds_neBot /-
/-- Let `R` be a topological ring such that zero is not an isolated point (e.g., a nontrivially
normed field, see `normed_field.punctured_nhds_ne_bot`). Let `M` be a nontrivial module over `R`
such that `c • x = 0` implies `c = 0 ∨ x = 0`. Then `M` has no isolated points. We formulate this
@@ -137,6 +142,7 @@ theorem Module.punctured_nhds_neBot [Nontrivial M] [NeBot (𝓝[≠] (0 : R))] [
· intro c hc
simpa [hy] using hc
#align module.punctured_nhds_ne_bot Module.punctured_nhds_neBot
+-/
end
@@ -146,6 +152,7 @@ variable {ι R M₁ M₂ : Type _} [Semiring R] [AddCommMonoid M₁] [AddCommMon
[Module R M₂] [u : TopologicalSpace R] {t : TopologicalSpace M₂} [ContinuousSMul R M₂]
(f : M₁ →ₗ[R] M₂)
+#print continuousSMul_induced /-
theorem continuousSMul_induced : @ContinuousSMul R M₁ _ u (t.induced f) :=
{
continuous_smul := by
@@ -154,6 +161,7 @@ theorem continuousSMul_induced : @ContinuousSMul R M₁ _ u (t.induced f) :=
simp_rw [Function.comp, f.map_smul]
refine' continuous_fst.smul (continuous_induced_dom.comp continuous_snd) }
#align has_continuous_smul_induced continuousSMul_induced
+-/
end LatticeOps
@@ -207,6 +215,7 @@ theorem Submodule.closure_smul_self_eq (s : Submodule R M) :
variable [ContinuousAdd M]
+#print Submodule.topologicalClosure /-
/-- The (topological-space) closure of a submodule of a topological `R`-module `M` is itself
a submodule. -/
def Submodule.topologicalClosure (s : Submodule R M) : Submodule R M :=
@@ -215,48 +224,64 @@ def Submodule.topologicalClosure (s : Submodule R M) : Submodule R M :=
carrier := closure (s : Set M)
smul_mem' := fun c x hx => s.closure_smul_self_subset ⟨⟨c, x⟩, ⟨Set.mem_univ _, hx⟩, rfl⟩ }
#align submodule.topological_closure Submodule.topologicalClosure
+-/
+#print Submodule.topologicalClosure_coe /-
@[simp]
theorem Submodule.topologicalClosure_coe (s : Submodule R M) :
(s.topologicalClosure : Set M) = closure (s : Set M) :=
rfl
#align submodule.topological_closure_coe Submodule.topologicalClosure_coe
+-/
+#print Submodule.le_topologicalClosure /-
theorem Submodule.le_topologicalClosure (s : Submodule R M) : s ≤ s.topologicalClosure :=
subset_closure
#align submodule.le_topological_closure Submodule.le_topologicalClosure
+-/
+#print Submodule.isClosed_topologicalClosure /-
theorem Submodule.isClosed_topologicalClosure (s : Submodule R M) :
IsClosed (s.topologicalClosure : Set M) := by convert isClosed_closure
#align submodule.is_closed_topological_closure Submodule.isClosed_topologicalClosure
+-/
+#print Submodule.topologicalClosure_minimal /-
theorem Submodule.topologicalClosure_minimal (s : Submodule R M) {t : Submodule R M} (h : s ≤ t)
(ht : IsClosed (t : Set M)) : s.topologicalClosure ≤ t :=
closure_minimal h ht
#align submodule.topological_closure_minimal Submodule.topologicalClosure_minimal
+-/
+#print Submodule.topologicalClosure_mono /-
theorem Submodule.topologicalClosure_mono {s : Submodule R M} {t : Submodule R M} (h : s ≤ t) :
s.topologicalClosure ≤ t.topologicalClosure :=
s.topologicalClosure_minimal (h.trans t.le_topologicalClosure) t.isClosed_topologicalClosure
#align submodule.topological_closure_mono Submodule.topologicalClosure_mono
+-/
+#print IsClosed.submodule_topologicalClosure_eq /-
/-- The topological closure of a closed submodule `s` is equal to `s`. -/
theorem IsClosed.submodule_topologicalClosure_eq {s : Submodule R M} (hs : IsClosed (s : Set M)) :
s.topologicalClosure = s :=
le_antisymm (s.topologicalClosure_minimal rfl.le hs) s.le_topologicalClosure
#align is_closed.submodule_topological_closure_eq IsClosed.submodule_topologicalClosure_eq
+-/
+#print Submodule.dense_iff_topologicalClosure_eq_top /-
/-- A subspace is dense iff its topological closure is the entire space. -/
theorem Submodule.dense_iff_topologicalClosure_eq_top {s : Submodule R M} :
Dense (s : Set M) ↔ s.topologicalClosure = ⊤ := by
rw [← SetLike.coe_set_eq, dense_iff_closure_eq]; simp
#align submodule.dense_iff_topological_closure_eq_top Submodule.dense_iff_topologicalClosure_eq_top
+-/
instance {M' : Type _} [AddCommMonoid M'] [Module R M'] [UniformSpace M'] [ContinuousAdd M']
[ContinuousSMul R M'] [CompleteSpace M'] (U : Submodule R M') :
CompleteSpace U.topologicalClosure :=
isClosed_closure.completeSpace_coe
+#print Submodule.isClosed_or_dense_of_isCoatom /-
/-- A maximal proper subspace of a topological module (i.e a `submodule` satisfying `is_coatom`)
is either closed or dense. -/
theorem Submodule.isClosed_or_dense_of_isCoatom (s : Submodule R M) (hs : IsCoatom s) :
@@ -264,11 +289,13 @@ theorem Submodule.isClosed_or_dense_of_isCoatom (s : Submodule R M) (hs : IsCoat
(hs.le_iff.mp s.le_topologicalClosure).symm.imp (isClosed_of_closure_subset ∘ Eq.le)
Submodule.dense_iff_topologicalClosure_eq_top.mpr
#align submodule.is_closed_or_dense_of_is_coatom Submodule.isClosed_or_dense_of_isCoatom
+-/
end closure
section Pi
+#print LinearMap.continuous_on_pi /-
theorem LinearMap.continuous_on_pi {ι : Type _} {R : Type _} {M : Type _} [Finite ι] [Semiring R]
[TopologicalSpace R] [AddCommMonoid M] [Module R M] [TopologicalSpace M] [ContinuousAdd M]
[ContinuousSMul R M] (f : (ι → R) →ₗ[R] M) : Continuous f :=
@@ -283,6 +310,7 @@ theorem LinearMap.continuous_on_pi {ι : Type _} {R : Type _} {M : Type _} [Fini
refine' continuous_finset_sum _ fun i hi => _
exact (continuous_apply i).smul continuous_const
#align linear_map.continuous_on_pi LinearMap.continuous_on_pi
+-/
end Pi
@@ -297,13 +325,10 @@ structure ContinuousLinearMap {R : Type _} {S : Type _} [Semiring R] [Semiring S
#align continuous_linear_map ContinuousLinearMap
-/
--- mathport name: «expr →SL[ ] »
notation:25 M " →SL[" σ "] " M₂ => ContinuousLinearMap σ M M₂
--- mathport name: «expr →L[ ] »
notation:25 M " →L[" R "] " M₂ => ContinuousLinearMap (RingHom.id R) M M₂
--- mathport name: «expr →L⋆[ ] »
notation:25 M " →L⋆[" R "] " M₂ => ContinuousLinearMap (starRingEnd R) M M₂
#print ContinuousSemilinearMapClass /-
@@ -347,13 +372,10 @@ structure ContinuousLinearEquiv {R : Type _} {S : Type _} [Semiring R] [Semiring
#align continuous_linear_equiv ContinuousLinearEquiv
-/
--- mathport name: «expr ≃SL[ ] »
notation:50 M " ≃SL[" σ "] " M₂ => ContinuousLinearEquiv σ M M₂
--- mathport name: «expr ≃L[ ] »
notation:50 M " ≃L[" R "] " M₂ => ContinuousLinearEquiv (RingHom.id R) M M₂
--- mathport name: «expr ≃L⋆[ ] »
notation:50 M " ≃L⋆[" R "] " M₂ => ContinuousLinearEquiv (starRingEnd R) M M₂
#print ContinuousSemilinearEquivClass /-
@@ -390,8 +412,6 @@ variable (F : Type _) {R : Type _} {S : Type _} [Semiring R] [Semiring S] (σ :
[AddCommMonoid M] (M₂ : Type _) [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M]
[Module S M₂]
-include σ'
-
-- `σ'` becomes a metavariable, but it's OK since it's an outparam
@[nolint dangerous_instance]
instance (priority := 100) [s : ContinuousSemilinearEquivClass F σ M M₂] :
@@ -400,8 +420,6 @@ instance (priority := 100) [s : ContinuousSemilinearEquivClass F σ M M₂] :
coe := (coe : F → M → M₂)
coe_injective' := @FunLike.coe_injective F _ _ _ }
-omit σ'
-
end ContinuousSemilinearEquivClass
section PointwiseLimits
@@ -425,6 +443,7 @@ end
variable [ContinuousAdd M₂] {σ : R →+* S} {l : Filter α}
+#print linearMapOfMemClosureRangeCoe /-
/-- Constructs a bundled linear map from a function and a proof that this function belongs to the
closure of the set of linear maps. -/
@[simps (config := { fullyApplied := false })]
@@ -436,7 +455,9 @@ def linearMapOfMemClosureRangeCoe (f : M₁ → M₂)
(isClosed_setOf_map_smul M₁ M₂ σ).closure_subset_iff.2
(Set.range_subset_iff.2 LinearMap.map_smulₛₗ) hf }
#align linear_map_of_mem_closure_range_coe linearMapOfMemClosureRangeCoe
+-/
+#print linearMapOfTendsto /-
/-- Construct a bundled linear map from a pointwise limit of linear maps -/
@[simps (config := { fullyApplied := false })]
def linearMapOfTendsto (f : M₁ → M₂) (g : α → M₁ →ₛₗ[σ] M₂) [l.ne_bot]
@@ -444,12 +465,15 @@ def linearMapOfTendsto (f : M₁ → M₂) (g : α → M₁ →ₛₗ[σ] M₂)
linearMapOfMemClosureRangeCoe f <|
mem_closure_of_tendsto h <| eventually_of_forall fun a => Set.mem_range_self _
#align linear_map_of_tendsto linearMapOfTendsto
+-/
variable (M₁ M₂ σ)
+#print LinearMap.isClosed_range_coe /-
theorem LinearMap.isClosed_range_coe : IsClosed (Set.range (coeFn : (M₁ →ₛₗ[σ] M₂) → M₁ → M₂)) :=
isClosed_of_closure_subset fun f hf => ⟨linearMapOfMemClosureRangeCoe f hf, rfl⟩
#align linear_map.is_closed_range_coe LinearMap.isClosed_range_coe
+-/
end PointwiseLimits
@@ -479,9 +503,11 @@ theorem toLinearMap_eq_coe (f : M₁ →SL[σ₁₂] M₂) : f.toLinearMap = f :
rfl
#align continuous_linear_map.to_linear_map_eq_coe ContinuousLinearMap.toLinearMap_eq_coe
+#print ContinuousLinearMap.coe_injective /-
theorem coe_injective : Function.Injective (coe : (M₁ →SL[σ₁₂] M₂) → M₁ →ₛₗ[σ₁₂] M₂) := by
intro f g H; cases f; cases g; congr
#align continuous_linear_map.coe_injective ContinuousLinearMap.coe_injective
+-/
instance : ContinuousSemilinearMapClass (M₁ →SL[σ₁₂] M₂) σ₁₂ M₁ M₂
where
@@ -497,35 +523,47 @@ instance toFun : CoeFun (M₁ →SL[σ₁₂] M₂) fun _ => M₁ → M₂ :=
⟨fun f => f.toFun⟩
#align continuous_linear_map.to_fun ContinuousLinearMap.toFun
+#print ContinuousLinearMap.coe_mk /-
@[simp]
theorem coe_mk (f : M₁ →ₛₗ[σ₁₂] M₂) (h) : (mk f h : M₁ →ₛₗ[σ₁₂] M₂) = f :=
rfl
#align continuous_linear_map.coe_mk ContinuousLinearMap.coe_mk
+-/
+#print ContinuousLinearMap.coe_mk' /-
@[simp]
theorem coe_mk' (f : M₁ →ₛₗ[σ₁₂] M₂) (h) : (mk f h : M₁ → M₂) = f :=
rfl
#align continuous_linear_map.coe_mk' ContinuousLinearMap.coe_mk'
+-/
+#print ContinuousLinearMap.continuous /-
@[continuity]
protected theorem continuous (f : M₁ →SL[σ₁₂] M₂) : Continuous f :=
f.2
#align continuous_linear_map.continuous ContinuousLinearMap.continuous
+-/
+#print ContinuousLinearMap.uniformContinuous /-
protected theorem uniformContinuous {E₁ E₂ : Type _} [UniformSpace E₁] [UniformSpace E₂]
[AddCommGroup E₁] [AddCommGroup E₂] [Module R₁ E₁] [Module R₂ E₂] [UniformAddGroup E₁]
[UniformAddGroup E₂] (f : E₁ →SL[σ₁₂] E₂) : UniformContinuous f :=
uniformContinuous_addMonoidHom_of_continuous f.Continuous
#align continuous_linear_map.uniform_continuous ContinuousLinearMap.uniformContinuous
+-/
+#print ContinuousLinearMap.coe_inj /-
@[simp, norm_cast]
theorem coe_inj {f g : M₁ →SL[σ₁₂] M₂} : (f : M₁ →ₛₗ[σ₁₂] M₂) = g ↔ f = g :=
coe_injective.eq_iff
#align continuous_linear_map.coe_inj ContinuousLinearMap.coe_inj
+-/
+#print ContinuousLinearMap.coeFn_injective /-
theorem coeFn_injective : @Function.Injective (M₁ →SL[σ₁₂] M₂) (M₁ → M₂) coeFn :=
FunLike.coe_injective
#align continuous_linear_map.coe_fn_injective ContinuousLinearMap.coeFn_injective
+-/
#print ContinuousLinearMap.Simps.apply /-
/-- See Note [custom simps projection]. We need to specify this projection explicitly in this case,
@@ -544,15 +582,20 @@ def Simps.coe (h : M₁ →SL[σ₁₂] M₂) : M₁ →ₛₗ[σ₁₂] M₂ :=
initialize_simps_projections ContinuousLinearMap (to_linear_map_to_fun → apply, toLinearMap → coe)
+#print ContinuousLinearMap.ext /-
@[ext]
theorem ext {f g : M₁ →SL[σ₁₂] M₂} (h : ∀ x, f x = g x) : f = g :=
FunLike.ext f g h
#align continuous_linear_map.ext ContinuousLinearMap.ext
+-/
+#print ContinuousLinearMap.ext_iff /-
theorem ext_iff {f g : M₁ →SL[σ₁₂] M₂} : f = g ↔ ∀ x, f x = g x :=
FunLike.ext_iff
#align continuous_linear_map.ext_iff ContinuousLinearMap.ext_iff
+-/
+#print ContinuousLinearMap.copy /-
/-- Copy of a `continuous_linear_map` with a new `to_fun` equal to the old one. Useful to fix
definitional equalities. -/
protected def copy (f : M₁ →SL[σ₁₂] M₂) (f' : M₁ → M₂) (h : f' = ⇑f) : M₁ →SL[σ₁₂] M₂
@@ -560,75 +603,103 @@ protected def copy (f : M₁ →SL[σ₁₂] M₂) (f' : M₁ → M₂) (h : f'
toLinearMap := f.toLinearMap.copy f' h
cont := show Continuous f' from h.symm ▸ f.Continuous
#align continuous_linear_map.copy ContinuousLinearMap.copy
+-/
+#print ContinuousLinearMap.coe_copy /-
@[simp]
theorem coe_copy (f : M₁ →SL[σ₁₂] M₂) (f' : M₁ → M₂) (h : f' = ⇑f) : ⇑(f.copy f' h) = f' :=
rfl
#align continuous_linear_map.coe_copy ContinuousLinearMap.coe_copy
+-/
+#print ContinuousLinearMap.copy_eq /-
theorem copy_eq (f : M₁ →SL[σ₁₂] M₂) (f' : M₁ → M₂) (h : f' = ⇑f) : f.copy f' h = f :=
FunLike.ext' h
#align continuous_linear_map.copy_eq ContinuousLinearMap.copy_eq
+-/
+#print ContinuousLinearMap.map_zero /-
-- make some straightforward lemmas available to `simp`.
protected theorem map_zero (f : M₁ →SL[σ₁₂] M₂) : f (0 : M₁) = 0 :=
map_zero f
#align continuous_linear_map.map_zero ContinuousLinearMap.map_zero
+-/
+#print ContinuousLinearMap.map_add /-
protected theorem map_add (f : M₁ →SL[σ₁₂] M₂) (x y : M₁) : f (x + y) = f x + f y :=
map_add f x y
#align continuous_linear_map.map_add ContinuousLinearMap.map_add
+-/
+#print ContinuousLinearMap.map_smulₛₗ /-
@[simp]
protected theorem map_smulₛₗ (f : M₁ →SL[σ₁₂] M₂) (c : R₁) (x : M₁) : f (c • x) = σ₁₂ c • f x :=
(toLinearMap _).map_smulₛₗ _ _
#align continuous_linear_map.map_smulₛₗ ContinuousLinearMap.map_smulₛₗ
+-/
+#print ContinuousLinearMap.map_smul /-
@[simp]
protected theorem map_smul [Module R₁ M₂] (f : M₁ →L[R₁] M₂) (c : R₁) (x : M₁) :
f (c • x) = c • f x := by simp only [RingHom.id_apply, ContinuousLinearMap.map_smulₛₗ]
#align continuous_linear_map.map_smul ContinuousLinearMap.map_smul
+-/
+#print ContinuousLinearMap.map_smul_of_tower /-
@[simp]
theorem map_smul_of_tower {R S : Type _} [Semiring S] [SMul R M₁] [Module S M₁] [SMul R M₂]
[Module S M₂] [LinearMap.CompatibleSMul M₁ M₂ R S] (f : M₁ →L[S] M₂) (c : R) (x : M₁) :
f (c • x) = c • f x :=
LinearMap.CompatibleSMul.map_smul f c x
#align continuous_linear_map.map_smul_of_tower ContinuousLinearMap.map_smul_of_tower
+-/
+#print ContinuousLinearMap.map_sum /-
protected theorem map_sum {ι : Type _} (f : M₁ →SL[σ₁₂] M₂) (s : Finset ι) (g : ι → M₁) :
f (∑ i in s, g i) = ∑ i in s, f (g i) :=
f.toLinearMap.map_sum
#align continuous_linear_map.map_sum ContinuousLinearMap.map_sum
+-/
+#print ContinuousLinearMap.coe_coe /-
@[simp, norm_cast]
theorem coe_coe (f : M₁ →SL[σ₁₂] M₂) : ⇑(f : M₁ →ₛₗ[σ₁₂] M₂) = f :=
rfl
#align continuous_linear_map.coe_coe ContinuousLinearMap.coe_coe
+-/
+#print ContinuousLinearMap.ext_ring /-
@[ext]
theorem ext_ring [TopologicalSpace R₁] {f g : R₁ →L[R₁] M₁} (h : f 1 = g 1) : f = g :=
coe_inj.1 <| LinearMap.ext_ring h
#align continuous_linear_map.ext_ring ContinuousLinearMap.ext_ring
+-/
+#print ContinuousLinearMap.ext_ring_iff /-
theorem ext_ring_iff [TopologicalSpace R₁] {f g : R₁ →L[R₁] M₁} : f = g ↔ f 1 = g 1 :=
⟨fun h => h ▸ rfl, ext_ring⟩
#align continuous_linear_map.ext_ring_iff ContinuousLinearMap.ext_ring_iff
+-/
+#print ContinuousLinearMap.eqOn_closure_span /-
/-- If two continuous linear maps are equal on a set `s`, then they are equal on the closure
of the `submodule.span` of this set. -/
theorem eqOn_closure_span [T2Space M₂] {s : Set M₁} {f g : M₁ →SL[σ₁₂] M₂} (h : Set.EqOn f g s) :
Set.EqOn f g (closure (Submodule.span R₁ s : Set M₁)) :=
(LinearMap.eqOn_span' h).closure f.Continuous g.Continuous
#align continuous_linear_map.eq_on_closure_span ContinuousLinearMap.eqOn_closure_span
+-/
+#print ContinuousLinearMap.ext_on /-
/-- If the submodule generated by a set `s` is dense in the ambient module, then two continuous
linear maps equal on `s` are equal. -/
theorem ext_on [T2Space M₂] {s : Set M₁} (hs : Dense (Submodule.span R₁ s : Set M₁))
{f g : M₁ →SL[σ₁₂] M₂} (h : Set.EqOn f g s) : f = g :=
ext fun x => eqOn_closure_span h (hs x)
#align continuous_linear_map.ext_on ContinuousLinearMap.ext_on
+-/
+#print Submodule.topologicalClosure_map /-
/-- Under a continuous linear map, the image of the `topological_closure` of a submodule is
contained in the `topological_closure` of its image. -/
theorem Submodule.topologicalClosure_map [RingHomSurjective σ₁₂] [TopologicalSpace R₁]
@@ -638,7 +709,9 @@ theorem Submodule.topologicalClosure_map [RingHomSurjective σ₁₂] [Topologic
(s.map (f : M₁ →ₛₗ[σ₁₂] M₂)).topologicalClosure :=
image_closure_subset_closure_image f.Continuous
#align submodule.topological_closure_map Submodule.topologicalClosure_map
+-/
+#print DenseRange.topologicalClosure_map_submodule /-
/-- Under a dense continuous linear map, a submodule whose `topological_closure` is `⊤` is sent to
another such submodule. That is, the image of a dense set under a map with dense range is dense.
-/
@@ -651,6 +724,7 @@ theorem DenseRange.topologicalClosure_map_submodule [RingHomSurjective σ₁₂]
simp only [Submodule.topologicalClosure_coe, Submodule.top_coe, ← dense_iff_closure_eq] at hs ⊢
exact hf'.dense_image f.continuous hs
#align dense_range.topological_closure_map_submodule DenseRange.topologicalClosure_map_submodule
+-/
section SmulMonoid
@@ -666,19 +740,25 @@ instance : MulAction S₂ (M₁ →SL[σ₁₂] M₂)
one_smul f := ext fun x => one_smul _ _
mul_smul a b f := ext fun x => mul_smul _ _ _
+#print ContinuousLinearMap.smul_apply /-
theorem smul_apply (c : S₂) (f : M₁ →SL[σ₁₂] M₂) (x : M₁) : (c • f) x = c • f x :=
rfl
#align continuous_linear_map.smul_apply ContinuousLinearMap.smul_apply
+-/
+#print ContinuousLinearMap.coe_smul /-
@[simp, norm_cast]
theorem coe_smul (c : S₂) (f : M₁ →SL[σ₁₂] M₂) : (↑(c • f) : M₁ →ₛₗ[σ₁₂] M₂) = c • f :=
rfl
#align continuous_linear_map.coe_smul ContinuousLinearMap.coe_smul
+-/
+#print ContinuousLinearMap.coe_smul' /-
@[simp, norm_cast]
theorem coe_smul' (c : S₂) (f : M₁ →SL[σ₁₂] M₂) : ⇑(c • f) = c • f :=
rfl
#align continuous_linear_map.coe_smul' ContinuousLinearMap.coe_smul'
+-/
instance [SMul S₂ T₂] [IsScalarTower S₂ T₂ M₂] : IsScalarTower S₂ T₂ (M₁ →SL[σ₁₂] M₂) :=
⟨fun a b f => ext fun x => smul_assoc a b (f x)⟩
@@ -695,21 +775,28 @@ instance : Zero (M₁ →SL[σ₁₂] M₂) :=
instance : Inhabited (M₁ →SL[σ₁₂] M₂) :=
⟨0⟩
+#print ContinuousLinearMap.default_def /-
@[simp]
theorem default_def : (default : M₁ →SL[σ₁₂] M₂) = 0 :=
rfl
#align continuous_linear_map.default_def ContinuousLinearMap.default_def
+-/
+#print ContinuousLinearMap.zero_apply /-
@[simp]
theorem zero_apply (x : M₁) : (0 : M₁ →SL[σ₁₂] M₂) x = 0 :=
rfl
#align continuous_linear_map.zero_apply ContinuousLinearMap.zero_apply
+-/
+#print ContinuousLinearMap.coe_zero /-
@[simp, norm_cast]
theorem coe_zero : ((0 : M₁ →SL[σ₁₂] M₂) : M₁ →ₛₗ[σ₁₂] M₂) = 0 :=
rfl
#align continuous_linear_map.coe_zero ContinuousLinearMap.coe_zero
+-/
+#print ContinuousLinearMap.coe_zero' /-
/- no simp attribute on the next line as simp does not always simplify `0 x` to `0`
when `0` is the zero function, while it does for the zero continuous linear map,
and this is the most important property we care about. -/
@@ -717,6 +804,7 @@ and this is the most important property we care about. -/
theorem coe_zero' : ⇑(0 : M₁ →SL[σ₁₂] M₂) = 0 :=
rfl
#align continuous_linear_map.coe_zero' ContinuousLinearMap.coe_zero'
+-/
#print ContinuousLinearMap.uniqueOfLeft /-
instance uniqueOfLeft [Subsingleton M₁] : Unique (M₁ →SL[σ₁₂] M₂) :=
@@ -730,9 +818,11 @@ instance uniqueOfRight [Subsingleton M₂] : Unique (M₁ →SL[σ₁₂] M₂)
#align continuous_linear_map.unique_of_right ContinuousLinearMap.uniqueOfRight
-/
+#print ContinuousLinearMap.exists_ne_zero /-
theorem exists_ne_zero {f : M₁ →SL[σ₁₂] M₂} (hf : f ≠ 0) : ∃ x, f x ≠ 0 := by by_contra' h;
exact hf (ContinuousLinearMap.ext h)
#align continuous_linear_map.exists_ne_zero ContinuousLinearMap.exists_ne_zero
+-/
section
@@ -756,9 +846,11 @@ theorem one_def : (1 : M₁ →L[R₁] M₁) = id R₁ M₁ :=
#align continuous_linear_map.one_def ContinuousLinearMap.one_def
-/
+#print ContinuousLinearMap.id_apply /-
theorem id_apply (x : M₁) : id R₁ M₁ x = x :=
rfl
#align continuous_linear_map.id_apply ContinuousLinearMap.id_apply
+-/
#print ContinuousLinearMap.coe_id /-
@[simp, norm_cast]
@@ -767,20 +859,26 @@ theorem coe_id : (id R₁ M₁ : M₁ →ₗ[R₁] M₁) = LinearMap.id :=
#align continuous_linear_map.coe_id ContinuousLinearMap.coe_id
-/
+#print ContinuousLinearMap.coe_id' /-
@[simp, norm_cast]
theorem coe_id' : ⇑(id R₁ M₁) = id :=
rfl
#align continuous_linear_map.coe_id' ContinuousLinearMap.coe_id'
+-/
+#print ContinuousLinearMap.coe_eq_id /-
@[simp, norm_cast]
theorem coe_eq_id {f : M₁ →L[R₁] M₁} : (f : M₁ →ₗ[R₁] M₁) = LinearMap.id ↔ f = id _ _ := by
rw [← coe_id, coe_inj]
#align continuous_linear_map.coe_eq_id ContinuousLinearMap.coe_eq_id
+-/
+#print ContinuousLinearMap.one_apply /-
@[simp]
theorem one_apply (x : M₁) : (1 : M₁ →L[R₁] M₁) x = x :=
rfl
#align continuous_linear_map.one_apply ContinuousLinearMap.one_apply
+-/
section Add
@@ -789,20 +887,26 @@ variable [ContinuousAdd M₂]
instance : Add (M₁ →SL[σ₁₂] M₂) :=
⟨fun f g => ⟨f + g, f.2.add g.2⟩⟩
+#print ContinuousLinearMap.add_apply /-
@[simp]
theorem add_apply (f g : M₁ →SL[σ₁₂] M₂) (x : M₁) : (f + g) x = f x + g x :=
rfl
#align continuous_linear_map.add_apply ContinuousLinearMap.add_apply
+-/
+#print ContinuousLinearMap.coe_add /-
@[simp, norm_cast]
theorem coe_add (f g : M₁ →SL[σ₁₂] M₂) : (↑(f + g) : M₁ →ₛₗ[σ₁₂] M₂) = f + g :=
rfl
#align continuous_linear_map.coe_add ContinuousLinearMap.coe_add
+-/
+#print ContinuousLinearMap.coe_add' /-
@[norm_cast]
theorem coe_add' (f g : M₁ →SL[σ₁₂] M₂) : ⇑(f + g) = f + g :=
rfl
#align continuous_linear_map.coe_add' ContinuousLinearMap.coe_add'
+-/
instance : AddCommMonoid (M₁ →SL[σ₁₂] M₂)
where
@@ -820,20 +924,26 @@ instance : AddCommMonoid (M₁ →SL[σ₁₂] M₂)
nsmul_zero f := by ext; simp
nsmul_succ n f := by ext; simp [Nat.succ_eq_one_add, add_smul]
+#print ContinuousLinearMap.coe_sum /-
@[simp, norm_cast]
theorem coe_sum {ι : Type _} (t : Finset ι) (f : ι → M₁ →SL[σ₁₂] M₂) :
↑(∑ d in t, f d) = (∑ d in t, f d : M₁ →ₛₗ[σ₁₂] M₂) :=
(AddMonoidHom.mk (coe : (M₁ →SL[σ₁₂] M₂) → M₁ →ₛₗ[σ₁₂] M₂) rfl fun _ _ => rfl).map_sum _ _
#align continuous_linear_map.coe_sum ContinuousLinearMap.coe_sum
+-/
+#print ContinuousLinearMap.coe_sum' /-
@[simp, norm_cast]
theorem coe_sum' {ι : Type _} (t : Finset ι) (f : ι → M₁ →SL[σ₁₂] M₂) :
⇑(∑ d in t, f d) = ∑ d in t, f d := by simp only [← coe_coe, coe_sum, LinearMap.coeFn_sum]
#align continuous_linear_map.coe_sum' ContinuousLinearMap.coe_sum'
+-/
+#print ContinuousLinearMap.sum_apply /-
theorem sum_apply {ι : Type _} (t : Finset ι) (f : ι → M₁ →SL[σ₁₂] M₂) (b : M₁) :
(∑ d in t, f d) b = ∑ d in t, f d b := by simp only [coe_sum', Finset.sum_apply]
#align continuous_linear_map.sum_apply ContinuousLinearMap.sum_apply
+-/
end Add
@@ -846,84 +956,101 @@ def comp (g : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) : M₁
#align continuous_linear_map.comp ContinuousLinearMap.comp
-/
--- mathport name: «expr ∘L »
infixr:80 " ∘L " =>
@ContinuousLinearMap.comp _ _ _ _ _ _ (RingHom.id _) (RingHom.id _) (RingHom.id _) _ _ _ _ _ _ _ _
_ _ _ _ RingHomCompTriple.ids
+#print ContinuousLinearMap.coe_comp /-
@[simp, norm_cast]
theorem coe_comp (h : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) :
(h.comp f : M₁ →ₛₗ[σ₁₃] M₃) = (h : M₂ →ₛₗ[σ₂₃] M₃).comp (f : M₁ →ₛₗ[σ₁₂] M₂) :=
rfl
#align continuous_linear_map.coe_comp ContinuousLinearMap.coe_comp
+-/
-include σ₁₃
-
+#print ContinuousLinearMap.coe_comp' /-
@[simp, norm_cast]
theorem coe_comp' (h : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) : ⇑(h.comp f) = h ∘ f :=
rfl
#align continuous_linear_map.coe_comp' ContinuousLinearMap.coe_comp'
+-/
+#print ContinuousLinearMap.comp_apply /-
theorem comp_apply (g : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) (x : M₁) : (g.comp f) x = g (f x) :=
rfl
#align continuous_linear_map.comp_apply ContinuousLinearMap.comp_apply
+-/
-omit σ₁₃
-
+#print ContinuousLinearMap.comp_id /-
@[simp]
theorem comp_id (f : M₁ →SL[σ₁₂] M₂) : f.comp (id R₁ M₁) = f :=
ext fun x => rfl
#align continuous_linear_map.comp_id ContinuousLinearMap.comp_id
+-/
+#print ContinuousLinearMap.id_comp /-
@[simp]
theorem id_comp (f : M₁ →SL[σ₁₂] M₂) : (id R₂ M₂).comp f = f :=
ext fun x => rfl
#align continuous_linear_map.id_comp ContinuousLinearMap.id_comp
+-/
-include σ₁₃
-
+#print ContinuousLinearMap.comp_zero /-
@[simp]
theorem comp_zero (g : M₂ →SL[σ₂₃] M₃) : g.comp (0 : M₁ →SL[σ₁₂] M₂) = 0 := by ext; simp
#align continuous_linear_map.comp_zero ContinuousLinearMap.comp_zero
+-/
+#print ContinuousLinearMap.zero_comp /-
@[simp]
theorem zero_comp (f : M₁ →SL[σ₁₂] M₂) : (0 : M₂ →SL[σ₂₃] M₃).comp f = 0 := by ext; simp
#align continuous_linear_map.zero_comp ContinuousLinearMap.zero_comp
+-/
+#print ContinuousLinearMap.comp_add /-
@[simp]
theorem comp_add [ContinuousAdd M₂] [ContinuousAdd M₃] (g : M₂ →SL[σ₂₃] M₃)
(f₁ f₂ : M₁ →SL[σ₁₂] M₂) : g.comp (f₁ + f₂) = g.comp f₁ + g.comp f₂ := by ext; simp
#align continuous_linear_map.comp_add ContinuousLinearMap.comp_add
+-/
+#print ContinuousLinearMap.add_comp /-
@[simp]
theorem add_comp [ContinuousAdd M₃] (g₁ g₂ : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) :
(g₁ + g₂).comp f = g₁.comp f + g₂.comp f := by ext; simp
#align continuous_linear_map.add_comp ContinuousLinearMap.add_comp
+-/
-omit σ₁₃
-
+#print ContinuousLinearMap.comp_assoc /-
theorem comp_assoc {R₄ : Type _} [Semiring R₄] [Module R₄ M₄] {σ₁₄ : R₁ →+* R₄} {σ₂₄ : R₂ →+* R₄}
{σ₃₄ : R₃ →+* R₄} [RingHomCompTriple σ₁₃ σ₃₄ σ₁₄] [RingHomCompTriple σ₂₃ σ₃₄ σ₂₄]
[RingHomCompTriple σ₁₂ σ₂₄ σ₁₄] (h : M₃ →SL[σ₃₄] M₄) (g : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) :
(h.comp g).comp f = h.comp (g.comp f) :=
rfl
#align continuous_linear_map.comp_assoc ContinuousLinearMap.comp_assoc
+-/
instance : Mul (M₁ →L[R₁] M₁) :=
⟨comp⟩
+#print ContinuousLinearMap.mul_def /-
theorem mul_def (f g : M₁ →L[R₁] M₁) : f * g = f.comp g :=
rfl
#align continuous_linear_map.mul_def ContinuousLinearMap.mul_def
+-/
+#print ContinuousLinearMap.coe_mul /-
@[simp]
theorem coe_mul (f g : M₁ →L[R₁] M₁) : ⇑(f * g) = f ∘ g :=
rfl
#align continuous_linear_map.coe_mul ContinuousLinearMap.coe_mul
+-/
+#print ContinuousLinearMap.mul_apply /-
theorem mul_apply (f g : M₁ →L[R₁] M₁) (x : M₁) : (f * g) x = f (g x) :=
rfl
#align continuous_linear_map.mul_apply ContinuousLinearMap.mul_apply
+-/
instance : MonoidWithZero (M₁ →L[R₁] M₁)
where
@@ -944,6 +1071,7 @@ instance [ContinuousAdd M₁] : Semiring (M₁ →L[R₁] M₁) :=
left_distrib := fun f g h => ext fun x => map_add f (g x) (h x)
right_distrib := fun _ _ _ => ext fun _ => LinearMap.add_apply _ _ _ }
+#print ContinuousLinearMap.toLinearMapRingHom /-
/-- `continuous_linear_map.to_linear_map` as a `ring_hom`.-/
@[simps]
def toLinearMapRingHom [ContinuousAdd M₁] : (M₁ →L[R₁] M₁) →+* M₁ →ₗ[R₁] M₁
@@ -954,107 +1082,140 @@ def toLinearMapRingHom [ContinuousAdd M₁] : (M₁ →L[R₁] M₁) →+* M₁
map_add' _ _ := rfl
map_mul' _ _ := rfl
#align continuous_linear_map.to_linear_map_ring_hom ContinuousLinearMap.toLinearMapRingHom
+-/
section ApplyAction
variable [ContinuousAdd M₁]
+#print ContinuousLinearMap.applyModule /-
/-- The tautological action by `M₁ →L[R₁] M₁` on `M`.
This generalizes `function.End.apply_mul_action`. -/
instance applyModule : Module (M₁ →L[R₁] M₁) M₁ :=
Module.compHom _ toLinearMapRingHom
#align continuous_linear_map.apply_module ContinuousLinearMap.applyModule
+-/
+#print ContinuousLinearMap.smul_def /-
@[simp]
protected theorem smul_def (f : M₁ →L[R₁] M₁) (a : M₁) : f • a = f a :=
rfl
#align continuous_linear_map.smul_def ContinuousLinearMap.smul_def
+-/
+#print ContinuousLinearMap.applyFaithfulSMul /-
/-- `continuous_linear_map.apply_module` is faithful. -/
instance applyFaithfulSMul : FaithfulSMul (M₁ →L[R₁] M₁) M₁ :=
⟨fun _ _ => ContinuousLinearMap.ext⟩
#align continuous_linear_map.apply_has_faithful_smul ContinuousLinearMap.applyFaithfulSMul
+-/
+#print ContinuousLinearMap.applySMulCommClass /-
instance applySMulCommClass : SMulCommClass R₁ (M₁ →L[R₁] M₁) M₁
where smul_comm r e m := (e.map_smul r m).symm
#align continuous_linear_map.apply_smul_comm_class ContinuousLinearMap.applySMulCommClass
+-/
+#print ContinuousLinearMap.applySMulCommClass' /-
instance applySMulCommClass' : SMulCommClass (M₁ →L[R₁] M₁) R₁ M₁
where smul_comm := ContinuousLinearMap.map_smul
#align continuous_linear_map.apply_smul_comm_class' ContinuousLinearMap.applySMulCommClass'
+-/
instance : ContinuousConstSMul (M₁ →L[R₁] M₁) M₁ :=
⟨ContinuousLinearMap.continuous⟩
end ApplyAction
+#print ContinuousLinearMap.prod /-
/-- The cartesian product of two bounded linear maps, as a bounded linear map. -/
protected def prod [Module R₁ M₂] [Module R₁ M₃] (f₁ : M₁ →L[R₁] M₂) (f₂ : M₁ →L[R₁] M₃) :
M₁ →L[R₁] M₂ × M₃ :=
⟨(f₁ : M₁ →ₗ[R₁] M₂).Prod f₂, f₁.2.prod_mk f₂.2⟩
#align continuous_linear_map.prod ContinuousLinearMap.prod
+-/
+#print ContinuousLinearMap.coe_prod /-
@[simp, norm_cast]
theorem coe_prod [Module R₁ M₂] [Module R₁ M₃] (f₁ : M₁ →L[R₁] M₂) (f₂ : M₁ →L[R₁] M₃) :
(f₁.Prod f₂ : M₁ →ₗ[R₁] M₂ × M₃) = LinearMap.prod f₁ f₂ :=
rfl
#align continuous_linear_map.coe_prod ContinuousLinearMap.coe_prod
+-/
+#print ContinuousLinearMap.prod_apply /-
@[simp, norm_cast]
theorem prod_apply [Module R₁ M₂] [Module R₁ M₃] (f₁ : M₁ →L[R₁] M₂) (f₂ : M₁ →L[R₁] M₃) (x : M₁) :
f₁.Prod f₂ x = (f₁ x, f₂ x) :=
rfl
#align continuous_linear_map.prod_apply ContinuousLinearMap.prod_apply
+-/
section
variable (R₁ M₁ M₂)
+#print ContinuousLinearMap.inl /-
/-- The left injection into a product is a continuous linear map. -/
def inl [Module R₁ M₂] : M₁ →L[R₁] M₁ × M₂ :=
(id R₁ M₁).Prod 0
#align continuous_linear_map.inl ContinuousLinearMap.inl
+-/
+#print ContinuousLinearMap.inr /-
/-- The right injection into a product is a continuous linear map. -/
def inr [Module R₁ M₂] : M₂ →L[R₁] M₁ × M₂ :=
(0 : M₂ →L[R₁] M₁).Prod (id R₁ M₂)
#align continuous_linear_map.inr ContinuousLinearMap.inr
+-/
end
variable {F : Type _}
+#print ContinuousLinearMap.inl_apply /-
@[simp]
theorem inl_apply [Module R₁ M₂] (x : M₁) : inl R₁ M₁ M₂ x = (x, 0) :=
rfl
#align continuous_linear_map.inl_apply ContinuousLinearMap.inl_apply
+-/
+#print ContinuousLinearMap.inr_apply /-
@[simp]
theorem inr_apply [Module R₁ M₂] (x : M₂) : inr R₁ M₁ M₂ x = (0, x) :=
rfl
#align continuous_linear_map.inr_apply ContinuousLinearMap.inr_apply
+-/
+#print ContinuousLinearMap.coe_inl /-
@[simp, norm_cast]
theorem coe_inl [Module R₁ M₂] : (inl R₁ M₁ M₂ : M₁ →ₗ[R₁] M₁ × M₂) = LinearMap.inl R₁ M₁ M₂ :=
rfl
#align continuous_linear_map.coe_inl ContinuousLinearMap.coe_inl
+-/
+#print ContinuousLinearMap.coe_inr /-
@[simp, norm_cast]
theorem coe_inr [Module R₁ M₂] : (inr R₁ M₁ M₂ : M₂ →ₗ[R₁] M₁ × M₂) = LinearMap.inr R₁ M₁ M₂ :=
rfl
#align continuous_linear_map.coe_inr ContinuousLinearMap.coe_inr
+-/
+#print ContinuousLinearMap.isClosed_ker /-
theorem isClosed_ker [T1Space M₂] [ContinuousSemilinearMapClass F σ₁₂ M₁ M₂] (f : F) :
IsClosed (ker f : Set M₁) :=
continuous_iff_isClosed.1 (map_continuous f) _ isClosed_singleton
#align continuous_linear_map.is_closed_ker ContinuousLinearMap.isClosed_ker
+-/
+#print ContinuousLinearMap.isComplete_ker /-
theorem isComplete_ker {M' : Type _} [UniformSpace M'] [CompleteSpace M'] [AddCommMonoid M']
[Module R₁ M'] [T1Space M₂] [ContinuousSemilinearMapClass F σ₁₂ M' M₂] (f : F) :
IsComplete (ker f : Set M') :=
(isClosed_ker f).IsComplete
#align continuous_linear_map.is_complete_ker ContinuousLinearMap.isComplete_ker
+-/
#print ContinuousLinearMap.completeSpace_ker /-
instance (priority := 100) completeSpace_ker {M' : Type _} [UniformSpace M'] [CompleteSpace M']
@@ -1064,36 +1225,46 @@ instance (priority := 100) completeSpace_ker {M' : Type _} [UniformSpace M'] [Co
#align continuous_linear_map.complete_space_ker ContinuousLinearMap.completeSpace_ker
-/
+#print ContinuousLinearMap.ker_prod /-
@[simp]
theorem ker_prod [Module R₁ M₂] [Module R₁ M₃] (f : M₁ →L[R₁] M₂) (g : M₁ →L[R₁] M₃) :
ker (f.Prod g) = ker f ⊓ ker g :=
LinearMap.ker_prod f g
#align continuous_linear_map.ker_prod ContinuousLinearMap.ker_prod
+-/
+#print ContinuousLinearMap.codRestrict /-
/-- Restrict codomain of a continuous linear map. -/
def codRestrict (f : M₁ →SL[σ₁₂] M₂) (p : Submodule R₂ M₂) (h : ∀ x, f x ∈ p) : M₁ →SL[σ₁₂] p
where
cont := f.Continuous.subtype_mk _
toLinearMap := (f : M₁ →ₛₗ[σ₁₂] M₂).codRestrict p h
#align continuous_linear_map.cod_restrict ContinuousLinearMap.codRestrict
+-/
+#print ContinuousLinearMap.coe_codRestrict /-
@[norm_cast]
theorem coe_codRestrict (f : M₁ →SL[σ₁₂] M₂) (p : Submodule R₂ M₂) (h : ∀ x, f x ∈ p) :
(f.codRestrict p h : M₁ →ₛₗ[σ₁₂] p) = (f : M₁ →ₛₗ[σ₁₂] M₂).codRestrict p h :=
rfl
#align continuous_linear_map.coe_cod_restrict ContinuousLinearMap.coe_codRestrict
+-/
+#print ContinuousLinearMap.coe_codRestrict_apply /-
@[simp]
theorem coe_codRestrict_apply (f : M₁ →SL[σ₁₂] M₂) (p : Submodule R₂ M₂) (h : ∀ x, f x ∈ p) (x) :
(f.codRestrict p h x : M₂) = f x :=
rfl
#align continuous_linear_map.coe_cod_restrict_apply ContinuousLinearMap.coe_codRestrict_apply
+-/
+#print ContinuousLinearMap.ker_codRestrict /-
@[simp]
theorem ker_codRestrict (f : M₁ →SL[σ₁₂] M₂) (p : Submodule R₂ M₂) (h : ∀ x, f x ∈ p) :
ker (f.codRestrict p h) = ker f :=
(f : M₁ →ₛₗ[σ₁₂] M₂).ker_codRestrict p h
#align continuous_linear_map.ker_cod_restrict ContinuousLinearMap.ker_codRestrict
+-/
#print Submodule.subtypeL /-
/-- `submodule.subtype` as a `continuous_linear_map`. -/
@@ -1104,126 +1275,168 @@ def Submodule.subtypeL (p : Submodule R₁ M₁) : p →L[R₁] M₁
#align submodule.subtypeL Submodule.subtypeL
-/
+#print Submodule.coe_subtypeL /-
@[simp, norm_cast]
theorem Submodule.coe_subtypeL (p : Submodule R₁ M₁) : (p.subtypeL : p →ₗ[R₁] M₁) = p.Subtype :=
rfl
#align submodule.coe_subtypeL Submodule.coe_subtypeL
+-/
+#print Submodule.coe_subtypeL' /-
@[simp]
theorem Submodule.coe_subtypeL' (p : Submodule R₁ M₁) : ⇑p.subtypeL = p.Subtype :=
rfl
#align submodule.coe_subtypeL' Submodule.coe_subtypeL'
+-/
+#print Submodule.subtypeL_apply /-
@[simp, norm_cast]
theorem Submodule.subtypeL_apply (p : Submodule R₁ M₁) (x : p) : p.subtypeL x = x :=
rfl
#align submodule.subtypeL_apply Submodule.subtypeL_apply
+-/
+#print Submodule.range_subtypeL /-
@[simp]
theorem Submodule.range_subtypeL (p : Submodule R₁ M₁) : range p.subtypeL = p :=
Submodule.range_subtype _
#align submodule.range_subtypeL Submodule.range_subtypeL
+-/
+#print Submodule.ker_subtypeL /-
@[simp]
theorem Submodule.ker_subtypeL (p : Submodule R₁ M₁) : ker p.subtypeL = ⊥ :=
Submodule.ker_subtype _
#align submodule.ker_subtypeL Submodule.ker_subtypeL
+-/
variable (R₁ M₁ M₂)
+#print ContinuousLinearMap.fst /-
/-- `prod.fst` as a `continuous_linear_map`. -/
def fst [Module R₁ M₂] : M₁ × M₂ →L[R₁] M₁
where
cont := continuous_fst
toLinearMap := LinearMap.fst R₁ M₁ M₂
#align continuous_linear_map.fst ContinuousLinearMap.fst
+-/
+#print ContinuousLinearMap.snd /-
/-- `prod.snd` as a `continuous_linear_map`. -/
def snd [Module R₁ M₂] : M₁ × M₂ →L[R₁] M₂
where
cont := continuous_snd
toLinearMap := LinearMap.snd R₁ M₁ M₂
#align continuous_linear_map.snd ContinuousLinearMap.snd
+-/
variable {R₁ M₁ M₂}
+#print ContinuousLinearMap.coe_fst /-
@[simp, norm_cast]
theorem coe_fst [Module R₁ M₂] : ↑(fst R₁ M₁ M₂) = LinearMap.fst R₁ M₁ M₂ :=
rfl
#align continuous_linear_map.coe_fst ContinuousLinearMap.coe_fst
+-/
+#print ContinuousLinearMap.coe_fst' /-
@[simp, norm_cast]
theorem coe_fst' [Module R₁ M₂] : ⇑(fst R₁ M₁ M₂) = Prod.fst :=
rfl
#align continuous_linear_map.coe_fst' ContinuousLinearMap.coe_fst'
+-/
+#print ContinuousLinearMap.coe_snd /-
@[simp, norm_cast]
theorem coe_snd [Module R₁ M₂] : ↑(snd R₁ M₁ M₂) = LinearMap.snd R₁ M₁ M₂ :=
rfl
#align continuous_linear_map.coe_snd ContinuousLinearMap.coe_snd
+-/
+#print ContinuousLinearMap.coe_snd' /-
@[simp, norm_cast]
theorem coe_snd' [Module R₁ M₂] : ⇑(snd R₁ M₁ M₂) = Prod.snd :=
rfl
#align continuous_linear_map.coe_snd' ContinuousLinearMap.coe_snd'
+-/
+#print ContinuousLinearMap.fst_prod_snd /-
@[simp]
theorem fst_prod_snd [Module R₁ M₂] : (fst R₁ M₁ M₂).Prod (snd R₁ M₁ M₂) = id R₁ (M₁ × M₂) :=
ext fun ⟨x, y⟩ => rfl
#align continuous_linear_map.fst_prod_snd ContinuousLinearMap.fst_prod_snd
+-/
+#print ContinuousLinearMap.fst_comp_prod /-
@[simp]
theorem fst_comp_prod [Module R₁ M₂] [Module R₁ M₃] (f : M₁ →L[R₁] M₂) (g : M₁ →L[R₁] M₃) :
(fst R₁ M₂ M₃).comp (f.Prod g) = f :=
ext fun x => rfl
#align continuous_linear_map.fst_comp_prod ContinuousLinearMap.fst_comp_prod
+-/
+#print ContinuousLinearMap.snd_comp_prod /-
@[simp]
theorem snd_comp_prod [Module R₁ M₂] [Module R₁ M₃] (f : M₁ →L[R₁] M₂) (g : M₁ →L[R₁] M₃) :
(snd R₁ M₂ M₃).comp (f.Prod g) = g :=
ext fun x => rfl
#align continuous_linear_map.snd_comp_prod ContinuousLinearMap.snd_comp_prod
+-/
+#print ContinuousLinearMap.prodMap /-
/-- `prod.map` of two continuous linear maps. -/
def prodMap [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (f₁ : M₁ →L[R₁] M₂) (f₂ : M₃ →L[R₁] M₄) :
M₁ × M₃ →L[R₁] M₂ × M₄ :=
(f₁.comp (fst R₁ M₁ M₃)).Prod (f₂.comp (snd R₁ M₁ M₃))
#align continuous_linear_map.prod_map ContinuousLinearMap.prodMap
+-/
+#print ContinuousLinearMap.coe_prodMap /-
@[simp, norm_cast]
theorem coe_prodMap [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (f₁ : M₁ →L[R₁] M₂)
(f₂ : M₃ →L[R₁] M₄) : ↑(f₁.Prod_map f₂) = (f₁ : M₁ →ₗ[R₁] M₂).Prod_map (f₂ : M₃ →ₗ[R₁] M₄) :=
rfl
#align continuous_linear_map.coe_prod_map ContinuousLinearMap.coe_prodMap
+-/
+#print ContinuousLinearMap.coe_prodMap' /-
@[simp, norm_cast]
theorem coe_prodMap' [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (f₁ : M₁ →L[R₁] M₂)
(f₂ : M₃ →L[R₁] M₄) : ⇑(f₁.Prod_map f₂) = Prod.map f₁ f₂ :=
rfl
#align continuous_linear_map.coe_prod_map' ContinuousLinearMap.coe_prodMap'
+-/
+#print ContinuousLinearMap.coprod /-
/-- The continuous linear map given by `(x, y) ↦ f₁ x + f₂ y`. -/
def coprod [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃] (f₁ : M₁ →L[R₁] M₃)
(f₂ : M₂ →L[R₁] M₃) : M₁ × M₂ →L[R₁] M₃ :=
⟨LinearMap.coprod f₁ f₂, (f₁.cont.comp continuous_fst).add (f₂.cont.comp continuous_snd)⟩
#align continuous_linear_map.coprod ContinuousLinearMap.coprod
+-/
+#print ContinuousLinearMap.coe_coprod /-
@[norm_cast, simp]
theorem coe_coprod [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃] (f₁ : M₁ →L[R₁] M₃)
(f₂ : M₂ →L[R₁] M₃) : (f₁.coprod f₂ : M₁ × M₂ →ₗ[R₁] M₃) = LinearMap.coprod f₁ f₂ :=
rfl
#align continuous_linear_map.coe_coprod ContinuousLinearMap.coe_coprod
+-/
+#print ContinuousLinearMap.coprod_apply /-
@[simp]
theorem coprod_apply [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃] (f₁ : M₁ →L[R₁] M₃)
(f₂ : M₂ →L[R₁] M₃) (x) : f₁.coprod f₂ x = f₁ x.1 + f₂ x.2 :=
rfl
#align continuous_linear_map.coprod_apply ContinuousLinearMap.coprod_apply
+-/
+#print ContinuousLinearMap.range_coprod /-
theorem range_coprod [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃] (f₁ : M₁ →L[R₁] M₃)
(f₂ : M₂ →L[R₁] M₃) : range (f₁.coprod f₂) = range f₁ ⊔ range f₂ :=
LinearMap.range_coprod _ _
#align continuous_linear_map.range_coprod ContinuousLinearMap.range_coprod
+-/
theorem comp_fst_add_comp_snd [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃] (f : M₁ →L[R₁] M₃)
(g : M₂ →L[R₁] M₃) :
@@ -1252,32 +1465,40 @@ def smulRight (c : M₁ →L[R] S) (f : M₂) : M₁ →L[R] M₂ :=
#align continuous_linear_map.smul_right ContinuousLinearMap.smulRight
-/
+#print ContinuousLinearMap.smulRight_apply /-
@[simp]
theorem smulRight_apply {c : M₁ →L[R] S} {f : M₂} {x : M₁} :
(smulRight c f : M₁ → M₂) x = c x • f :=
rfl
#align continuous_linear_map.smul_right_apply ContinuousLinearMap.smulRight_apply
+-/
end
variable [Module R₁ M₂] [TopologicalSpace R₁] [ContinuousSMul R₁ M₂]
+#print ContinuousLinearMap.smulRight_one_one /-
@[simp]
theorem smulRight_one_one (c : R₁ →L[R₁] M₂) : smulRight (1 : R₁ →L[R₁] R₁) (c 1) = c := by
ext <;> simp [← ContinuousLinearMap.map_smul_of_tower]
#align continuous_linear_map.smul_right_one_one ContinuousLinearMap.smulRight_one_one
+-/
+#print ContinuousLinearMap.smulRight_one_eq_iff /-
@[simp]
theorem smulRight_one_eq_iff {f f' : M₂} :
smulRight (1 : R₁ →L[R₁] R₁) f = smulRight (1 : R₁ →L[R₁] R₁) f' ↔ f = f' := by
simp only [ext_ring_iff, smul_right_apply, one_apply, one_smul]
#align continuous_linear_map.smul_right_one_eq_iff ContinuousLinearMap.smulRight_one_eq_iff
+-/
+#print ContinuousLinearMap.smulRight_comp /-
theorem smulRight_comp [ContinuousMul R₁] {x : M₂} {c : R₁} :
(smulRight (1 : R₁ →L[R₁] R₁) x).comp (smulRight (1 : R₁ →L[R₁] R₁) c) =
smulRight (1 : R₁ →L[R₁] R₁) (c • x) :=
by ext; simp [mul_smul]
#align continuous_linear_map.smul_right_comp ContinuousLinearMap.smulRight_comp
+-/
end Semiring
@@ -1295,32 +1516,44 @@ def pi (f : ∀ i, M →L[R] φ i) : M →L[R] ∀ i, φ i :=
#align continuous_linear_map.pi ContinuousLinearMap.pi
-/
+#print ContinuousLinearMap.coe_pi' /-
@[simp]
theorem coe_pi' (f : ∀ i, M →L[R] φ i) : ⇑(pi f) = fun c i => f i c :=
rfl
#align continuous_linear_map.coe_pi' ContinuousLinearMap.coe_pi'
+-/
+#print ContinuousLinearMap.coe_pi /-
@[simp]
theorem coe_pi (f : ∀ i, M →L[R] φ i) : (pi f : M →ₗ[R] ∀ i, φ i) = LinearMap.pi fun i => f i :=
rfl
#align continuous_linear_map.coe_pi ContinuousLinearMap.coe_pi
+-/
+#print ContinuousLinearMap.pi_apply /-
theorem pi_apply (f : ∀ i, M →L[R] φ i) (c : M) (i : ι) : pi f c i = f i c :=
rfl
#align continuous_linear_map.pi_apply ContinuousLinearMap.pi_apply
+-/
+#print ContinuousLinearMap.pi_eq_zero /-
theorem pi_eq_zero (f : ∀ i, M →L[R] φ i) : pi f = 0 ↔ ∀ i, f i = 0 := by
simp only [ext_iff, pi_apply, Function.funext_iff]; exact forall_swap
#align continuous_linear_map.pi_eq_zero ContinuousLinearMap.pi_eq_zero
+-/
+#print ContinuousLinearMap.pi_zero /-
theorem pi_zero : pi (fun i => 0 : ∀ i, M →L[R] φ i) = 0 :=
ext fun _ => rfl
#align continuous_linear_map.pi_zero ContinuousLinearMap.pi_zero
+-/
+#print ContinuousLinearMap.pi_comp /-
theorem pi_comp (f : ∀ i, M →L[R] φ i) (g : M₂ →L[R] M) :
(pi f).comp g = pi fun i => (f i).comp g :=
rfl
#align continuous_linear_map.pi_comp ContinuousLinearMap.pi_comp
+-/
#print ContinuousLinearMap.proj /-
/-- The projections from a family of topological modules are continuous linear maps. -/
@@ -1329,21 +1562,28 @@ def proj (i : ι) : (∀ i, φ i) →L[R] φ i :=
#align continuous_linear_map.proj ContinuousLinearMap.proj
-/
+#print ContinuousLinearMap.proj_apply /-
@[simp]
theorem proj_apply (i : ι) (b : ∀ i, φ i) : (proj i : (∀ i, φ i) →L[R] φ i) b = b i :=
rfl
#align continuous_linear_map.proj_apply ContinuousLinearMap.proj_apply
+-/
+#print ContinuousLinearMap.proj_pi /-
theorem proj_pi (f : ∀ i, M₂ →L[R] φ i) (i : ι) : (proj i).comp (pi f) = f i :=
ext fun c => rfl
#align continuous_linear_map.proj_pi ContinuousLinearMap.proj_pi
+-/
+#print ContinuousLinearMap.iInf_ker_proj /-
theorem iInf_ker_proj : (⨅ i, ker (proj i : (∀ i, φ i) →L[R] φ i) : Submodule R (∀ i, φ i)) = ⊥ :=
LinearMap.iInf_ker_proj
#align continuous_linear_map.infi_ker_proj ContinuousLinearMap.iInf_ker_proj
+-/
variable (R φ)
+#print ContinuousLinearMap.iInfKerProjEquiv /-
/-- If `I` and `J` are complementary index sets, the product of the kernels of the `J`th projections
of `φ` is linearly equivalent to the product over `I`. -/
def iInfKerProjEquiv {I J : Set ι} [DecidablePred fun i => i ∈ I] (hd : Disjoint I J)
@@ -1365,6 +1605,7 @@ def iInfKerProjEquiv {I J : Set ι} [DecidablePred fun i => i ∈ I] (hd : Disjo
split_ifs <;> [apply continuous_apply; exact continuous_zero])
_
#align continuous_linear_map.infi_ker_proj_equiv ContinuousLinearMap.iInfKerProjEquiv
+-/
end Pi
@@ -1378,18 +1619,24 @@ variable {R : Type _} [Ring R] {R₂ : Type _} [Ring R₂] {R₃ : Type _} [Ring
section
+#print ContinuousLinearMap.map_neg /-
protected theorem map_neg (f : M →SL[σ₁₂] M₂) (x : M) : f (-x) = -f x :=
map_neg _ _
#align continuous_linear_map.map_neg ContinuousLinearMap.map_neg
+-/
+#print ContinuousLinearMap.map_sub /-
protected theorem map_sub (f : M →SL[σ₁₂] M₂) (x y : M) : f (x - y) = f x - f y :=
map_sub _ _ _
#align continuous_linear_map.map_sub ContinuousLinearMap.map_sub
+-/
+#print ContinuousLinearMap.sub_apply' /-
@[simp]
theorem sub_apply' (f g : M →SL[σ₁₂] M₂) (x : M) : ((f : M →ₛₗ[σ₁₂] M₂) - g) x = f x - g x :=
rfl
#align continuous_linear_map.sub_apply' ContinuousLinearMap.sub_apply'
+-/
end
@@ -1397,21 +1644,27 @@ section
variable [Module R M₂] [Module R M₃] [Module R M₄]
+#print ContinuousLinearMap.range_prod_eq /-
theorem range_prod_eq {f : M →L[R] M₂} {g : M →L[R] M₃} (h : ker f ⊔ ker g = ⊤) :
range (f.Prod g) = (range f).Prod (range g) :=
LinearMap.range_prod_eq h
#align continuous_linear_map.range_prod_eq ContinuousLinearMap.range_prod_eq
+-/
+#print ContinuousLinearMap.ker_prod_ker_le_ker_coprod /-
theorem ker_prod_ker_le_ker_coprod [ContinuousAdd M₃] (f : M →L[R] M₃) (g : M₂ →L[R] M₃) :
(LinearMap.ker f).Prod (LinearMap.ker g) ≤ LinearMap.ker (f.coprod g) :=
LinearMap.ker_prod_ker_le_ker_coprod f.toLinearMap g.toLinearMap
#align continuous_linear_map.ker_prod_ker_le_ker_coprod ContinuousLinearMap.ker_prod_ker_le_ker_coprod
+-/
+#print ContinuousLinearMap.ker_coprod_of_disjoint_range /-
theorem ker_coprod_of_disjoint_range [ContinuousAdd M₃] (f : M →L[R] M₃) (g : M₂ →L[R] M₃)
(hd : Disjoint (range f) (range g)) :
LinearMap.ker (f.coprod g) = (LinearMap.ker f).Prod (LinearMap.ker g) :=
LinearMap.ker_coprod_of_disjoint_range f.toLinearMap g.toLinearMap hd
#align continuous_linear_map.ker_coprod_of_disjoint_range ContinuousLinearMap.ker_coprod_of_disjoint_range
+-/
end
@@ -1422,20 +1675,26 @@ variable [TopologicalAddGroup M₂]
instance : Neg (M →SL[σ₁₂] M₂) :=
⟨fun f => ⟨-f, f.2.neg⟩⟩
+#print ContinuousLinearMap.neg_apply /-
@[simp]
theorem neg_apply (f : M →SL[σ₁₂] M₂) (x : M) : (-f) x = -f x :=
rfl
#align continuous_linear_map.neg_apply ContinuousLinearMap.neg_apply
+-/
+#print ContinuousLinearMap.coe_neg /-
@[simp, norm_cast]
theorem coe_neg (f : M →SL[σ₁₂] M₂) : (↑(-f) : M →ₛₗ[σ₁₂] M₂) = -f :=
rfl
#align continuous_linear_map.coe_neg ContinuousLinearMap.coe_neg
+-/
+#print ContinuousLinearMap.coe_neg' /-
@[norm_cast]
theorem coe_neg' (f : M →SL[σ₁₂] M₂) : ⇑(-f) = -f :=
rfl
#align continuous_linear_map.coe_neg' ContinuousLinearMap.coe_neg'
+-/
instance : Sub (M →SL[σ₁₂] M₂) :=
⟨fun f g => ⟨f - g, f.2.sub g.2⟩⟩
@@ -1457,42 +1716,56 @@ instance : AddCommGroup (M →SL[σ₁₂] M₂) := by
ext <;>
apply_rules [zero_add, add_assoc, add_zero, add_left_neg, add_comm, sub_eq_add_neg]
+#print ContinuousLinearMap.sub_apply /-
theorem sub_apply (f g : M →SL[σ₁₂] M₂) (x : M) : (f - g) x = f x - g x :=
rfl
#align continuous_linear_map.sub_apply ContinuousLinearMap.sub_apply
+-/
+#print ContinuousLinearMap.coe_sub /-
@[simp, norm_cast]
theorem coe_sub (f g : M →SL[σ₁₂] M₂) : (↑(f - g) : M →ₛₗ[σ₁₂] M₂) = f - g :=
rfl
#align continuous_linear_map.coe_sub ContinuousLinearMap.coe_sub
+-/
+#print ContinuousLinearMap.coe_sub' /-
@[simp, norm_cast]
theorem coe_sub' (f g : M →SL[σ₁₂] M₂) : ⇑(f - g) = f - g :=
rfl
#align continuous_linear_map.coe_sub' ContinuousLinearMap.coe_sub'
+-/
end
+#print ContinuousLinearMap.comp_neg /-
@[simp]
theorem comp_neg [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₂] [TopologicalAddGroup M₃]
(g : M₂ →SL[σ₂₃] M₃) (f : M →SL[σ₁₂] M₂) : g.comp (-f) = -g.comp f := by ext; simp
#align continuous_linear_map.comp_neg ContinuousLinearMap.comp_neg
+-/
+#print ContinuousLinearMap.neg_comp /-
@[simp]
theorem neg_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₃] (g : M₂ →SL[σ₂₃] M₃)
(f : M →SL[σ₁₂] M₂) : (-g).comp f = -g.comp f := by ext; simp
#align continuous_linear_map.neg_comp ContinuousLinearMap.neg_comp
+-/
+#print ContinuousLinearMap.comp_sub /-
@[simp]
theorem comp_sub [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₂] [TopologicalAddGroup M₃]
(g : M₂ →SL[σ₂₃] M₃) (f₁ f₂ : M →SL[σ₁₂] M₂) : g.comp (f₁ - f₂) = g.comp f₁ - g.comp f₂ := by
ext; simp
#align continuous_linear_map.comp_sub ContinuousLinearMap.comp_sub
+-/
+#print ContinuousLinearMap.sub_comp /-
@[simp]
theorem sub_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₃] (g₁ g₂ : M₂ →SL[σ₂₃] M₃)
(f : M →SL[σ₁₂] M₂) : (g₁ - g₂).comp f = g₁.comp f - g₂.comp f := by ext; simp
#align continuous_linear_map.sub_comp ContinuousLinearMap.sub_comp
+-/
instance [TopologicalAddGroup M] : Ring (M →L[R] M) :=
{ ContinuousLinearMap.semiring,
@@ -1500,6 +1773,7 @@ instance [TopologicalAddGroup M] : Ring (M →L[R] M) :=
mul := (· * ·)
one := 1 }
+#print ContinuousLinearMap.smulRight_one_pow /-
theorem smulRight_one_pow [TopologicalSpace R] [TopologicalRing R] (c : R) (n : ℕ) :
smulRight (1 : R →L[R] R) c ^ n = smulRight (1 : R →L[R] R) (c ^ n) :=
by
@@ -1507,38 +1781,47 @@ theorem smulRight_one_pow [TopologicalSpace R] [TopologicalRing R] (c : R) (n :
· ext; simp
· rw [pow_succ, ihn, mul_def, smul_right_comp, smul_eq_mul, pow_succ']
#align continuous_linear_map.smul_right_one_pow ContinuousLinearMap.smulRight_one_pow
+-/
section
variable {σ₂₁ : R₂ →+* R} [RingHomInvPair σ₁₂ σ₂₁]
+#print ContinuousLinearMap.projKerOfRightInverse /-
/-- Given a right inverse `f₂ : M₂ →L[R] M` to `f₁ : M →L[R] M₂`,
`proj_ker_of_right_inverse f₁ f₂ h` is the projection `M →L[R] f₁.ker` along `f₂.range`. -/
def projKerOfRightInverse [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂) (f₂ : M₂ →SL[σ₂₁] M)
(h : Function.RightInverse f₂ f₁) : M →L[R] LinearMap.ker f₁ :=
(id R M - f₂.comp f₁).codRestrict (LinearMap.ker f₁) fun x => by simp [h (f₁ x)]
#align continuous_linear_map.proj_ker_of_right_inverse ContinuousLinearMap.projKerOfRightInverse
+-/
+#print ContinuousLinearMap.coe_projKerOfRightInverse_apply /-
@[simp]
theorem coe_projKerOfRightInverse_apply [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂)
(f₂ : M₂ →SL[σ₂₁] M) (h : Function.RightInverse f₂ f₁) (x : M) :
(f₁.projKerOfRightInverse f₂ h x : M) = x - f₂ (f₁ x) :=
rfl
#align continuous_linear_map.coe_proj_ker_of_right_inverse_apply ContinuousLinearMap.coe_projKerOfRightInverse_apply
+-/
+#print ContinuousLinearMap.projKerOfRightInverse_apply_idem /-
@[simp]
theorem projKerOfRightInverse_apply_idem [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂)
(f₂ : M₂ →SL[σ₂₁] M) (h : Function.RightInverse f₂ f₁) (x : LinearMap.ker f₁) :
f₁.projKerOfRightInverse f₂ h x = x :=
Subtype.ext_iff_val.2 <| by simp
#align continuous_linear_map.proj_ker_of_right_inverse_apply_idem ContinuousLinearMap.projKerOfRightInverse_apply_idem
+-/
+#print ContinuousLinearMap.projKerOfRightInverse_comp_inv /-
@[simp]
theorem projKerOfRightInverse_comp_inv [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂)
(f₂ : M₂ →SL[σ₂₁] M) (h : Function.RightInverse f₂ f₁) (y : M₂) :
f₁.projKerOfRightInverse f₂ h (f₂ y) = 0 :=
Subtype.ext_iff_val.2 <| by simp [h y]
#align continuous_linear_map.proj_ker_of_right_inverse_comp_inv ContinuousLinearMap.projKerOfRightInverse_comp_inv
+-/
end
@@ -1548,6 +1831,7 @@ section DivisionMonoid
variable {R M : Type _}
+#print ContinuousLinearMap.isOpenMap_of_ne_zero /-
/-- A nonzero continuous linear functional is open. -/
protected theorem isOpenMap_of_ne_zero [TopologicalSpace R] [DivisionRing R] [ContinuousSub R]
[AddCommGroup M] [TopologicalSpace M] [ContinuousAdd M] [Module R M] [ContinuousSMul R M]
@@ -1557,6 +1841,7 @@ protected theorem isOpenMap_of_ne_zero [TopologicalSpace R] [DivisionRing R] [Co
⟨fun a => y + (a - f y) • (f x)⁻¹ • x, Continuous.continuousAt <| by continuity, by simp,
fun a => by simp [hx]⟩
#align continuous_linear_map.is_open_map_of_ne_zero ContinuousLinearMap.isOpenMap_of_ne_zero
+-/
end DivisionMonoid
@@ -1572,28 +1857,27 @@ variable {R R₂ R₃ S S₃ : Type _} [Semiring R] [Semiring R₂] [Semiring R
[DistribMulAction S N₃] [SMulCommClass R S N₃] [ContinuousConstSMul S N₃] {σ₁₂ : R →+* R₂}
{σ₂₃ : R₂ →+* R₃} {σ₁₃ : R →+* R₃} [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃]
-include σ₁₃
-
+#print ContinuousLinearMap.smul_comp /-
@[simp]
theorem smul_comp (c : S₃) (h : M₂ →SL[σ₂₃] M₃) (f : M →SL[σ₁₂] M₂) :
(c • h).comp f = c • h.comp f :=
rfl
#align continuous_linear_map.smul_comp ContinuousLinearMap.smul_comp
-
-omit σ₁₃
+-/
variable [DistribMulAction S₃ M₂] [ContinuousConstSMul S₃ M₂] [SMulCommClass R₂ S₃ M₂]
variable [DistribMulAction S N₂] [ContinuousConstSMul S N₂] [SMulCommClass R S N₂]
+#print ContinuousLinearMap.comp_smul /-
@[simp]
theorem comp_smul [LinearMap.CompatibleSMul N₂ N₃ S R] (hₗ : N₂ →L[R] N₃) (c : S)
(fₗ : M →L[R] N₂) : hₗ.comp (c • fₗ) = c • hₗ.comp fₗ := by ext x;
exact hₗ.map_smul_of_tower c (fₗ x)
#align continuous_linear_map.comp_smul ContinuousLinearMap.comp_smul
+-/
-include σ₁₃
-
+#print ContinuousLinearMap.comp_smulₛₗ /-
@[simp]
theorem comp_smulₛₗ [SMulCommClass R₂ R₂ M₂] [SMulCommClass R₃ R₃ M₃] [ContinuousConstSMul R₂ M₂]
[ContinuousConstSMul R₃ M₃] (h : M₂ →SL[σ₂₃] M₃) (c : R₂) (f : M →SL[σ₁₂] M₂) :
@@ -1601,8 +1885,7 @@ theorem comp_smulₛₗ [SMulCommClass R₂ R₂ M₂] [SMulCommClass R₃ R₃
simp only [coe_smul', coe_comp', Function.comp_apply, Pi.smul_apply,
ContinuousLinearMap.map_smulₛₗ]
#align continuous_linear_map.comp_smulₛₗ ContinuousLinearMap.comp_smulₛₗ
-
-omit σ₁₃
+-/
instance [ContinuousAdd M₂] : DistribMulAction S₃ (M →SL[σ₁₂] M₂)
where
@@ -1624,6 +1907,7 @@ variable {R R₂ R₃ S S₃ : Type _} [Semiring R] [Semiring R₂] [Semiring R
{σ₁₂ : R →+* R₂} {σ₂₃ : R₂ →+* R₃} {σ₁₃ : R →+* R₃} [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] (c : S)
(h : M₂ →SL[σ₂₃] M₃) (f g : M →SL[σ₁₂] M₂) (x y z : M)
+#print ContinuousLinearMap.prodEquiv /-
/-- `continuous_linear_map.prod` as an `equiv`. -/
@[simps apply]
def prodEquiv : (M →L[R] N₂) × (M →L[R] N₃) ≃ (M →L[R] N₂ × N₃)
@@ -1633,17 +1917,22 @@ def prodEquiv : (M →L[R] N₂) × (M →L[R] N₃) ≃ (M →L[R] N₂ × N₃
left_inv f := by ext <;> rfl
right_inv f := by ext <;> rfl
#align continuous_linear_map.prod_equiv ContinuousLinearMap.prodEquiv
+-/
+#print ContinuousLinearMap.prod_ext_iff /-
theorem prod_ext_iff {f g : M × N₂ →L[R] N₃} :
f = g ↔ f.comp (inl _ _ _) = g.comp (inl _ _ _) ∧ f.comp (inr _ _ _) = g.comp (inr _ _ _) := by
simp only [← coe_inj, LinearMap.prod_ext_iff]; rfl
#align continuous_linear_map.prod_ext_iff ContinuousLinearMap.prod_ext_iff
+-/
+#print ContinuousLinearMap.prod_ext /-
@[ext]
theorem prod_ext {f g : M × N₂ →L[R] N₃} (hl : f.comp (inl _ _ _) = g.comp (inl _ _ _))
(hr : f.comp (inr _ _ _) = g.comp (inr _ _ _)) : f = g :=
prod_ext_iff.2 ⟨hl, hr⟩
#align continuous_linear_map.prod_ext ContinuousLinearMap.prod_ext
+-/
variable [ContinuousAdd M₂] [ContinuousAdd M₃] [ContinuousAdd N₂]
@@ -1657,6 +1946,7 @@ instance [Module S₃ᵐᵒᵖ M₃] [IsCentralScalar S₃ M₃] : IsCentralScal
variable (S) [ContinuousAdd N₃]
+#print ContinuousLinearMap.prodₗ /-
/-- `continuous_linear_map.prod` as a `linear_equiv`. -/
@[simps apply]
def prodₗ : ((M →L[R] N₂) × (M →L[R] N₃)) ≃ₗ[S] M →L[R] N₂ × N₃ :=
@@ -1664,7 +1954,9 @@ def prodₗ : ((M →L[R] N₂) × (M →L[R] N₃)) ≃ₗ[S] M →L[R] N₂ ×
map_add' := fun f g => rfl
map_smul' := fun c f => rfl }
#align continuous_linear_map.prodₗ ContinuousLinearMap.prodₗ
+-/
+#print ContinuousLinearMap.coeLM /-
/-- The coercion from `M →L[R] M₂` to `M →ₗ[R] M₂`, as a linear map. -/
@[simps]
def coeLM : (M →L[R] N₃) →ₗ[S] M →ₗ[R] N₃
@@ -1673,9 +1965,11 @@ def coeLM : (M →L[R] N₃) →ₗ[S] M →ₗ[R] N₃
map_add' f g := coe_add f g
map_smul' c f := coe_smul c f
#align continuous_linear_map.coe_lm ContinuousLinearMap.coeLM
+-/
variable {S} (σ₁₃)
+#print ContinuousLinearMap.coeLMₛₗ /-
/-- The coercion from `M →SL[σ] M₂` to `M →ₛₗ[σ] M₂`, as a linear map. -/
@[simps]
def coeLMₛₗ : (M →SL[σ₁₃] M₃) →ₗ[S₃] M →ₛₗ[σ₁₃] M₃
@@ -1684,6 +1978,7 @@ def coeLMₛₗ : (M →SL[σ₁₃] M₃) →ₗ[S₃] M →ₛₗ[σ₁₃] M
map_add' f g := coe_add f g
map_smul' c f := coe_smul c f
#align continuous_linear_map.coe_lmₛₗ ContinuousLinearMap.coeLMₛₗ
+-/
variable {σ₁₃}
@@ -1697,6 +1992,7 @@ variable {R S T M M₂ : Type _} [Semiring R] [Semiring S] [Semiring T] [Module
[ContinuousAdd M₂] [Module T M₂] [ContinuousConstSMul T M₂] [SMulCommClass R T M₂]
[SMulCommClass S T M₂]
+#print ContinuousLinearMap.smulRightₗ /-
/-- Given `c : E →L[𝕜] 𝕜`, `c.smul_rightₗ` is the linear map from `F` to `E →L[𝕜] F`
sending `f` to `λ e, c e • f`. See also `continuous_linear_map.smul_rightL`. -/
def smulRightₗ (c : M →L[R] S) : M₂ →ₗ[T] M →L[R] M₂
@@ -1705,11 +2001,14 @@ def smulRightₗ (c : M →L[R] S) : M₂ →ₗ[T] M →L[R] M₂
map_add' x y := by ext e; apply smul_add
map_smul' a x := by ext e; dsimp; apply smul_comm
#align continuous_linear_map.smul_rightₗ ContinuousLinearMap.smulRightₗ
+-/
+#print ContinuousLinearMap.coe_smulRightₗ /-
@[simp]
theorem coe_smulRightₗ (c : M →L[R] S) : ⇑(smulRightₗ c : M₂ →ₗ[T] M →L[R] M₂) = c.smul_right :=
rfl
#align continuous_linear_map.coe_smul_rightₗ ContinuousLinearMap.coe_smulRightₗ
+-/
end SmulRightₗ
@@ -1743,47 +2042,59 @@ def restrictScalars (f : M →L[A] M₂) : M →L[R] M₂ :=
variable {R}
+#print ContinuousLinearMap.coe_restrictScalars /-
@[simp, norm_cast]
theorem coe_restrictScalars (f : M →L[A] M₂) :
(f.restrictScalars R : M →ₗ[R] M₂) = (f : M →ₗ[A] M₂).restrictScalars R :=
rfl
#align continuous_linear_map.coe_restrict_scalars ContinuousLinearMap.coe_restrictScalars
+-/
+#print ContinuousLinearMap.coe_restrictScalars' /-
@[simp]
theorem coe_restrictScalars' (f : M →L[A] M₂) : ⇑(f.restrictScalars R) = f :=
rfl
#align continuous_linear_map.coe_restrict_scalars' ContinuousLinearMap.coe_restrictScalars'
+-/
+#print ContinuousLinearMap.restrictScalars_zero /-
@[simp]
theorem restrictScalars_zero : (0 : M →L[A] M₂).restrictScalars R = 0 :=
rfl
#align continuous_linear_map.restrict_scalars_zero ContinuousLinearMap.restrictScalars_zero
+-/
section
variable [TopologicalAddGroup M₂]
+#print ContinuousLinearMap.restrictScalars_add /-
@[simp]
theorem restrictScalars_add (f g : M →L[A] M₂) :
(f + g).restrictScalars R = f.restrictScalars R + g.restrictScalars R :=
rfl
#align continuous_linear_map.restrict_scalars_add ContinuousLinearMap.restrictScalars_add
+-/
+#print ContinuousLinearMap.restrictScalars_neg /-
@[simp]
theorem restrictScalars_neg (f : M →L[A] M₂) : (-f).restrictScalars R = -f.restrictScalars R :=
rfl
#align continuous_linear_map.restrict_scalars_neg ContinuousLinearMap.restrictScalars_neg
+-/
end
variable {S : Type _} [Ring S] [Module S M₂] [ContinuousConstSMul S M₂] [SMulCommClass A S M₂]
[SMulCommClass R S M₂]
+#print ContinuousLinearMap.restrictScalars_smul /-
@[simp]
theorem restrictScalars_smul (c : S) (f : M →L[A] M₂) :
(c • f).restrictScalars R = c • f.restrictScalars R :=
rfl
#align continuous_linear_map.restrict_scalars_smul ContinuousLinearMap.restrictScalars_smul
+-/
variable (A M M₂ R S) [TopologicalAddGroup M₂]
@@ -1800,10 +2111,12 @@ def restrictScalarsₗ : (M →L[A] M₂) →ₗ[S] M →L[R] M₂
variable {A M M₂ R S}
+#print ContinuousLinearMap.coe_restrictScalarsₗ /-
@[simp]
theorem coe_restrictScalarsₗ : ⇑(restrictScalarsₗ A M M₂ R S) = restrictScalars R :=
rfl
#align continuous_linear_map.coe_restrict_scalarsₗ ContinuousLinearMap.coe_restrictScalarsₗ
+-/
end RestrictScalars
@@ -1823,8 +2136,6 @@ variable {R₁ : Type _} {R₂ : Type _} {R₃ : Type _} [Semiring R₁] [Semiri
[AddCommMonoid M₃] {M₄ : Type _} [TopologicalSpace M₄] [AddCommMonoid M₄] [Module R₁ M₁]
[Module R₁ M'₁] [Module R₂ M₂] [Module R₃ M₃]
-include σ₂₁
-
#print ContinuousLinearEquiv.toContinuousLinearMap /-
/-- A continuous linear equivalence induces a continuous linear map. -/
def toContinuousLinearMap (e : M₁ ≃SL[σ₁₂] M₂) : M₁ →SL[σ₁₂] M₂ :=
@@ -1860,38 +2171,52 @@ theorem coe_def_rev (e : M₁ ≃SL[σ₁₂] M₂) : e.toContinuousLinearMap =
rfl
#align continuous_linear_equiv.coe_def_rev ContinuousLinearEquiv.coe_def_rev
+#print ContinuousLinearEquiv.coe_apply /-
theorem coe_apply (e : M₁ ≃SL[σ₁₂] M₂) (b : M₁) : (e : M₁ →SL[σ₁₂] M₂) b = e b :=
rfl
#align continuous_linear_equiv.coe_apply ContinuousLinearEquiv.coe_apply
+-/
+#print ContinuousLinearEquiv.coe_toLinearEquiv /-
@[simp]
theorem coe_toLinearEquiv (f : M₁ ≃SL[σ₁₂] M₂) : ⇑f.toLinearEquiv = f :=
rfl
#align continuous_linear_equiv.coe_to_linear_equiv ContinuousLinearEquiv.coe_toLinearEquiv
+-/
+#print ContinuousLinearEquiv.coe_coe /-
@[simp, norm_cast]
theorem coe_coe (e : M₁ ≃SL[σ₁₂] M₂) : ⇑(e : M₁ →SL[σ₁₂] M₂) = e :=
rfl
#align continuous_linear_equiv.coe_coe ContinuousLinearEquiv.coe_coe
+-/
+#print ContinuousLinearEquiv.toLinearEquiv_injective /-
theorem toLinearEquiv_injective :
Function.Injective (toLinearEquiv : (M₁ ≃SL[σ₁₂] M₂) → M₁ ≃ₛₗ[σ₁₂] M₂)
| ⟨e, _, _⟩, ⟨e', _, _⟩, rfl => rfl
#align continuous_linear_equiv.to_linear_equiv_injective ContinuousLinearEquiv.toLinearEquiv_injective
+-/
+#print ContinuousLinearEquiv.ext /-
@[ext]
theorem ext {f g : M₁ ≃SL[σ₁₂] M₂} (h : (f : M₁ → M₂) = g) : f = g :=
toLinearEquiv_injective <| LinearEquiv.ext <| congr_fun h
#align continuous_linear_equiv.ext ContinuousLinearEquiv.ext
+-/
+#print ContinuousLinearEquiv.coe_injective /-
theorem coe_injective : Function.Injective (coe : (M₁ ≃SL[σ₁₂] M₂) → M₁ →SL[σ₁₂] M₂) :=
fun e e' h => ext <| funext <| ContinuousLinearMap.ext_iff.1 h
#align continuous_linear_equiv.coe_injective ContinuousLinearEquiv.coe_injective
+-/
+#print ContinuousLinearEquiv.coe_inj /-
@[simp, norm_cast]
theorem coe_inj {e e' : M₁ ≃SL[σ₁₂] M₂} : (e : M₁ →SL[σ₁₂] M₂) = e' ↔ e = e' :=
coe_injective.eq_iff
#align continuous_linear_equiv.coe_inj ContinuousLinearEquiv.coe_inj
+-/
#print ContinuousLinearEquiv.toHomeomorph /-
/-- A continuous linear equivalence induces a homeomorphism. -/
@@ -1900,95 +2225,123 @@ def toHomeomorph (e : M₁ ≃SL[σ₁₂] M₂) : M₁ ≃ₜ M₂ :=
#align continuous_linear_equiv.to_homeomorph ContinuousLinearEquiv.toHomeomorph
-/
+#print ContinuousLinearEquiv.coe_toHomeomorph /-
@[simp]
theorem coe_toHomeomorph (e : M₁ ≃SL[σ₁₂] M₂) : ⇑e.toHomeomorph = e :=
rfl
#align continuous_linear_equiv.coe_to_homeomorph ContinuousLinearEquiv.coe_toHomeomorph
+-/
+#print ContinuousLinearEquiv.image_closure /-
theorem image_closure (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₁) : e '' closure s = closure (e '' s) :=
e.toHomeomorph.image_closure s
#align continuous_linear_equiv.image_closure ContinuousLinearEquiv.image_closure
+-/
+#print ContinuousLinearEquiv.preimage_closure /-
theorem preimage_closure (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₂) : e ⁻¹' closure s = closure (e ⁻¹' s) :=
e.toHomeomorph.preimage_closure s
#align continuous_linear_equiv.preimage_closure ContinuousLinearEquiv.preimage_closure
+-/
+#print ContinuousLinearEquiv.isClosed_image /-
@[simp]
theorem isClosed_image (e : M₁ ≃SL[σ₁₂] M₂) {s : Set M₁} : IsClosed (e '' s) ↔ IsClosed s :=
e.toHomeomorph.isClosed_image
#align continuous_linear_equiv.is_closed_image ContinuousLinearEquiv.isClosed_image
+-/
+#print ContinuousLinearEquiv.map_nhds_eq /-
theorem map_nhds_eq (e : M₁ ≃SL[σ₁₂] M₂) (x : M₁) : map e (𝓝 x) = 𝓝 (e x) :=
e.toHomeomorph.map_nhds_eq x
#align continuous_linear_equiv.map_nhds_eq ContinuousLinearEquiv.map_nhds_eq
+-/
+#print ContinuousLinearEquiv.map_zero /-
-- Make some straightforward lemmas available to `simp`.
@[simp]
theorem map_zero (e : M₁ ≃SL[σ₁₂] M₂) : e (0 : M₁) = 0 :=
(e : M₁ →SL[σ₁₂] M₂).map_zero
#align continuous_linear_equiv.map_zero ContinuousLinearEquiv.map_zero
+-/
+#print ContinuousLinearEquiv.map_add /-
@[simp]
theorem map_add (e : M₁ ≃SL[σ₁₂] M₂) (x y : M₁) : e (x + y) = e x + e y :=
(e : M₁ →SL[σ₁₂] M₂).map_add x y
#align continuous_linear_equiv.map_add ContinuousLinearEquiv.map_add
+-/
+#print ContinuousLinearEquiv.map_smulₛₗ /-
@[simp]
theorem map_smulₛₗ (e : M₁ ≃SL[σ₁₂] M₂) (c : R₁) (x : M₁) : e (c • x) = σ₁₂ c • e x :=
(e : M₁ →SL[σ₁₂] M₂).map_smulₛₗ c x
#align continuous_linear_equiv.map_smulₛₗ ContinuousLinearEquiv.map_smulₛₗ
+-/
-omit σ₂₁
-
+#print ContinuousLinearEquiv.map_smul /-
@[simp]
theorem map_smul [Module R₁ M₂] (e : M₁ ≃L[R₁] M₂) (c : R₁) (x : M₁) : e (c • x) = c • e x :=
(e : M₁ →L[R₁] M₂).map_smul c x
#align continuous_linear_equiv.map_smul ContinuousLinearEquiv.map_smul
+-/
-include σ₂₁
-
+#print ContinuousLinearEquiv.map_eq_zero_iff /-
@[simp]
theorem map_eq_zero_iff (e : M₁ ≃SL[σ₁₂] M₂) {x : M₁} : e x = 0 ↔ x = 0 :=
e.toLinearEquiv.map_eq_zero_iff
#align continuous_linear_equiv.map_eq_zero_iff ContinuousLinearEquiv.map_eq_zero_iff
+-/
attribute [continuity] ContinuousLinearEquiv.continuous_toFun
ContinuousLinearEquiv.continuous_invFun
+#print ContinuousLinearEquiv.continuous /-
@[continuity]
protected theorem continuous (e : M₁ ≃SL[σ₁₂] M₂) : Continuous (e : M₁ → M₂) :=
e.continuous_toFun
#align continuous_linear_equiv.continuous ContinuousLinearEquiv.continuous
+-/
+#print ContinuousLinearEquiv.continuousOn /-
protected theorem continuousOn (e : M₁ ≃SL[σ₁₂] M₂) {s : Set M₁} : ContinuousOn (e : M₁ → M₂) s :=
e.Continuous.ContinuousOn
#align continuous_linear_equiv.continuous_on ContinuousLinearEquiv.continuousOn
+-/
+#print ContinuousLinearEquiv.continuousAt /-
protected theorem continuousAt (e : M₁ ≃SL[σ₁₂] M₂) {x : M₁} : ContinuousAt (e : M₁ → M₂) x :=
e.Continuous.ContinuousAt
#align continuous_linear_equiv.continuous_at ContinuousLinearEquiv.continuousAt
+-/
+#print ContinuousLinearEquiv.continuousWithinAt /-
protected theorem continuousWithinAt (e : M₁ ≃SL[σ₁₂] M₂) {s : Set M₁} {x : M₁} :
ContinuousWithinAt (e : M₁ → M₂) s x :=
e.Continuous.ContinuousWithinAt
#align continuous_linear_equiv.continuous_within_at ContinuousLinearEquiv.continuousWithinAt
+-/
+#print ContinuousLinearEquiv.comp_continuousOn_iff /-
theorem comp_continuousOn_iff {α : Type _} [TopologicalSpace α] (e : M₁ ≃SL[σ₁₂] M₂) {f : α → M₁}
{s : Set α} : ContinuousOn (e ∘ f) s ↔ ContinuousOn f s :=
e.toHomeomorph.comp_continuousOn_iff _ _
#align continuous_linear_equiv.comp_continuous_on_iff ContinuousLinearEquiv.comp_continuousOn_iff
+-/
+#print ContinuousLinearEquiv.comp_continuous_iff /-
theorem comp_continuous_iff {α : Type _} [TopologicalSpace α] (e : M₁ ≃SL[σ₁₂] M₂) {f : α → M₁} :
Continuous (e ∘ f) ↔ Continuous f :=
e.toHomeomorph.comp_continuous_iff
#align continuous_linear_equiv.comp_continuous_iff ContinuousLinearEquiv.comp_continuous_iff
+-/
-omit σ₂₁
-
+#print ContinuousLinearEquiv.ext₁ /-
/-- An extensionality lemma for `R ≃L[R] M`. -/
theorem ext₁ [TopologicalSpace R₁] {f g : R₁ ≃L[R₁] M₁} (h : f 1 = g 1) : f = g :=
ext <| funext fun x => mul_one x ▸ by rw [← smul_eq_mul, map_smul, h, map_smul]
#align continuous_linear_equiv.ext₁ ContinuousLinearEquiv.ext₁
+-/
section
@@ -2030,17 +2383,19 @@ protected def symm (e : M₁ ≃SL[σ₁₂] M₂) : M₂ ≃SL[σ₂₁] M₁ :
#align continuous_linear_equiv.symm ContinuousLinearEquiv.symm
-/
-include σ₂₁
-
+#print ContinuousLinearEquiv.symm_toLinearEquiv /-
@[simp]
theorem symm_toLinearEquiv (e : M₁ ≃SL[σ₁₂] M₂) : e.symm.toLinearEquiv = e.toLinearEquiv.symm := by
ext; rfl
#align continuous_linear_equiv.symm_to_linear_equiv ContinuousLinearEquiv.symm_toLinearEquiv
+-/
+#print ContinuousLinearEquiv.symm_toHomeomorph /-
@[simp]
theorem symm_toHomeomorph (e : M₁ ≃SL[σ₁₂] M₂) : e.toHomeomorph.symm = e.symm.toHomeomorph :=
rfl
#align continuous_linear_equiv.symm_to_homeomorph ContinuousLinearEquiv.symm_toHomeomorph
+-/
#print ContinuousLinearEquiv.Simps.apply /-
/-- See Note [custom simps projection]. We need to specify this projection explicitly in this case,
@@ -2060,13 +2415,11 @@ def Simps.symm_apply (h : M₁ ≃SL[σ₁₂] M₂) : M₂ → M₁ :=
initialize_simps_projections ContinuousLinearEquiv (to_linear_equiv_to_fun → apply,
to_linear_equiv_inv_fun → symm_apply)
+#print ContinuousLinearEquiv.symm_map_nhds_eq /-
theorem symm_map_nhds_eq (e : M₁ ≃SL[σ₁₂] M₂) (x : M₁) : map e.symm (𝓝 (e x)) = 𝓝 x :=
e.toHomeomorph.symm_map_nhds_eq x
#align continuous_linear_equiv.symm_map_nhds_eq ContinuousLinearEquiv.symm_map_nhds_eq
-
-omit σ₂₁
-
-include σ₂₁ σ₃₂ σ₃₁
+-/
#print ContinuousLinearEquiv.trans /-
/-- The composition of two continuous linear equivalences as a continuous linear equivalence. -/
@@ -2080,15 +2433,14 @@ protected def trans (e₁ : M₁ ≃SL[σ₁₂] M₂) (e₂ : M₂ ≃SL[σ₂
#align continuous_linear_equiv.trans ContinuousLinearEquiv.trans
-/
-include σ₁₃
-
+#print ContinuousLinearEquiv.trans_toLinearEquiv /-
@[simp]
theorem trans_toLinearEquiv (e₁ : M₁ ≃SL[σ₁₂] M₂) (e₂ : M₂ ≃SL[σ₂₃] M₃) :
(e₁.trans e₂).toLinearEquiv = e₁.toLinearEquiv.trans e₂.toLinearEquiv := by ext; rfl
#align continuous_linear_equiv.trans_to_linear_equiv ContinuousLinearEquiv.trans_toLinearEquiv
+-/
-omit σ₁₃ σ₂₁ σ₃₂ σ₃₁
-
+#print ContinuousLinearEquiv.prod /-
/-- Product of two continuous linear equivalences. The map comes from `equiv.prod_congr`. -/
def prod [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M₁ ≃L[R₁] M₂) (e' : M₃ ≃L[R₁] M₄) :
(M₁ × M₃) ≃L[R₁] M₂ × M₄ :=
@@ -2098,118 +2450,137 @@ def prod [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M₁ ≃L
continuous_toFun := e.continuous_toFun.Prod_map e'.continuous_toFun
continuous_invFun := e.continuous_invFun.Prod_map e'.continuous_invFun }
#align continuous_linear_equiv.prod ContinuousLinearEquiv.prod
+-/
+#print ContinuousLinearEquiv.prod_apply /-
@[simp, norm_cast]
theorem prod_apply [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M₁ ≃L[R₁] M₂)
(e' : M₃ ≃L[R₁] M₄) (x) : e.Prod e' x = (e x.1, e' x.2) :=
rfl
#align continuous_linear_equiv.prod_apply ContinuousLinearEquiv.prod_apply
+-/
+#print ContinuousLinearEquiv.coe_prod /-
@[simp, norm_cast]
theorem coe_prod [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M₁ ≃L[R₁] M₂)
(e' : M₃ ≃L[R₁] M₄) :
(e.Prod e' : M₁ × M₃ →L[R₁] M₂ × M₄) = (e : M₁ →L[R₁] M₂).Prod_map (e' : M₃ →L[R₁] M₄) :=
rfl
#align continuous_linear_equiv.coe_prod ContinuousLinearEquiv.coe_prod
+-/
+#print ContinuousLinearEquiv.prod_symm /-
theorem prod_symm [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M₁ ≃L[R₁] M₂)
(e' : M₃ ≃L[R₁] M₄) : (e.Prod e').symm = e.symm.Prod e'.symm :=
rfl
#align continuous_linear_equiv.prod_symm ContinuousLinearEquiv.prod_symm
+-/
-include σ₂₁
-
+#print ContinuousLinearEquiv.bijective /-
protected theorem bijective (e : M₁ ≃SL[σ₁₂] M₂) : Function.Bijective e :=
e.toLinearEquiv.toEquiv.Bijective
#align continuous_linear_equiv.bijective ContinuousLinearEquiv.bijective
+-/
+#print ContinuousLinearEquiv.injective /-
protected theorem injective (e : M₁ ≃SL[σ₁₂] M₂) : Function.Injective e :=
e.toLinearEquiv.toEquiv.Injective
#align continuous_linear_equiv.injective ContinuousLinearEquiv.injective
+-/
+#print ContinuousLinearEquiv.surjective /-
protected theorem surjective (e : M₁ ≃SL[σ₁₂] M₂) : Function.Surjective e :=
e.toLinearEquiv.toEquiv.Surjective
#align continuous_linear_equiv.surjective ContinuousLinearEquiv.surjective
+-/
-include σ₃₂ σ₃₁ σ₁₃
-
+#print ContinuousLinearEquiv.trans_apply /-
@[simp]
theorem trans_apply (e₁ : M₁ ≃SL[σ₁₂] M₂) (e₂ : M₂ ≃SL[σ₂₃] M₃) (c : M₁) :
(e₁.trans e₂) c = e₂ (e₁ c) :=
rfl
#align continuous_linear_equiv.trans_apply ContinuousLinearEquiv.trans_apply
+-/
-omit σ₃₂ σ₃₁ σ₁₃
-
+#print ContinuousLinearEquiv.apply_symm_apply /-
@[simp]
theorem apply_symm_apply (e : M₁ ≃SL[σ₁₂] M₂) (c : M₂) : e (e.symm c) = c :=
e.1.right_inv c
#align continuous_linear_equiv.apply_symm_apply ContinuousLinearEquiv.apply_symm_apply
+-/
+#print ContinuousLinearEquiv.symm_apply_apply /-
@[simp]
theorem symm_apply_apply (e : M₁ ≃SL[σ₁₂] M₂) (b : M₁) : e.symm (e b) = b :=
e.1.left_inv b
#align continuous_linear_equiv.symm_apply_apply ContinuousLinearEquiv.symm_apply_apply
+-/
-include σ₁₂ σ₂₃ σ₁₃ σ₃₁
-
+#print ContinuousLinearEquiv.symm_trans_apply /-
@[simp]
theorem symm_trans_apply (e₁ : M₂ ≃SL[σ₂₁] M₁) (e₂ : M₃ ≃SL[σ₃₂] M₂) (c : M₁) :
(e₂.trans e₁).symm c = e₂.symm (e₁.symm c) :=
rfl
#align continuous_linear_equiv.symm_trans_apply ContinuousLinearEquiv.symm_trans_apply
+-/
-omit σ₁₂ σ₂₃ σ₁₃ σ₃₁
-
+#print ContinuousLinearEquiv.symm_image_image /-
@[simp]
theorem symm_image_image (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₁) : e.symm '' (e '' s) = s :=
e.toLinearEquiv.toEquiv.symm_image_image s
#align continuous_linear_equiv.symm_image_image ContinuousLinearEquiv.symm_image_image
+-/
+#print ContinuousLinearEquiv.image_symm_image /-
@[simp]
theorem image_symm_image (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₂) : e '' (e.symm '' s) = s :=
e.symm.symm_image_image s
#align continuous_linear_equiv.image_symm_image ContinuousLinearEquiv.image_symm_image
+-/
-include σ₃₂ σ₃₁
-
+#print ContinuousLinearEquiv.comp_coe /-
@[simp, norm_cast]
theorem comp_coe (f : M₁ ≃SL[σ₁₂] M₂) (f' : M₂ ≃SL[σ₂₃] M₃) :
(f' : M₂ →SL[σ₂₃] M₃).comp (f : M₁ →SL[σ₁₂] M₂) = (f.trans f' : M₁ →SL[σ₁₃] M₃) :=
rfl
#align continuous_linear_equiv.comp_coe ContinuousLinearEquiv.comp_coe
+-/
-omit σ₃₂ σ₃₁ σ₂₁
-
+#print ContinuousLinearEquiv.coe_comp_coe_symm /-
@[simp]
theorem coe_comp_coe_symm (e : M₁ ≃SL[σ₁₂] M₂) :
(e : M₁ →SL[σ₁₂] M₂).comp (e.symm : M₂ →SL[σ₂₁] M₁) = ContinuousLinearMap.id R₂ M₂ :=
ContinuousLinearMap.ext e.apply_symm_apply
#align continuous_linear_equiv.coe_comp_coe_symm ContinuousLinearEquiv.coe_comp_coe_symm
+-/
+#print ContinuousLinearEquiv.coe_symm_comp_coe /-
@[simp]
theorem coe_symm_comp_coe (e : M₁ ≃SL[σ₁₂] M₂) :
(e.symm : M₂ →SL[σ₂₁] M₁).comp (e : M₁ →SL[σ₁₂] M₂) = ContinuousLinearMap.id R₁ M₁ :=
ContinuousLinearMap.ext e.symm_apply_apply
#align continuous_linear_equiv.coe_symm_comp_coe ContinuousLinearEquiv.coe_symm_comp_coe
+-/
-include σ₂₁
-
+#print ContinuousLinearEquiv.symm_comp_self /-
@[simp]
theorem symm_comp_self (e : M₁ ≃SL[σ₁₂] M₂) : (e.symm : M₂ → M₁) ∘ (e : M₁ → M₂) = id := by ext x;
exact symm_apply_apply e x
#align continuous_linear_equiv.symm_comp_self ContinuousLinearEquiv.symm_comp_self
+-/
+#print ContinuousLinearEquiv.self_comp_symm /-
@[simp]
theorem self_comp_symm (e : M₁ ≃SL[σ₁₂] M₂) : (e : M₁ → M₂) ∘ (e.symm : M₂ → M₁) = id := by ext x;
exact apply_symm_apply e x
#align continuous_linear_equiv.self_comp_symm ContinuousLinearEquiv.self_comp_symm
+-/
+#print ContinuousLinearEquiv.symm_symm /-
@[simp]
theorem symm_symm (e : M₁ ≃SL[σ₁₂] M₂) : e.symm.symm = e := by ext x; rfl
#align continuous_linear_equiv.symm_symm ContinuousLinearEquiv.symm_symm
-
-omit σ₂₁
+-/
#print ContinuousLinearEquiv.refl_symm /-
@[simp]
@@ -2218,47 +2589,62 @@ theorem refl_symm : (ContinuousLinearEquiv.refl R₁ M₁).symm = ContinuousLine
#align continuous_linear_equiv.refl_symm ContinuousLinearEquiv.refl_symm
-/
-include σ₂₁
-
+#print ContinuousLinearEquiv.symm_symm_apply /-
theorem symm_symm_apply (e : M₁ ≃SL[σ₁₂] M₂) (x : M₁) : e.symm.symm x = e x :=
rfl
#align continuous_linear_equiv.symm_symm_apply ContinuousLinearEquiv.symm_symm_apply
+-/
+#print ContinuousLinearEquiv.symm_apply_eq /-
theorem symm_apply_eq (e : M₁ ≃SL[σ₁₂] M₂) {x y} : e.symm x = y ↔ x = e y :=
e.toLinearEquiv.symm_apply_eq
#align continuous_linear_equiv.symm_apply_eq ContinuousLinearEquiv.symm_apply_eq
+-/
+#print ContinuousLinearEquiv.eq_symm_apply /-
theorem eq_symm_apply (e : M₁ ≃SL[σ₁₂] M₂) {x y} : y = e.symm x ↔ e y = x :=
e.toLinearEquiv.eq_symm_apply
#align continuous_linear_equiv.eq_symm_apply ContinuousLinearEquiv.eq_symm_apply
+-/
+#print ContinuousLinearEquiv.image_eq_preimage /-
protected theorem image_eq_preimage (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₁) : e '' s = e.symm ⁻¹' s :=
e.toLinearEquiv.toEquiv.image_eq_preimage s
#align continuous_linear_equiv.image_eq_preimage ContinuousLinearEquiv.image_eq_preimage
+-/
+#print ContinuousLinearEquiv.image_symm_eq_preimage /-
protected theorem image_symm_eq_preimage (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₂) :
e.symm '' s = e ⁻¹' s := by rw [e.symm.image_eq_preimage, e.symm_symm]
#align continuous_linear_equiv.image_symm_eq_preimage ContinuousLinearEquiv.image_symm_eq_preimage
+-/
+#print ContinuousLinearEquiv.symm_preimage_preimage /-
@[simp]
protected theorem symm_preimage_preimage (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₂) :
e.symm ⁻¹' (e ⁻¹' s) = s :=
e.toLinearEquiv.toEquiv.symm_preimage_preimage s
#align continuous_linear_equiv.symm_preimage_preimage ContinuousLinearEquiv.symm_preimage_preimage
+-/
+#print ContinuousLinearEquiv.preimage_symm_preimage /-
@[simp]
protected theorem preimage_symm_preimage (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₁) :
e ⁻¹' (e.symm ⁻¹' s) = s :=
e.symm.symm_preimage_preimage s
#align continuous_linear_equiv.preimage_symm_preimage ContinuousLinearEquiv.preimage_symm_preimage
+-/
+#print ContinuousLinearEquiv.uniformEmbedding /-
protected theorem uniformEmbedding {E₁ E₂ : Type _} [UniformSpace E₁] [UniformSpace E₂]
[AddCommGroup E₁] [AddCommGroup E₂] [Module R₁ E₁] [Module R₂ E₂] [UniformAddGroup E₁]
[UniformAddGroup E₂] (e : E₁ ≃SL[σ₁₂] E₂) : UniformEmbedding e :=
e.toLinearEquiv.toEquiv.UniformEmbedding e.toContinuousLinearMap.UniformContinuous
e.symm.toContinuousLinearMap.UniformContinuous
#align continuous_linear_equiv.uniform_embedding ContinuousLinearEquiv.uniformEmbedding
+-/
+#print LinearEquiv.uniformEmbedding /-
protected theorem LinearEquiv.uniformEmbedding {E₁ E₂ : Type _} [UniformSpace E₁] [UniformSpace E₂]
[AddCommGroup E₁] [AddCommGroup E₂] [Module R₁ E₁] [Module R₂ E₂] [UniformAddGroup E₁]
[UniformAddGroup E₂] (e : E₁ ≃ₛₗ[σ₁₂] E₂) (h₁ : Continuous e) (h₂ : Continuous e.symm) :
@@ -2269,9 +2655,9 @@ protected theorem LinearEquiv.uniformEmbedding {E₁ E₂ : Type _} [UniformSpac
continuous_invFun := h₂ } :
E₁ ≃SL[σ₁₂] E₂)
#align linear_equiv.uniform_embedding LinearEquiv.uniformEmbedding
+-/
-omit σ₂₁
-
+#print ContinuousLinearEquiv.equivOfInverse /-
/-- Create a `continuous_linear_equiv` from two `continuous_linear_map`s that are
inverse of each other. -/
def equivOfInverse (f₁ : M₁ →SL[σ₁₂] M₂) (f₂ : M₂ →SL[σ₂₁] M₁) (h₁ : Function.LeftInverse f₂ f₁)
@@ -2284,22 +2670,23 @@ def equivOfInverse (f₁ : M₁ →SL[σ₁₂] M₂) (f₂ : M₂ →SL[σ₂
left_inv := h₁
right_inv := h₂ }
#align continuous_linear_equiv.equiv_of_inverse ContinuousLinearEquiv.equivOfInverse
+-/
-include σ₂₁
-
+#print ContinuousLinearEquiv.equivOfInverse_apply /-
@[simp]
theorem equivOfInverse_apply (f₁ : M₁ →SL[σ₁₂] M₂) (f₂ h₁ h₂ x) :
equivOfInverse f₁ f₂ h₁ h₂ x = f₁ x :=
rfl
#align continuous_linear_equiv.equiv_of_inverse_apply ContinuousLinearEquiv.equivOfInverse_apply
+-/
+#print ContinuousLinearEquiv.symm_equivOfInverse /-
@[simp]
theorem symm_equivOfInverse (f₁ : M₁ →SL[σ₁₂] M₂) (f₂ h₁ h₂) :
(equivOfInverse f₁ f₂ h₁ h₂).symm = equivOfInverse f₂ f₁ h₂ h₁ :=
rfl
#align continuous_linear_equiv.symm_equiv_of_inverse ContinuousLinearEquiv.symm_equivOfInverse
-
-omit σ₂₁
+-/
variable (M₁)
@@ -2332,8 +2719,6 @@ def ulift : ULift M₁ ≃L[R₁] M₁ :=
#align continuous_linear_equiv.ulift ContinuousLinearEquiv.ulift
-/
-include σ₂₁ σ₃₄ σ₂₃ σ₂₄ σ₁₃
-
#print ContinuousLinearEquiv.arrowCongrEquiv /-
/-- A pair of continuous (semi)linear equivalences generates an equivalence between the spaces of
continuous linear maps. See also `continuous_linear_equiv.arrow_congr`. -/
@@ -2363,6 +2748,7 @@ variable {R : Type _} [Semiring R] {M : Type _} [TopologicalSpace M] [AddCommGro
variable [TopologicalAddGroup M₄]
+#print ContinuousLinearEquiv.skewProd /-
/-- Equivalence given by a block lower diagonal matrix. `e` and `e'` are diagonal square blocks,
and `f` is a rectangular block below the diagonal. -/
def skewProd (e : M ≃L[R] M₂) (e' : M₃ ≃L[R] M₄) (f : M →L[R] M₄) : (M × M₃) ≃L[R] M₂ × M₄ :=
@@ -2377,18 +2763,23 @@ def skewProd (e : M ≃L[R] M₂) (e' : M₃ ≃L[R] M₄) (f : M →L[R] M₄)
(e'.continuous_invFun.comp <|
continuous_snd.sub <| f.Continuous.comp <| e.continuous_invFun.comp continuous_fst) }
#align continuous_linear_equiv.skew_prod ContinuousLinearEquiv.skewProd
+-/
+#print ContinuousLinearEquiv.skewProd_apply /-
@[simp]
theorem skewProd_apply (e : M ≃L[R] M₂) (e' : M₃ ≃L[R] M₄) (f : M →L[R] M₄) (x) :
e.skewProd e' f x = (e x.1, e' x.2 + f x.1) :=
rfl
#align continuous_linear_equiv.skew_prod_apply ContinuousLinearEquiv.skewProd_apply
+-/
+#print ContinuousLinearEquiv.skewProd_symm_apply /-
@[simp]
theorem skewProd_symm_apply (e : M ≃L[R] M₂) (e' : M₃ ≃L[R] M₄) (f : M →L[R] M₄) (x) :
(e.skewProd e' f).symm x = (e.symm x.1, e'.symm (x.2 - f (e.symm x.1))) :=
rfl
#align continuous_linear_equiv.skew_prod_symm_apply ContinuousLinearEquiv.skewProd_symm_apply
+-/
end AddCommGroup
@@ -2399,19 +2790,19 @@ variable {R : Type _} [Ring R] {R₂ : Type _} [Ring R₂] {M : Type _} [Topolog
variable {σ₁₂ : R →+* R₂} {σ₂₁ : R₂ →+* R} [RingHomInvPair σ₁₂ σ₂₁] [RingHomInvPair σ₂₁ σ₁₂]
-include σ₂₁
-
+#print ContinuousLinearEquiv.map_sub /-
@[simp]
theorem map_sub (e : M ≃SL[σ₁₂] M₂) (x y : M) : e (x - y) = e x - e y :=
(e : M →SL[σ₁₂] M₂).map_sub x y
#align continuous_linear_equiv.map_sub ContinuousLinearEquiv.map_sub
+-/
+#print ContinuousLinearEquiv.map_neg /-
@[simp]
theorem map_neg (e : M ≃SL[σ₁₂] M₂) (x : M) : e (-x) = -e x :=
(e : M →SL[σ₁₂] M₂).map_neg x
#align continuous_linear_equiv.map_neg ContinuousLinearEquiv.map_neg
-
-omit σ₂₁
+-/
section
@@ -2421,6 +2812,7 @@ section
variable [TopologicalAddGroup M]
+#print ContinuousLinearEquiv.ofUnit /-
/-- An invertible continuous linear map `f` determines a continuous equivalence from `M` to itself.
-/
def ofUnit (f : (M →L[R] M)ˣ) : M ≃L[R] M
@@ -2435,7 +2827,9 @@ def ofUnit (f : (M →L[R] M)ˣ) : M ≃L[R] M
continuous_toFun := f.val.Continuous
continuous_invFun := f.inv.Continuous
#align continuous_linear_equiv.of_unit ContinuousLinearEquiv.ofUnit
+-/
+#print ContinuousLinearEquiv.toUnit /-
/-- A continuous equivalence from `M` to itself determines an invertible continuous linear map. -/
def toUnit (f : M ≃L[R] M) : (M →L[R] M)ˣ where
val := f
@@ -2443,9 +2837,11 @@ def toUnit (f : M ≃L[R] M) : (M →L[R] M)ˣ where
val_inv := by ext; simp
inv_val := by ext; simp
#align continuous_linear_equiv.to_unit ContinuousLinearEquiv.toUnit
+-/
variable (R M)
+#print ContinuousLinearEquiv.unitsEquiv /-
/-- The units of the algebra of continuous `R`-linear endomorphisms of `M` is multiplicatively
equivalent to the type of continuous linear equivalences between `M` and itself. -/
def unitsEquiv : (M →L[R] M)ˣ ≃* M ≃L[R] M
@@ -2456,11 +2852,14 @@ def unitsEquiv : (M →L[R] M)ˣ ≃* M ≃L[R] M
right_inv f := by ext; rfl
map_mul' x y := by ext; rfl
#align continuous_linear_equiv.units_equiv ContinuousLinearEquiv.unitsEquiv
+-/
+#print ContinuousLinearEquiv.unitsEquiv_apply /-
@[simp]
theorem unitsEquiv_apply (f : (M →L[R] M)ˣ) (x : M) : unitsEquiv R M f x = f x :=
rfl
#align continuous_linear_equiv.units_equiv_apply ContinuousLinearEquiv.unitsEquiv_apply
+-/
end
@@ -2468,6 +2867,7 @@ section
variable (R) [TopologicalSpace R] [ContinuousMul R]
+#print ContinuousLinearEquiv.unitsEquivAut /-
/-- Continuous linear equivalences `R ≃L[R] R` are enumerated by `Rˣ`. -/
def unitsEquivAut : Rˣ ≃ R ≃L[R] R
where
@@ -2480,23 +2880,30 @@ def unitsEquivAut : Rˣ ≃ R ≃L[R] R
left_inv u := Units.ext <| by simp
right_inv e := ext₁ <| by simp
#align continuous_linear_equiv.units_equiv_aut ContinuousLinearEquiv.unitsEquivAut
+-/
variable {R}
+#print ContinuousLinearEquiv.unitsEquivAut_apply /-
@[simp]
theorem unitsEquivAut_apply (u : Rˣ) (x : R) : unitsEquivAut R u x = x * u :=
rfl
#align continuous_linear_equiv.units_equiv_aut_apply ContinuousLinearEquiv.unitsEquivAut_apply
+-/
+#print ContinuousLinearEquiv.unitsEquivAut_apply_symm /-
@[simp]
theorem unitsEquivAut_apply_symm (u : Rˣ) (x : R) : (unitsEquivAut R u).symm x = x * ↑u⁻¹ :=
rfl
#align continuous_linear_equiv.units_equiv_aut_apply_symm ContinuousLinearEquiv.unitsEquivAut_apply_symm
+-/
+#print ContinuousLinearEquiv.unitsEquivAut_symm_apply /-
@[simp]
theorem unitsEquivAut_symm_apply (e : R ≃L[R] R) : ↑((unitsEquivAut R).symm e) = e 1 :=
rfl
#align continuous_linear_equiv.units_equiv_aut_symm_apply ContinuousLinearEquiv.unitsEquivAut_symm_apply
+-/
end
@@ -2506,6 +2913,7 @@ open _Root_.ContinuousLinearMap (id fst snd)
open _Root_.LinearMap (mem_ker)
+#print ContinuousLinearEquiv.equivOfRightInverse /-
/-- A pair of continuous linear maps such that `f₁ ∘ f₂ = id` generates a continuous
linear equivalence `e` between `M` and `M₂ × f₁.ker` such that `(e x).2 = x` for `x ∈ f₁.ker`,
`(e x).1 = f₁ x`, and `(e (f₂ y)).2 = 0`. The map is given by `e x = (f₁ x, x - f₂ (f₁ x))`. -/
@@ -2514,26 +2922,33 @@ def equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M) (h : Fun
equivOfInverse (f₁.Prod (f₁.projKerOfRightInverse f₂ h)) (f₂.coprod (ker f₁).subtypeL)
(fun x => by simp) fun ⟨x, y⟩ => by simp [h x]
#align continuous_linear_equiv.equiv_of_right_inverse ContinuousLinearEquiv.equivOfRightInverse
+-/
+#print ContinuousLinearEquiv.fst_equivOfRightInverse /-
@[simp]
theorem fst_equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
(h : Function.RightInverse f₂ f₁) (x : M) : (equivOfRightInverse f₁ f₂ h x).1 = f₁ x :=
rfl
#align continuous_linear_equiv.fst_equiv_of_right_inverse ContinuousLinearEquiv.fst_equivOfRightInverse
+-/
+#print ContinuousLinearEquiv.snd_equivOfRightInverse /-
@[simp]
theorem snd_equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
(h : Function.RightInverse f₂ f₁) (x : M) :
((equivOfRightInverse f₁ f₂ h x).2 : M) = x - f₂ (f₁ x) :=
rfl
#align continuous_linear_equiv.snd_equiv_of_right_inverse ContinuousLinearEquiv.snd_equivOfRightInverse
+-/
+#print ContinuousLinearEquiv.equivOfRightInverse_symm_apply /-
@[simp]
theorem equivOfRightInverse_symm_apply (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
(h : Function.RightInverse f₂ f₁) (y : M₂ × ker f₁) :
(equivOfRightInverse f₁ f₂ h).symm y = f₂ y.1 + y.2 :=
rfl
#align continuous_linear_equiv.equiv_of_right_inverse_symm_apply ContinuousLinearEquiv.equivOfRightInverse_symm_apply
+-/
end Ring
@@ -2551,30 +2966,38 @@ def funUnique : (ι → M) ≃L[R] M :=
variable {ι R M}
+#print ContinuousLinearEquiv.coe_funUnique /-
@[simp]
theorem coe_funUnique : ⇑(funUnique ι R M) = Function.eval default :=
rfl
#align continuous_linear_equiv.coe_fun_unique ContinuousLinearEquiv.coe_funUnique
+-/
+#print ContinuousLinearEquiv.coe_funUnique_symm /-
@[simp]
theorem coe_funUnique_symm : ⇑(funUnique ι R M).symm = Function.const ι :=
rfl
#align continuous_linear_equiv.coe_fun_unique_symm ContinuousLinearEquiv.coe_funUnique_symm
+-/
variable (R M)
+#print ContinuousLinearEquiv.piFinTwo /-
/-- Continuous linear equivalence between dependent functions `Π i : fin 2, M i` and `M 0 × M 1`. -/
@[simps (config := { fullyApplied := false })]
def piFinTwo (M : Fin 2 → Type _) [∀ i, AddCommMonoid (M i)] [∀ i, Module R (M i)]
[∀ i, TopologicalSpace (M i)] : (∀ i, M i) ≃L[R] M 0 × M 1 :=
{ Homeomorph.piFinTwo M with toLinearEquiv := LinearEquiv.piFinTwo R M }
#align continuous_linear_equiv.pi_fin_two ContinuousLinearEquiv.piFinTwo
+-/
+#print ContinuousLinearEquiv.finTwoArrow /-
/-- Continuous linear equivalence between vectors in `M² = fin 2 → M` and `M × M`. -/
@[simps (config := { fullyApplied := false })]
def finTwoArrow : (Fin 2 → M) ≃L[R] M × M :=
{ piFinTwo R fun _ => M with toLinearEquiv := LinearEquiv.finTwoArrow R M }
#align continuous_linear_equiv.fin_two_arrow ContinuousLinearEquiv.finTwoArrow
+-/
end
@@ -2604,6 +3027,7 @@ noncomputable def inverse : (M →L[R] M₂) → M₂ →L[R] M := fun f =>
#align continuous_linear_map.inverse ContinuousLinearMap.inverse
-/
+#print ContinuousLinearMap.inverse_equiv /-
/-- By definition, if `f` is invertible then `inverse f = f.symm`. -/
@[simp]
theorem inverse_equiv (e : M ≃L[R] M₂) : inverse (e : M →L[R] M₂) = e.symm :=
@@ -2613,12 +3037,15 @@ theorem inverse_equiv (e : M ≃L[R] M₂) : inverse (e : M →L[R] M₂) = e.sy
congr
exact_mod_cast Classical.choose_spec h
#align continuous_linear_map.inverse_equiv ContinuousLinearMap.inverse_equiv
+-/
+#print ContinuousLinearMap.inverse_non_equiv /-
/-- By definition, if `f` is not invertible then `inverse f = 0`. -/
@[simp]
theorem inverse_non_equiv (f : M →L[R] M₂) (h : ¬∃ e' : M ≃L[R] M₂, ↑e' = f) : inverse f = 0 :=
dif_neg h
#align continuous_linear_map.inverse_non_equiv ContinuousLinearMap.inverse_non_equiv
+-/
end
@@ -2630,6 +3057,7 @@ variable [AddCommGroup M] [TopologicalAddGroup M] [Module R M]
variable [AddCommGroup M₂] [Module R M₂]
+#print ContinuousLinearMap.ring_inverse_equiv /-
@[simp]
theorem ring_inverse_equiv (e : M ≃L[R] M) : Ring.inverse ↑e = inverse (e : M →L[R] M) :=
by
@@ -2638,7 +3066,9 @@ theorem ring_inverse_equiv (e : M ≃L[R] M) : Ring.inverse ↑e = inverse (e :
simp
rfl
#align continuous_linear_map.ring_inverse_equiv ContinuousLinearMap.ring_inverse_equiv
+-/
+#print ContinuousLinearMap.to_ring_inverse /-
/-- The function `continuous_linear_equiv.inverse` can be written in terms of `ring.inverse` for the
ring of self-maps of the domain. -/
theorem to_ring_inverse (e : M ≃L[R] M₂) (f : M →L[R] M₂) :
@@ -2657,12 +3087,15 @@ theorem to_ring_inverse (e : M ≃L[R] M₂) (f : M →L[R] M₂) :
ext
dsimp; rw [coeFn_coe_base' F, hF]; simp
#align continuous_linear_map.to_ring_inverse ContinuousLinearMap.to_ring_inverse
+-/
+#print ContinuousLinearMap.ring_inverse_eq_map_inverse /-
theorem ring_inverse_eq_map_inverse : Ring.inverse = @inverse R M M _ _ _ _ _ _ _ :=
by
ext
simp [to_ring_inverse (ContinuousLinearEquiv.refl R M)]
#align continuous_linear_map.ring_inverse_eq_map_inverse ContinuousLinearMap.ring_inverse_eq_map_inverse
+-/
end
@@ -2682,10 +3115,12 @@ def ClosedComplemented (p : Submodule R M) : Prop :=
#align submodule.closed_complemented Submodule.ClosedComplemented
-/
+#print Submodule.ClosedComplemented.has_closed_complement /-
theorem ClosedComplemented.has_closed_complement {p : Submodule R M} [T1Space p]
(h : ClosedComplemented p) : ∃ (q : Submodule R M) (hq : IsClosed (q : Set M)), IsCompl p q :=
Exists.elim h fun f hf => ⟨ker f, f.isClosed_ker, LinearMap.isCompl_of_proj hf⟩
#align submodule.closed_complemented.has_closed_complement Submodule.ClosedComplemented.has_closed_complement
+-/
#print Submodule.ClosedComplemented.isClosed /-
protected theorem ClosedComplemented.isClosed [TopologicalAddGroup M] [T1Space M]
@@ -2697,24 +3132,30 @@ protected theorem ClosedComplemented.isClosed [TopologicalAddGroup M] [T1Space M
#align submodule.closed_complemented.is_closed Submodule.ClosedComplemented.isClosed
-/
+#print Submodule.closedComplemented_bot /-
@[simp]
theorem closedComplemented_bot : ClosedComplemented (⊥ : Submodule R M) :=
⟨0, fun x => by simp only [zero_apply, eq_zero_of_bot_submodule x]⟩
#align submodule.closed_complemented_bot Submodule.closedComplemented_bot
+-/
+#print Submodule.closedComplemented_top /-
@[simp]
theorem closedComplemented_top : ClosedComplemented (⊤ : Submodule R M) :=
⟨(id R M).codRestrict ⊤ fun x => trivial, fun x => Subtype.ext_iff_val.2 <| by simp⟩
#align submodule.closed_complemented_top Submodule.closedComplemented_top
+-/
end Submodule
+#print ContinuousLinearMap.closedComplemented_ker_of_rightInverse /-
theorem ContinuousLinearMap.closedComplemented_ker_of_rightInverse {R : Type _} [Ring R]
{M : Type _} [TopologicalSpace M] [AddCommGroup M] {M₂ : Type _} [TopologicalSpace M₂]
[AddCommGroup M₂] [Module R M] [Module R M₂] [TopologicalAddGroup M] (f₁ : M →L[R] M₂)
(f₂ : M₂ →L[R] M) (h : Function.RightInverse f₂ f₁) : (ker f₁).ClosedComplemented :=
⟨f₁.projKerOfRightInverse f₂ h, f₁.projKerOfRightInverse_apply_idem f₂ h⟩
#align continuous_linear_map.closed_complemented_ker_of_right_inverse ContinuousLinearMap.closedComplemented_ker_of_rightInverse
+-/
section Quotient
@@ -2723,9 +3164,11 @@ namespace Submodule
variable {R M : Type _} [Ring R] [AddCommGroup M] [Module R M] [TopologicalSpace M]
(S : Submodule R M)
+#print Submodule.isOpenMap_mkQ /-
theorem isOpenMap_mkQ [TopologicalAddGroup M] : IsOpenMap S.mkQ :=
QuotientAddGroup.isOpenMap_coe S.toAddSubgroup
#align submodule.is_open_map_mkq Submodule.isOpenMap_mkQ
+-/
#print Submodule.topologicalAddGroup_quotient /-
instance topologicalAddGroup_quotient [TopologicalAddGroup M] : TopologicalAddGroup (M ⧸ S) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0
@@ -197,7 +197,6 @@ theorem Submodule.closure_smul_self_subset (s : Submodule R M) :
refine' ⟨_, fun hx => ⟨⟨1, x⟩, ⟨Set.mem_univ _, hx⟩, one_smul R _⟩⟩
rintro ⟨⟨c, y⟩, ⟨hc, hy⟩, rfl⟩
simp [s.smul_mem c hy]
-
#align submodule.closure_smul_self_subset Submodule.closure_smul_self_subset
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004
@@ -5,7 +5,7 @@ Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov, Fréd
Heather Macbeth
! This file was ported from Lean 3 source module topology.algebra.module.basic
-! leanprover-community/mathlib commit d64d67d000b974f0d86a2be7918cf800be6271c8
+! leanprover-community/mathlib commit e354e865255654389cc46e6032160238df2e0f40
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -1226,6 +1226,19 @@ theorem range_coprod [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃]
LinearMap.range_coprod _ _
#align continuous_linear_map.range_coprod ContinuousLinearMap.range_coprod
+theorem comp_fst_add_comp_snd [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃] (f : M₁ →L[R₁] M₃)
+ (g : M₂ →L[R₁] M₃) :
+ f.comp (ContinuousLinearMap.fst R₁ M₁ M₂) + g.comp (ContinuousLinearMap.snd R₁ M₁ M₂) =
+ f.coprod g :=
+ rfl
+#align continuous_linear_map.comp_fst_add_comp_snd ContinuousLinearMap.comp_fst_add_comp_snd
+
+theorem coprod_inl_inr [ContinuousAdd M₁] [ContinuousAdd M'₁] :
+ (ContinuousLinearMap.inl R₁ M₁ M'₁).coprod (ContinuousLinearMap.inr R₁ M₁ M'₁) =
+ ContinuousLinearMap.id R₁ (M₁ × M'₁) :=
+ by apply coe_injective; apply LinearMap.coprod_inl_inr
+#align continuous_linear_map.coprod_inl_inr ContinuousLinearMap.coprod_inl_inr
+
section
variable {R S : Type _} [Semiring R] [Semiring S] [Module R M₁] [Module R M₂] [Module R S]
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -100,13 +100,13 @@ variable {R : Type _} {M : Type _} [Ring R] [TopologicalSpace R] [TopologicalSpa
/-- If `M` is a topological module over `R` and `0` is a limit of invertible elements of `R`, then
`⊤` is the only submodule of `M` with a nonempty interior.
This is the case, e.g., if `R` is a nontrivially normed field. -/
-theorem Submodule.eq_top_of_nonempty_interior' [NeBot (𝓝[{ x : R | IsUnit x }] 0)]
- (s : Submodule R M) (hs : (interior (s : Set M)).Nonempty) : s = ⊤ :=
+theorem Submodule.eq_top_of_nonempty_interior' [NeBot (𝓝[{x : R | IsUnit x}] 0)] (s : Submodule R M)
+ (hs : (interior (s : Set M)).Nonempty) : s = ⊤ :=
by
rcases hs with ⟨y, hy⟩
refine' Submodule.eq_top_iff'.2 fun x => _
rw [mem_interior_iff_mem_nhds] at hy
- have : tendsto (fun c : R => y + c • x) (𝓝[{ x : R | IsUnit x }] 0) (𝓝 (y + (0 : R) • x)) :=
+ have : tendsto (fun c : R => y + c • x) (𝓝[{x : R | IsUnit x}] 0) (𝓝 (y + (0 : R) • x)) :=
tendsto_const_nhds.add ((tendsto_nhdsWithin_of_tendsto_nhds tendsto_id).smul tendsto_const_nhds)
rw [zero_smul, add_zero] at this
obtain ⟨_, hu : y + _ • _ ∈ s, u, rfl⟩ :=
@@ -276,13 +276,13 @@ theorem LinearMap.continuous_on_pi {ι : Type _} {R : Type _} {M : Type _} [Fini
by
cases nonempty_fintype ι
classical
- -- for the proof, write `f` in the standard basis, and use that each coordinate is a continuous
- -- function.
- have : (f : (ι → R) → M) = fun x => ∑ i : ι, x i • f fun j => if i = j then 1 else 0 := by
- ext x; exact f.pi_apply_eq_sum_univ x
- rw [this]
- refine' continuous_finset_sum _ fun i hi => _
- exact (continuous_apply i).smul continuous_const
+ -- for the proof, write `f` in the standard basis, and use that each coordinate is a continuous
+ -- function.
+ have : (f : (ι → R) → M) = fun x => ∑ i : ι, x i • f fun j => if i = j then 1 else 0 := by ext x;
+ exact f.pi_apply_eq_sum_univ x
+ rw [this]
+ refine' continuous_finset_sum _ fun i hi => _
+ exact (continuous_apply i).smul continuous_const
#align linear_map.continuous_on_pi LinearMap.continuous_on_pi
end Pi
@@ -414,7 +414,7 @@ section
variable (M₁ M₂) (σ : R →+* S)
-theorem isClosed_setOf_map_smul : IsClosed { f : M₁ → M₂ | ∀ c x, f (c • x) = σ c • f x } :=
+theorem isClosed_setOf_map_smul : IsClosed {f : M₁ → M₂ | ∀ c x, f (c • x) = σ c • f x} :=
by
simp only [Set.setOf_forall]
exact
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -105,14 +105,14 @@ theorem Submodule.eq_top_of_nonempty_interior' [NeBot (𝓝[{ x : R | IsUnit x }
by
rcases hs with ⟨y, hy⟩
refine' Submodule.eq_top_iff'.2 fun x => _
- rw [mem_interior_iff_mem_nhds] at hy
+ rw [mem_interior_iff_mem_nhds] at hy
have : tendsto (fun c : R => y + c • x) (𝓝[{ x : R | IsUnit x }] 0) (𝓝 (y + (0 : R) • x)) :=
tendsto_const_nhds.add ((tendsto_nhdsWithin_of_tendsto_nhds tendsto_id).smul tendsto_const_nhds)
- rw [zero_smul, add_zero] at this
+ rw [zero_smul, add_zero] at this
obtain ⟨_, hu : y + _ • _ ∈ s, u, rfl⟩ :=
nonempty_of_mem (inter_mem (mem_map.1 (this hy)) self_mem_nhdsWithin)
have hy' : y ∈ ↑s := mem_of_mem_nhds hy
- rwa [s.add_mem_iff_right hy', ← Units.smul_def, s.smul_mem_iff' u] at hu
+ rwa [s.add_mem_iff_right hy', ← Units.smul_def, s.smul_mem_iff' u] at hu
#align submodule.eq_top_of_nonempty_interior' Submodule.eq_top_of_nonempty_interior'
variable (R M)
@@ -292,8 +292,8 @@ end Pi
definition, although in applications `M` and `M₂` will be topological modules over the topological
ring `R`. -/
structure ContinuousLinearMap {R : Type _} {S : Type _} [Semiring R] [Semiring S] (σ : R →+* S)
- (M : Type _) [TopologicalSpace M] [AddCommMonoid M] (M₂ : Type _) [TopologicalSpace M₂]
- [AddCommMonoid M₂] [Module R M] [Module S M₂] extends M →ₛₗ[σ] M₂ where
+ (M : Type _) [TopologicalSpace M] [AddCommMonoid M] (M₂ : Type _) [TopologicalSpace M₂]
+ [AddCommMonoid M₂] [Module R M] [Module S M₂] extends M →ₛₗ[σ] M₂ where
cont : Continuous to_fun := by continuity
#align continuous_linear_map ContinuousLinearMap
-/
@@ -314,9 +314,9 @@ notation:25 M " →L⋆[" R "] " M₂ => ContinuousLinearMap (starRingEnd R) M M
homomorphism `σ : R →+* S` is semilinear if it satisfies the two properties `f (x + y) = f x + f y`
and `f (c • x) = (σ c) • f x`. -/
class ContinuousSemilinearMapClass (F : Type _) {R S : outParam (Type _)} [Semiring R] [Semiring S]
- (σ : outParam <| R →+* S) (M : outParam (Type _)) [TopologicalSpace M] [AddCommMonoid M]
- (M₂ : outParam (Type _)) [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M]
- [Module S M₂] extends SemilinearMapClass F σ M M₂, ContinuousMapClass F M M₂
+ (σ : outParam <| R →+* S) (M : outParam (Type _)) [TopologicalSpace M] [AddCommMonoid M]
+ (M₂ : outParam (Type _)) [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M]
+ [Module S M₂] extends SemilinearMapClass F σ M M₂, ContinuousMapClass F M M₂
#align continuous_semilinear_map_class ContinuousSemilinearMapClass
-/
@@ -340,9 +340,9 @@ for the definition, although in applications `M` and `M₂` will be topological
topological semiring `R`. -/
@[nolint has_nonempty_instance]
structure ContinuousLinearEquiv {R : Type _} {S : Type _} [Semiring R] [Semiring S] (σ : R →+* S)
- {σ' : S →+* R} [RingHomInvPair σ σ'] [RingHomInvPair σ' σ] (M : Type _) [TopologicalSpace M]
- [AddCommMonoid M] (M₂ : Type _) [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M]
- [Module S M₂] extends M ≃ₛₗ[σ] M₂ where
+ {σ' : S →+* R} [RingHomInvPair σ σ'] [RingHomInvPair σ' σ] (M : Type _) [TopologicalSpace M]
+ [AddCommMonoid M] (M₂ : Type _) [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M]
+ [Module S M₂] extends M ≃ₛₗ[σ] M₂ where
continuous_toFun : Continuous to_fun := by continuity
continuous_invFun : Continuous inv_fun := by continuity
#align continuous_linear_equiv ContinuousLinearEquiv
@@ -364,10 +364,10 @@ where `σ` is the identity map on `R`. A map `f` between an `R`-module and an `
homomorphism `σ : R →+* S` is semilinear if it satisfies the two properties `f (x + y) = f x + f y`
and `f (c • x) = (σ c) • f x`. -/
class ContinuousSemilinearEquivClass (F : Type _) {R : outParam (Type _)} {S : outParam (Type _)}
- [Semiring R] [Semiring S] (σ : outParam <| R →+* S) {σ' : outParam <| S →+* R}
- [RingHomInvPair σ σ'] [RingHomInvPair σ' σ] (M : outParam (Type _)) [TopologicalSpace M]
- [AddCommMonoid M] (M₂ : outParam (Type _)) [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M]
- [Module S M₂] extends SemilinearEquivClass F σ M M₂ where
+ [Semiring R] [Semiring S] (σ : outParam <| R →+* S) {σ' : outParam <| S →+* R}
+ [RingHomInvPair σ σ'] [RingHomInvPair σ' σ] (M : outParam (Type _)) [TopologicalSpace M]
+ [AddCommMonoid M] (M₂ : outParam (Type _)) [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M]
+ [Module S M₂] extends SemilinearEquivClass F σ M M₂ where
map_continuous : ∀ f : F, Continuous f := by continuity
inv_continuous : ∀ f : F, Continuous (inv f) := by continuity
#align continuous_semilinear_equiv_class ContinuousSemilinearEquivClass
@@ -648,8 +648,8 @@ theorem DenseRange.topologicalClosure_map_submodule [RingHomSurjective σ₁₂]
[ContinuousAdd M₂] {f : M₁ →SL[σ₁₂] M₂} (hf' : DenseRange f) {s : Submodule R₁ M₁}
(hs : s.topologicalClosure = ⊤) : (s.map (f : M₁ →ₛₗ[σ₁₂] M₂)).topologicalClosure = ⊤ :=
by
- rw [SetLike.ext'_iff] at hs⊢
- simp only [Submodule.topologicalClosure_coe, Submodule.top_coe, ← dense_iff_closure_eq] at hs⊢
+ rw [SetLike.ext'_iff] at hs ⊢
+ simp only [Submodule.topologicalClosure_coe, Submodule.top_coe, ← dense_iff_closure_eq] at hs ⊢
exact hf'.dense_image f.continuous hs
#align dense_range.topological_closure_map_submodule DenseRange.topologicalClosure_map_submodule
@@ -1350,7 +1350,7 @@ def iInfKerProjEquiv {I J : Set ι} [DecidablePred fun i => i ∈ I] (hd : Disjo
continuous_invFun :=
Continuous.subtype_mk
(continuous_pi fun i => by dsimp;
- split_ifs <;> [apply continuous_apply;exact continuous_zero])
+ split_ifs <;> [apply continuous_apply; exact continuous_zero])
_
#align continuous_linear_map.infi_ker_proj_equiv ContinuousLinearMap.iInfKerProjEquiv
@@ -1440,7 +1440,7 @@ instance : AddCommGroup (M →SL[σ₁₂] M₂) := by
zsmul := (· • ·)
zsmul_zero' := fun f => by ext; simp
zsmul_succ' := fun n f => by ext; simp [add_smul, add_comm]
- zsmul_neg' := fun n f => by ext; simp [Nat.succ_eq_add_one, add_smul].. } <;>
+ zsmul_neg' := fun n f => by ext; simp [Nat.succ_eq_add_one, add_smul] .. } <;>
intros <;>
ext <;>
apply_rules [zero_add, add_assoc, add_zero, add_left_neg, add_comm, sub_eq_add_neg]
@@ -1940,8 +1940,8 @@ theorem map_eq_zero_iff (e : M₁ ≃SL[σ₁₂] M₂) {x : M₁} : e x = 0 ↔
e.toLinearEquiv.map_eq_zero_iff
#align continuous_linear_equiv.map_eq_zero_iff ContinuousLinearEquiv.map_eq_zero_iff
-attribute [continuity]
- ContinuousLinearEquiv.continuous_toFun ContinuousLinearEquiv.continuous_invFun
+attribute [continuity] ContinuousLinearEquiv.continuous_toFun
+ ContinuousLinearEquiv.continuous_invFun
@[continuity]
protected theorem continuous (e : M₁ ≃SL[σ₁₂] M₂) : Continuous (e : M₁ → M₂) :=
@@ -2671,7 +2671,7 @@ def ClosedComplemented (p : Submodule R M) : Prop :=
-/
theorem ClosedComplemented.has_closed_complement {p : Submodule R M} [T1Space p]
- (h : ClosedComplemented p) : ∃ (q : Submodule R M)(hq : IsClosed (q : Set M)), IsCompl p q :=
+ (h : ClosedComplemented p) : ∃ (q : Submodule R M) (hq : IsClosed (q : Set M)), IsCompl p q :=
Exists.elim h fun f hf => ⟨ker f, f.isClosed_ker, LinearMap.isCompl_of_proj hf⟩
#align submodule.closed_complemented.has_closed_complement Submodule.ClosedComplemented.has_closed_complement
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -474,13 +474,11 @@ variable {R₁ : Type _} {R₂ : Type _} {R₃ : Type _} [Semiring R₁] [Semiri
instance : Coe (M₁ →SL[σ₁₂] M₂) (M₁ →ₛₗ[σ₁₂] M₂) :=
⟨toLinearMap⟩
-/- warning: continuous_linear_map.to_linear_map_eq_coe clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.to_linear_map_eq_coe [anonymous]ₓ'. -/
-- make the coercion the preferred form
@[simp]
-theorem [anonymous] (f : M₁ →SL[σ₁₂] M₂) : f.toLinearMap = f :=
+theorem toLinearMap_eq_coe (f : M₁ →SL[σ₁₂] M₂) : f.toLinearMap = f :=
rfl
-#align continuous_linear_map.to_linear_map_eq_coe [anonymous]
+#align continuous_linear_map.to_linear_map_eq_coe ContinuousLinearMap.toLinearMap_eq_coe
theorem coe_injective : Function.Injective (coe : (M₁ →SL[σ₁₂] M₂) → M₁ →ₛₗ[σ₁₂] M₂) := by
intro f g H; cases f; cases g; congr
@@ -1845,12 +1843,10 @@ instance : ContinuousSemilinearEquivClass (M₁ ≃SL[σ₁₂] M₂) σ₁₂ M
instance : CoeFun (M₁ ≃SL[σ₁₂] M₂) fun _ => M₁ → M₂ :=
⟨fun f => f⟩
-/- warning: continuous_linear_equiv.coe_def_rev clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_def_rev [anonymous]ₓ'. -/
@[simp]
-theorem [anonymous] (e : M₁ ≃SL[σ₁₂] M₂) : e.toContinuousLinearMap = e :=
+theorem coe_def_rev (e : M₁ ≃SL[σ₁₂] M₂) : e.toContinuousLinearMap = e :=
rfl
-#align continuous_linear_equiv.coe_def_rev [anonymous]
+#align continuous_linear_equiv.coe_def_rev ContinuousLinearEquiv.coe_def_rev
theorem coe_apply (e : M₁ ≃SL[σ₁₂] M₂) (b : M₁) : (e : M₁ →SL[σ₁₂] M₂) b = e b :=
rfl
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -39,7 +39,7 @@ open Filter
open LinearMap (ker range)
-open Topology BigOperators Filter
+open scoped Topology BigOperators Filter
universe u v w u'
@@ -2574,7 +2574,7 @@ end ContinuousLinearEquiv
namespace ContinuousLinearMap
-open Classical
+open scoped Classical
variable {R : Type _} {M : Type _} {M₂ : Type _} [TopologicalSpace M] [TopologicalSpace M₂]
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -48,9 +48,6 @@ section
variable {R : Type _} {M : Type _} [Ring R] [TopologicalSpace R] [TopologicalSpace M]
[AddCommGroup M] [Module R M]
-/- warning: has_continuous_smul.of_nhds_zero -> ContinuousSMul.of_nhds_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_continuous_smul.of_nhds_zero ContinuousSMul.of_nhds_zeroₓ'. -/
theorem ContinuousSMul.of_nhds_zero [TopologicalRing R] [TopologicalAddGroup M]
(hmul : Tendsto (fun p : R × M => p.1 • p.2) (𝓝 0 ×ᶠ 𝓝 0) (𝓝 0))
(hmulleft : ∀ m : M, Tendsto (fun a : R => a • m) (𝓝 0) (𝓝 0))
@@ -100,12 +97,6 @@ section
variable {R : Type _} {M : Type _} [Ring R] [TopologicalSpace R] [TopologicalSpace M]
[AddCommGroup M] [ContinuousAdd M] [Module R M] [ContinuousSMul R M]
-/- warning: submodule.eq_top_of_nonempty_interior' -> Submodule.eq_top_of_nonempty_interior' is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_4)))))] [_inst_6 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_7 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6)))) _inst_2 _inst_3] [_inst_8 : Filter.NeBot.{u1} R (nhdsWithin.{u1} R _inst_2 (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))))) (setOf.{u1} R (fun (x : R) => IsUnit.{u1} R (Ring.toMonoid.{u1} R _inst_1) x)))] (s : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6), (Set.Nonempty.{u2} M (interior.{u2} M _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6)))) s))) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6) s (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6)))
-but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : TopologicalSpace.{u2} R] [_inst_3 : TopologicalSpace.{u1} M] [_inst_4 : AddCommGroup.{u1} M] [_inst_5 : ContinuousAdd.{u1} M _inst_3 (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_4)))))] [_inst_6 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4)] [_inst_7 : ContinuousSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_6)))) _inst_2 _inst_3] [_inst_8 : Filter.NeBot.{u2} R (nhdsWithin.{u2} R _inst_2 (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (setOf.{u2} R (fun (x : R) => IsUnit.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) x)))] (s : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_6), (Set.Nonempty.{u1} M (interior.{u1} M _inst_3 (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_6) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_6) s))) -> (Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_6) s (Top.top.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_6) (Submodule.instTopSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_6)))
-Case conversion may be inaccurate. Consider using '#align submodule.eq_top_of_nonempty_interior' Submodule.eq_top_of_nonempty_interior'ₓ'. -/
/-- If `M` is a topological module over `R` and `0` is a limit of invertible elements of `R`, then
`⊤` is the only submodule of `M` with a nonempty interior.
This is the case, e.g., if `R` is a nontrivially normed field. -/
@@ -126,12 +117,6 @@ theorem Submodule.eq_top_of_nonempty_interior' [NeBot (𝓝[{ x : R | IsUnit x }
variable (R M)
-/- warning: module.punctured_nhds_ne_bot -> Module.punctured_nhds_neBot is a dubious translation:
-lean 3 declaration is
- forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Ring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_4)))))] [_inst_6 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_7 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6)))) _inst_2 _inst_3] [_inst_8 : Nontrivial.{u2} M] [_inst_9 : Filter.NeBot.{u1} R (nhdsWithin.{u1} R _inst_2 (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))))) (HasCompl.compl.{u1} (Set.{u1} R) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} R) (Set.booleanAlgebra.{u1} R)) (Singleton.singleton.{u1, u1} R (Set.{u1} R) (Set.hasSingleton.{u1} R) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))))))))] [_inst_10 : NoZeroSMulDivisors.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_4))))) (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6))))] (x : M), Filter.NeBot.{u2} M (nhdsWithin.{u2} M _inst_3 x (HasCompl.compl.{u2} (Set.{u2} M) (BooleanAlgebra.toHasCompl.{u2} (Set.{u2} M) (Set.booleanAlgebra.{u2} M)) (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x)))
-but is expected to have type
- forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Ring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_4)))))] [_inst_6 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_7 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_4))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6)))) _inst_2 _inst_3] [_inst_8 : Nontrivial.{u2} M] [_inst_9 : Filter.NeBot.{u1} R (nhdsWithin.{u1} R _inst_2 (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (HasCompl.compl.{u1} (Set.{u1} R) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} R) (Set.instBooleanAlgebraSet.{u1} R)) (Singleton.singleton.{u1, u1} R (Set.{u1} R) (Set.instSingletonSet.{u1} R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))] [_inst_10 : NoZeroSMulDivisors.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} R M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_4))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6))))] (x : M), Filter.NeBot.{u2} M (nhdsWithin.{u2} M _inst_3 x (HasCompl.compl.{u2} (Set.{u2} M) (BooleanAlgebra.toHasCompl.{u2} (Set.{u2} M) (Set.instBooleanAlgebraSet.{u2} M)) (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)))
-Case conversion may be inaccurate. Consider using '#align module.punctured_nhds_ne_bot Module.punctured_nhds_neBotₓ'. -/
/-- Let `R` be a topological ring such that zero is not an isolated point (e.g., a nontrivially
normed field, see `normed_field.punctured_nhds_ne_bot`). Let `M` be a nontrivial module over `R`
such that `c • x = 0` implies `c = 0 ∨ x = 0`. Then `M` has no isolated points. We formulate this
@@ -161,9 +146,6 @@ variable {ι R M₁ M₂ : Type _} [Semiring R] [AddCommMonoid M₁] [AddCommMon
[Module R M₂] [u : TopologicalSpace R] {t : TopologicalSpace M₂} [ContinuousSMul R M₂]
(f : M₁ →ₗ[R] M₂)
-/- warning: has_continuous_smul_induced -> continuousSMul_induced is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_continuous_smul_induced continuousSMul_inducedₓ'. -/
theorem continuousSMul_induced : @ContinuousSMul R M₁ _ u (t.induced f) :=
{
continuous_smul := by
@@ -226,12 +208,6 @@ theorem Submodule.closure_smul_self_eq (s : Submodule R M) :
variable [ContinuousAdd M]
-/- warning: submodule.topological_closure -> Submodule.topologicalClosure is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))], (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) -> (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5)
-but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] [_inst_5 : ContinuousConstSMul.{u1, u2} R M _inst_2 (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_3 _inst_4))))] [_inst_6 : ContinuousAdd.{u2} M _inst_2 (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))], (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) -> (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)
-Case conversion may be inaccurate. Consider using '#align submodule.topological_closure Submodule.topologicalClosureₓ'. -/
/-- The (topological-space) closure of a submodule of a topological `R`-module `M` is itself
a submodule. -/
def Submodule.topologicalClosure (s : Submodule R M) : Submodule R M :=
@@ -241,78 +217,36 @@ def Submodule.topologicalClosure (s : Submodule R M) : Submodule R M :=
smul_mem' := fun c x hx => s.closure_smul_self_subset ⟨⟨c, x⟩, ⟨Set.mem_univ _, hx⟩, rfl⟩ }
#align submodule.topological_closure Submodule.topologicalClosure
-/- warning: submodule.topological_closure_coe -> Submodule.topologicalClosure_coe is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))] (s : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5), Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 s)) (closure.{u2} M _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) s))
-but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] [_inst_5 : ContinuousConstSMul.{u1, u2} R M _inst_2 (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_3 _inst_4))))] [_inst_6 : ContinuousAdd.{u2} M _inst_2 (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))] (_inst_7 : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4), Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7)) (closure.{u2} M _inst_2 (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) _inst_7))
-Case conversion may be inaccurate. Consider using '#align submodule.topological_closure_coe Submodule.topologicalClosure_coeₓ'. -/
@[simp]
theorem Submodule.topologicalClosure_coe (s : Submodule R M) :
(s.topologicalClosure : Set M) = closure (s : Set M) :=
rfl
#align submodule.topological_closure_coe Submodule.topologicalClosure_coe
-/- warning: submodule.le_topological_closure -> Submodule.le_topologicalClosure is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))] (s : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5), LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) s (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 s)
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- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] [_inst_5 : ContinuousConstSMul.{u1, u2} R M _inst_2 (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_3 _inst_4))))] [_inst_6 : ContinuousAdd.{u2} M _inst_2 (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))] (_inst_7 : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4), LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))))) _inst_7 (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7)
-Case conversion may be inaccurate. Consider using '#align submodule.le_topological_closure Submodule.le_topologicalClosureₓ'. -/
theorem Submodule.le_topologicalClosure (s : Submodule R M) : s ≤ s.topologicalClosure :=
subset_closure
#align submodule.le_topological_closure Submodule.le_topologicalClosure
-/- warning: submodule.is_closed_topological_closure -> Submodule.isClosed_topologicalClosure is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))] (s : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5), IsClosed.{u2} M _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 s))
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- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] [_inst_5 : ContinuousConstSMul.{u1, u2} R M _inst_2 (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_3 _inst_4))))] [_inst_6 : ContinuousAdd.{u2} M _inst_2 (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))] (_inst_7 : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4), IsClosed.{u2} M _inst_2 (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7))
-Case conversion may be inaccurate. Consider using '#align submodule.is_closed_topological_closure Submodule.isClosed_topologicalClosureₓ'. -/
theorem Submodule.isClosed_topologicalClosure (s : Submodule R M) :
IsClosed (s.topologicalClosure : Set M) := by convert isClosed_closure
#align submodule.is_closed_topological_closure Submodule.isClosed_topologicalClosure
-/- warning: submodule.topological_closure_minimal -> Submodule.topologicalClosure_minimal is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))] (s : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) {t : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5}, (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) s t) -> (IsClosed.{u2} M _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) t)) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 s) t)
-but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] [_inst_5 : ContinuousConstSMul.{u1, u2} R M _inst_2 (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_3 _inst_4))))] [_inst_6 : ContinuousAdd.{u2} M _inst_2 (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))] (_inst_7 : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) {s : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))))) _inst_7 s) -> (IsClosed.{u2} M _inst_2 (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) s)) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))))) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) s)
-Case conversion may be inaccurate. Consider using '#align submodule.topological_closure_minimal Submodule.topologicalClosure_minimalₓ'. -/
theorem Submodule.topologicalClosure_minimal (s : Submodule R M) {t : Submodule R M} (h : s ≤ t)
(ht : IsClosed (t : Set M)) : s.topologicalClosure ≤ t :=
closure_minimal h ht
#align submodule.topological_closure_minimal Submodule.topologicalClosure_minimal
-/- warning: submodule.topological_closure_mono -> Submodule.topologicalClosure_mono is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))] {s : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5} {t : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5}, (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) s t) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 s) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 t))
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- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] [_inst_5 : ContinuousConstSMul.{u1, u2} R M _inst_2 (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_3 _inst_4))))] [_inst_6 : ContinuousAdd.{u2} M _inst_2 (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))] {_inst_7 : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {s : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))))) _inst_7 s) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))))) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))
-Case conversion may be inaccurate. Consider using '#align submodule.topological_closure_mono Submodule.topologicalClosure_monoₓ'. -/
theorem Submodule.topologicalClosure_mono {s : Submodule R M} {t : Submodule R M} (h : s ≤ t) :
s.topologicalClosure ≤ t.topologicalClosure :=
s.topologicalClosure_minimal (h.trans t.le_topologicalClosure) t.isClosed_topologicalClosure
#align submodule.topological_closure_mono Submodule.topologicalClosure_mono
-/- warning: is_closed.submodule_topological_closure_eq -> IsClosed.submodule_topologicalClosure_eq is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))] {s : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5}, (IsClosed.{u2} M _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) s)) -> (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 s) s)
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- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] [_inst_5 : ContinuousConstSMul.{u1, u2} R M _inst_2 (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_3 _inst_4))))] [_inst_6 : ContinuousAdd.{u2} M _inst_2 (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))] {_inst_7 : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, (IsClosed.{u2} M _inst_2 (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) _inst_7)) -> (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) _inst_7)
-Case conversion may be inaccurate. Consider using '#align is_closed.submodule_topological_closure_eq IsClosed.submodule_topologicalClosure_eqₓ'. -/
/-- The topological closure of a closed submodule `s` is equal to `s`. -/
theorem IsClosed.submodule_topologicalClosure_eq {s : Submodule R M} (hs : IsClosed (s : Set M)) :
s.topologicalClosure = s :=
le_antisymm (s.topologicalClosure_minimal rfl.le hs) s.le_topologicalClosure
#align is_closed.submodule_topological_closure_eq IsClosed.submodule_topologicalClosure_eq
-/- warning: submodule.dense_iff_topological_closure_eq_top -> Submodule.dense_iff_topologicalClosure_eq_top is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))] {s : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5}, Iff (Dense.{u2} M _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) s)) (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 s) (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Submodule.hasTop.{u1, u2} R M _inst_1 _inst_4 _inst_5)))
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- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] [_inst_5 : ContinuousConstSMul.{u1, u2} R M _inst_2 (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_3 _inst_4))))] [_inst_6 : ContinuousAdd.{u2} M _inst_2 (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))] {_inst_7 : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, Iff (Dense.{u2} M _inst_2 (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) _inst_7)) (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instTopSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)))
-Case conversion may be inaccurate. Consider using '#align submodule.dense_iff_topological_closure_eq_top Submodule.dense_iff_topologicalClosure_eq_topₓ'. -/
/-- A subspace is dense iff its topological closure is the entire space. -/
theorem Submodule.dense_iff_topologicalClosure_eq_top {s : Submodule R M} :
Dense (s : Set M) ↔ s.topologicalClosure = ⊤ := by
@@ -324,12 +258,6 @@ instance {M' : Type _} [AddCommMonoid M'] [Module R M'] [UniformSpace M'] [Conti
CompleteSpace U.topologicalClosure :=
isClosed_closure.completeSpace_coe
-/- warning: submodule.is_closed_or_dense_of_is_coatom -> Submodule.isClosed_or_dense_of_isCoatom is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))] (s : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5), (IsCoatom.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5))) (Submodule.orderTop.{u1, u2} R M _inst_1 _inst_4 _inst_5) s) -> (Or (IsClosed.{u2} M _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) s)) (Dense.{u2} M _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) s)))
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- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] [_inst_5 : ContinuousConstSMul.{u1, u2} R M _inst_2 (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_3 _inst_4))))] [_inst_6 : ContinuousAdd.{u2} M _inst_2 (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))] (_inst_7 : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4), (IsCoatom.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderTopSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) _inst_7) -> (Or (IsClosed.{u2} M _inst_2 (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) _inst_7)) (Dense.{u2} M _inst_2 (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) _inst_7)))
-Case conversion may be inaccurate. Consider using '#align submodule.is_closed_or_dense_of_is_coatom Submodule.isClosed_or_dense_of_isCoatomₓ'. -/
/-- A maximal proper subspace of a topological module (i.e a `submodule` satisfying `is_coatom`)
is either closed or dense. -/
theorem Submodule.isClosed_or_dense_of_isCoatom (s : Submodule R M) (hs : IsCoatom s) :
@@ -342,12 +270,6 @@ end closure
section Pi
-/- warning: linear_map.continuous_on_pi -> LinearMap.continuous_on_pi is a dubious translation:
-lean 3 declaration is
- forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Finite.{succ u1} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : TopologicalSpace.{u2} R] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_2 _inst_4] [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : ContinuousAdd.{u3} M _inst_6 (AddZeroClass.toHasAdd.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)))] [_inst_8 : ContinuousSMul.{u2, u3} R M (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_4 _inst_5)))) _inst_3 _inst_6] (f : LinearMap.{u2, u2, max u1 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.Function.module.{u1, u2, u2} ι R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_5), Continuous.{max u1 u2, u3} (ι -> R) M (Pi.topologicalSpace.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (a : ι) => _inst_3)) _inst_6 (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.Function.module.{u1, u2, u2} ι R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.Function.module.{u1, u2, u2} ι R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_5) => (ι -> R) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (ι -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.Function.module.{u1, u2, u2} ι R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) f)
-but is expected to have type
- forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Finite.{succ u3} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : TopologicalSpace.{u2} R] [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_2 _inst_4] [_inst_6 : TopologicalSpace.{u1} M] [_inst_7 : ContinuousAdd.{u1} M _inst_6 (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)))] [_inst_8 : ContinuousSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (Module.toMulActionWithZero.{u2, u1} R M _inst_2 _inst_4 _inst_5)))) _inst_3 _inst_6] (f : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5), Continuous.{max u3 u2, u1} (ι -> R) M (Pi.topologicalSpace.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (a : ι) => _inst_3)) _inst_6 (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5) (ι -> R) (fun (_x : ι -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (ι -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) f)
-Case conversion may be inaccurate. Consider using '#align linear_map.continuous_on_pi LinearMap.continuous_on_piₓ'. -/
theorem LinearMap.continuous_on_pi {ι : Type _} {R : Type _} {M : Type _} [Finite ι] [Semiring R]
[TopologicalSpace R] [AddCommMonoid M] [Module R M] [TopologicalSpace M] [ContinuousAdd M]
[ContinuousSMul R M] (f : (ι → R) →ₗ[R] M) : Continuous f :=
@@ -504,9 +426,6 @@ end
variable [ContinuousAdd M₂] {σ : R →+* S} {l : Filter α}
-/- warning: linear_map_of_mem_closure_range_coe -> linearMapOfMemClosureRangeCoe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map_of_mem_closure_range_coe linearMapOfMemClosureRangeCoeₓ'. -/
/-- Constructs a bundled linear map from a function and a proof that this function belongs to the
closure of the set of linear maps. -/
@[simps (config := { fullyApplied := false })]
@@ -519,9 +438,6 @@ def linearMapOfMemClosureRangeCoe (f : M₁ → M₂)
(Set.range_subset_iff.2 LinearMap.map_smulₛₗ) hf }
#align linear_map_of_mem_closure_range_coe linearMapOfMemClosureRangeCoe
-/- warning: linear_map_of_tendsto -> linearMapOfTendsto is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map_of_tendsto linearMapOfTendstoₓ'. -/
/-- Construct a bundled linear map from a pointwise limit of linear maps -/
@[simps (config := { fullyApplied := false })]
def linearMapOfTendsto (f : M₁ → M₂) (g : α → M₁ →ₛₗ[σ] M₂) [l.ne_bot]
@@ -532,9 +448,6 @@ def linearMapOfTendsto (f : M₁ → M₂) (g : α → M₁ →ₛₗ[σ] M₂)
variable (M₁ M₂ σ)
-/- warning: linear_map.is_closed_range_coe -> LinearMap.isClosed_range_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.is_closed_range_coe LinearMap.isClosed_range_coeₓ'. -/
theorem LinearMap.isClosed_range_coe : IsClosed (Set.range (coeFn : (M₁ →ₛₗ[σ] M₂) → M₁ → M₂)) :=
isClosed_of_closure_subset fun f hf => ⟨linearMapOfMemClosureRangeCoe f hf, rfl⟩
#align linear_map.is_closed_range_coe LinearMap.isClosed_range_coe
@@ -562,8 +475,6 @@ instance : Coe (M₁ →SL[σ₁₂] M₂) (M₁ →ₛₗ[σ₁₂] M₂) :=
⟨toLinearMap⟩
/- warning: continuous_linear_map.to_linear_map_eq_coe clashes with [anonymous] -> [anonymous]
-warning: continuous_linear_map.to_linear_map_eq_coe -> [anonymous] is a dubious translation:
-<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.to_linear_map_eq_coe [anonymous]ₓ'. -/
-- make the coercion the preferred form
@[simp]
@@ -571,9 +482,6 @@ theorem [anonymous] (f : M₁ →SL[σ₁₂] M₂) : f.toLinearMap = f :=
rfl
#align continuous_linear_map.to_linear_map_eq_coe [anonymous]
-/- warning: continuous_linear_map.coe_injective -> ContinuousLinearMap.coe_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_injective ContinuousLinearMap.coe_injectiveₓ'. -/
theorem coe_injective : Function.Injective (coe : (M₁ →SL[σ₁₂] M₂) → M₁ →ₛₗ[σ₁₂] M₂) := by
intro f g H; cases f; cases g; congr
#align continuous_linear_map.coe_injective ContinuousLinearMap.coe_injective
@@ -592,50 +500,32 @@ instance toFun : CoeFun (M₁ →SL[σ₁₂] M₂) fun _ => M₁ → M₂ :=
⟨fun f => f.toFun⟩
#align continuous_linear_map.to_fun ContinuousLinearMap.toFun
-/- warning: continuous_linear_map.coe_mk -> ContinuousLinearMap.coe_mk is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_mk ContinuousLinearMap.coe_mkₓ'. -/
@[simp]
theorem coe_mk (f : M₁ →ₛₗ[σ₁₂] M₂) (h) : (mk f h : M₁ →ₛₗ[σ₁₂] M₂) = f :=
rfl
#align continuous_linear_map.coe_mk ContinuousLinearMap.coe_mk
-/- warning: continuous_linear_map.coe_mk' -> ContinuousLinearMap.coe_mk' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_mk' ContinuousLinearMap.coe_mk'ₓ'. -/
@[simp]
theorem coe_mk' (f : M₁ →ₛₗ[σ₁₂] M₂) (h) : (mk f h : M₁ → M₂) = f :=
rfl
#align continuous_linear_map.coe_mk' ContinuousLinearMap.coe_mk'
-/- warning: continuous_linear_map.continuous -> ContinuousLinearMap.continuous is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.continuous ContinuousLinearMap.continuousₓ'. -/
@[continuity]
protected theorem continuous (f : M₁ →SL[σ₁₂] M₂) : Continuous f :=
f.2
#align continuous_linear_map.continuous ContinuousLinearMap.continuous
-/- warning: continuous_linear_map.uniform_continuous -> ContinuousLinearMap.uniformContinuous is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.uniform_continuous ContinuousLinearMap.uniformContinuousₓ'. -/
protected theorem uniformContinuous {E₁ E₂ : Type _} [UniformSpace E₁] [UniformSpace E₂]
[AddCommGroup E₁] [AddCommGroup E₂] [Module R₁ E₁] [Module R₂ E₂] [UniformAddGroup E₁]
[UniformAddGroup E₂] (f : E₁ →SL[σ₁₂] E₂) : UniformContinuous f :=
uniformContinuous_addMonoidHom_of_continuous f.Continuous
#align continuous_linear_map.uniform_continuous ContinuousLinearMap.uniformContinuous
-/- warning: continuous_linear_map.coe_inj -> ContinuousLinearMap.coe_inj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_inj ContinuousLinearMap.coe_injₓ'. -/
@[simp, norm_cast]
theorem coe_inj {f g : M₁ →SL[σ₁₂] M₂} : (f : M₁ →ₛₗ[σ₁₂] M₂) = g ↔ f = g :=
coe_injective.eq_iff
#align continuous_linear_map.coe_inj ContinuousLinearMap.coe_inj
-/- warning: continuous_linear_map.coe_fn_injective -> ContinuousLinearMap.coeFn_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_fn_injective ContinuousLinearMap.coeFn_injectiveₓ'. -/
theorem coeFn_injective : @Function.Injective (M₁ →SL[σ₁₂] M₂) (M₁ → M₂) coeFn :=
FunLike.coe_injective
#align continuous_linear_map.coe_fn_injective ContinuousLinearMap.coeFn_injective
@@ -657,24 +547,15 @@ def Simps.coe (h : M₁ →SL[σ₁₂] M₂) : M₁ →ₛₗ[σ₁₂] M₂ :=
initialize_simps_projections ContinuousLinearMap (to_linear_map_to_fun → apply, toLinearMap → coe)
-/- warning: continuous_linear_map.ext -> ContinuousLinearMap.ext is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ext ContinuousLinearMap.extₓ'. -/
@[ext]
theorem ext {f g : M₁ →SL[σ₁₂] M₂} (h : ∀ x, f x = g x) : f = g :=
FunLike.ext f g h
#align continuous_linear_map.ext ContinuousLinearMap.ext
-/- warning: continuous_linear_map.ext_iff -> ContinuousLinearMap.ext_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ext_iff ContinuousLinearMap.ext_iffₓ'. -/
theorem ext_iff {f g : M₁ →SL[σ₁₂] M₂} : f = g ↔ ∀ x, f x = g x :=
FunLike.ext_iff
#align continuous_linear_map.ext_iff ContinuousLinearMap.ext_iff
-/- warning: continuous_linear_map.copy -> ContinuousLinearMap.copy is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.copy ContinuousLinearMap.copyₓ'. -/
/-- Copy of a `continuous_linear_map` with a new `to_fun` equal to the old one. Useful to fix
definitional equalities. -/
protected def copy (f : M₁ →SL[σ₁₂] M₂) (f' : M₁ → M₂) (h : f' = ⇑f) : M₁ →SL[σ₁₂] M₂
@@ -683,55 +564,34 @@ protected def copy (f : M₁ →SL[σ₁₂] M₂) (f' : M₁ → M₂) (h : f'
cont := show Continuous f' from h.symm ▸ f.Continuous
#align continuous_linear_map.copy ContinuousLinearMap.copy
-/- warning: continuous_linear_map.coe_copy -> ContinuousLinearMap.coe_copy is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_copy ContinuousLinearMap.coe_copyₓ'. -/
@[simp]
theorem coe_copy (f : M₁ →SL[σ₁₂] M₂) (f' : M₁ → M₂) (h : f' = ⇑f) : ⇑(f.copy f' h) = f' :=
rfl
#align continuous_linear_map.coe_copy ContinuousLinearMap.coe_copy
-/- warning: continuous_linear_map.copy_eq -> ContinuousLinearMap.copy_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.copy_eq ContinuousLinearMap.copy_eqₓ'. -/
theorem copy_eq (f : M₁ →SL[σ₁₂] M₂) (f' : M₁ → M₂) (h : f' = ⇑f) : f.copy f' h = f :=
FunLike.ext' h
#align continuous_linear_map.copy_eq ContinuousLinearMap.copy_eq
-/- warning: continuous_linear_map.map_zero -> ContinuousLinearMap.map_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_zero ContinuousLinearMap.map_zeroₓ'. -/
-- make some straightforward lemmas available to `simp`.
protected theorem map_zero (f : M₁ →SL[σ₁₂] M₂) : f (0 : M₁) = 0 :=
map_zero f
#align continuous_linear_map.map_zero ContinuousLinearMap.map_zero
-/- warning: continuous_linear_map.map_add -> ContinuousLinearMap.map_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_add ContinuousLinearMap.map_addₓ'. -/
protected theorem map_add (f : M₁ →SL[σ₁₂] M₂) (x y : M₁) : f (x + y) = f x + f y :=
map_add f x y
#align continuous_linear_map.map_add ContinuousLinearMap.map_add
-/- warning: continuous_linear_map.map_smulₛₗ -> ContinuousLinearMap.map_smulₛₗ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_smulₛₗ ContinuousLinearMap.map_smulₛₗₓ'. -/
@[simp]
protected theorem map_smulₛₗ (f : M₁ →SL[σ₁₂] M₂) (c : R₁) (x : M₁) : f (c • x) = σ₁₂ c • f x :=
(toLinearMap _).map_smulₛₗ _ _
#align continuous_linear_map.map_smulₛₗ ContinuousLinearMap.map_smulₛₗ
-/- warning: continuous_linear_map.map_smul -> ContinuousLinearMap.map_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_smul ContinuousLinearMap.map_smulₓ'. -/
@[simp]
protected theorem map_smul [Module R₁ M₂] (f : M₁ →L[R₁] M₂) (c : R₁) (x : M₁) :
f (c • x) = c • f x := by simp only [RingHom.id_apply, ContinuousLinearMap.map_smulₛₗ]
#align continuous_linear_map.map_smul ContinuousLinearMap.map_smul
-/- warning: continuous_linear_map.map_smul_of_tower -> ContinuousLinearMap.map_smul_of_tower is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_smul_of_tower ContinuousLinearMap.map_smul_of_towerₓ'. -/
@[simp]
theorem map_smul_of_tower {R S : Type _} [Semiring S] [SMul R M₁] [Module S M₁] [SMul R M₂]
[Module S M₂] [LinearMap.CompatibleSMul M₁ M₂ R S] (f : M₁ →L[S] M₂) (c : R) (x : M₁) :
@@ -739,40 +599,25 @@ theorem map_smul_of_tower {R S : Type _} [Semiring S] [SMul R M₁] [Module S M
LinearMap.CompatibleSMul.map_smul f c x
#align continuous_linear_map.map_smul_of_tower ContinuousLinearMap.map_smul_of_tower
-/- warning: continuous_linear_map.map_sum -> ContinuousLinearMap.map_sum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_sum ContinuousLinearMap.map_sumₓ'. -/
protected theorem map_sum {ι : Type _} (f : M₁ →SL[σ₁₂] M₂) (s : Finset ι) (g : ι → M₁) :
f (∑ i in s, g i) = ∑ i in s, f (g i) :=
f.toLinearMap.map_sum
#align continuous_linear_map.map_sum ContinuousLinearMap.map_sum
-/- warning: continuous_linear_map.coe_coe -> ContinuousLinearMap.coe_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_coe ContinuousLinearMap.coe_coeₓ'. -/
@[simp, norm_cast]
theorem coe_coe (f : M₁ →SL[σ₁₂] M₂) : ⇑(f : M₁ →ₛₗ[σ₁₂] M₂) = f :=
rfl
#align continuous_linear_map.coe_coe ContinuousLinearMap.coe_coe
-/- warning: continuous_linear_map.ext_ring -> ContinuousLinearMap.ext_ring is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ext_ring ContinuousLinearMap.ext_ringₓ'. -/
@[ext]
theorem ext_ring [TopologicalSpace R₁] {f g : R₁ →L[R₁] M₁} (h : f 1 = g 1) : f = g :=
coe_inj.1 <| LinearMap.ext_ring h
#align continuous_linear_map.ext_ring ContinuousLinearMap.ext_ring
-/- warning: continuous_linear_map.ext_ring_iff -> ContinuousLinearMap.ext_ring_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ext_ring_iff ContinuousLinearMap.ext_ring_iffₓ'. -/
theorem ext_ring_iff [TopologicalSpace R₁] {f g : R₁ →L[R₁] M₁} : f = g ↔ f 1 = g 1 :=
⟨fun h => h ▸ rfl, ext_ring⟩
#align continuous_linear_map.ext_ring_iff ContinuousLinearMap.ext_ring_iff
-/- warning: continuous_linear_map.eq_on_closure_span -> ContinuousLinearMap.eqOn_closure_span is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.eq_on_closure_span ContinuousLinearMap.eqOn_closure_spanₓ'. -/
/-- If two continuous linear maps are equal on a set `s`, then they are equal on the closure
of the `submodule.span` of this set. -/
theorem eqOn_closure_span [T2Space M₂] {s : Set M₁} {f g : M₁ →SL[σ₁₂] M₂} (h : Set.EqOn f g s) :
@@ -780,9 +625,6 @@ theorem eqOn_closure_span [T2Space M₂] {s : Set M₁} {f g : M₁ →SL[σ₁
(LinearMap.eqOn_span' h).closure f.Continuous g.Continuous
#align continuous_linear_map.eq_on_closure_span ContinuousLinearMap.eqOn_closure_span
-/- warning: continuous_linear_map.ext_on -> ContinuousLinearMap.ext_on is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ext_on ContinuousLinearMap.ext_onₓ'. -/
/-- If the submodule generated by a set `s` is dense in the ambient module, then two continuous
linear maps equal on `s` are equal. -/
theorem ext_on [T2Space M₂] {s : Set M₁} (hs : Dense (Submodule.span R₁ s : Set M₁))
@@ -790,9 +632,6 @@ theorem ext_on [T2Space M₂] {s : Set M₁} (hs : Dense (Submodule.span R₁ s
ext fun x => eqOn_closure_span h (hs x)
#align continuous_linear_map.ext_on ContinuousLinearMap.ext_on
-/- warning: submodule.topological_closure_map -> Submodule.topologicalClosure_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.topological_closure_map Submodule.topologicalClosure_mapₓ'. -/
/-- Under a continuous linear map, the image of the `topological_closure` of a submodule is
contained in the `topological_closure` of its image. -/
theorem Submodule.topologicalClosure_map [RingHomSurjective σ₁₂] [TopologicalSpace R₁]
@@ -803,9 +642,6 @@ theorem Submodule.topologicalClosure_map [RingHomSurjective σ₁₂] [Topologic
image_closure_subset_closure_image f.Continuous
#align submodule.topological_closure_map Submodule.topologicalClosure_map
-/- warning: dense_range.topological_closure_map_submodule -> DenseRange.topologicalClosure_map_submodule is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align dense_range.topological_closure_map_submodule DenseRange.topologicalClosure_map_submoduleₓ'. -/
/-- Under a dense continuous linear map, a submodule whose `topological_closure` is `⊤` is sent to
another such submodule. That is, the image of a dense set under a map with dense range is dense.
-/
@@ -833,24 +669,15 @@ instance : MulAction S₂ (M₁ →SL[σ₁₂] M₂)
one_smul f := ext fun x => one_smul _ _
mul_smul a b f := ext fun x => mul_smul _ _ _
-/- warning: continuous_linear_map.smul_apply -> ContinuousLinearMap.smul_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_apply ContinuousLinearMap.smul_applyₓ'. -/
theorem smul_apply (c : S₂) (f : M₁ →SL[σ₁₂] M₂) (x : M₁) : (c • f) x = c • f x :=
rfl
#align continuous_linear_map.smul_apply ContinuousLinearMap.smul_apply
-/- warning: continuous_linear_map.coe_smul -> ContinuousLinearMap.coe_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_smul ContinuousLinearMap.coe_smulₓ'. -/
@[simp, norm_cast]
theorem coe_smul (c : S₂) (f : M₁ →SL[σ₁₂] M₂) : (↑(c • f) : M₁ →ₛₗ[σ₁₂] M₂) = c • f :=
rfl
#align continuous_linear_map.coe_smul ContinuousLinearMap.coe_smul
-/- warning: continuous_linear_map.coe_smul' -> ContinuousLinearMap.coe_smul' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_smul' ContinuousLinearMap.coe_smul'ₓ'. -/
@[simp, norm_cast]
theorem coe_smul' (c : S₂) (f : M₁ →SL[σ₁₂] M₂) : ⇑(c • f) = c • f :=
rfl
@@ -871,33 +698,21 @@ instance : Zero (M₁ →SL[σ₁₂] M₂) :=
instance : Inhabited (M₁ →SL[σ₁₂] M₂) :=
⟨0⟩
-/- warning: continuous_linear_map.default_def -> ContinuousLinearMap.default_def is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.default_def ContinuousLinearMap.default_defₓ'. -/
@[simp]
theorem default_def : (default : M₁ →SL[σ₁₂] M₂) = 0 :=
rfl
#align continuous_linear_map.default_def ContinuousLinearMap.default_def
-/- warning: continuous_linear_map.zero_apply -> ContinuousLinearMap.zero_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.zero_apply ContinuousLinearMap.zero_applyₓ'. -/
@[simp]
theorem zero_apply (x : M₁) : (0 : M₁ →SL[σ₁₂] M₂) x = 0 :=
rfl
#align continuous_linear_map.zero_apply ContinuousLinearMap.zero_apply
-/- warning: continuous_linear_map.coe_zero -> ContinuousLinearMap.coe_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_zero ContinuousLinearMap.coe_zeroₓ'. -/
@[simp, norm_cast]
theorem coe_zero : ((0 : M₁ →SL[σ₁₂] M₂) : M₁ →ₛₗ[σ₁₂] M₂) = 0 :=
rfl
#align continuous_linear_map.coe_zero ContinuousLinearMap.coe_zero
-/- warning: continuous_linear_map.coe_zero' -> ContinuousLinearMap.coe_zero' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_zero' ContinuousLinearMap.coe_zero'ₓ'. -/
/- no simp attribute on the next line as simp does not always simplify `0 x` to `0`
when `0` is the zero function, while it does for the zero continuous linear map,
and this is the most important property we care about. -/
@@ -918,9 +733,6 @@ instance uniqueOfRight [Subsingleton M₂] : Unique (M₁ →SL[σ₁₂] M₂)
#align continuous_linear_map.unique_of_right ContinuousLinearMap.uniqueOfRight
-/
-/- warning: continuous_linear_map.exists_ne_zero -> ContinuousLinearMap.exists_ne_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.exists_ne_zero ContinuousLinearMap.exists_ne_zeroₓ'. -/
theorem exists_ne_zero {f : M₁ →SL[σ₁₂] M₂} (hf : f ≠ 0) : ∃ x, f x ≠ 0 := by by_contra' h;
exact hf (ContinuousLinearMap.ext h)
#align continuous_linear_map.exists_ne_zero ContinuousLinearMap.exists_ne_zero
@@ -947,9 +759,6 @@ theorem one_def : (1 : M₁ →L[R₁] M₁) = id R₁ M₁ :=
#align continuous_linear_map.one_def ContinuousLinearMap.one_def
-/
-/- warning: continuous_linear_map.id_apply -> ContinuousLinearMap.id_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.id_apply ContinuousLinearMap.id_applyₓ'. -/
theorem id_apply (x : M₁) : id R₁ M₁ x = x :=
rfl
#align continuous_linear_map.id_apply ContinuousLinearMap.id_apply
@@ -961,25 +770,16 @@ theorem coe_id : (id R₁ M₁ : M₁ →ₗ[R₁] M₁) = LinearMap.id :=
#align continuous_linear_map.coe_id ContinuousLinearMap.coe_id
-/
-/- warning: continuous_linear_map.coe_id' -> ContinuousLinearMap.coe_id' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_id' ContinuousLinearMap.coe_id'ₓ'. -/
@[simp, norm_cast]
theorem coe_id' : ⇑(id R₁ M₁) = id :=
rfl
#align continuous_linear_map.coe_id' ContinuousLinearMap.coe_id'
-/- warning: continuous_linear_map.coe_eq_id -> ContinuousLinearMap.coe_eq_id is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_eq_id ContinuousLinearMap.coe_eq_idₓ'. -/
@[simp, norm_cast]
theorem coe_eq_id {f : M₁ →L[R₁] M₁} : (f : M₁ →ₗ[R₁] M₁) = LinearMap.id ↔ f = id _ _ := by
rw [← coe_id, coe_inj]
#align continuous_linear_map.coe_eq_id ContinuousLinearMap.coe_eq_id
-/- warning: continuous_linear_map.one_apply -> ContinuousLinearMap.one_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.one_apply ContinuousLinearMap.one_applyₓ'. -/
@[simp]
theorem one_apply (x : M₁) : (1 : M₁ →L[R₁] M₁) x = x :=
rfl
@@ -992,25 +792,16 @@ variable [ContinuousAdd M₂]
instance : Add (M₁ →SL[σ₁₂] M₂) :=
⟨fun f g => ⟨f + g, f.2.add g.2⟩⟩
-/- warning: continuous_linear_map.add_apply -> ContinuousLinearMap.add_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.add_apply ContinuousLinearMap.add_applyₓ'. -/
@[simp]
theorem add_apply (f g : M₁ →SL[σ₁₂] M₂) (x : M₁) : (f + g) x = f x + g x :=
rfl
#align continuous_linear_map.add_apply ContinuousLinearMap.add_apply
-/- warning: continuous_linear_map.coe_add -> ContinuousLinearMap.coe_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_add ContinuousLinearMap.coe_addₓ'. -/
@[simp, norm_cast]
theorem coe_add (f g : M₁ →SL[σ₁₂] M₂) : (↑(f + g) : M₁ →ₛₗ[σ₁₂] M₂) = f + g :=
rfl
#align continuous_linear_map.coe_add ContinuousLinearMap.coe_add
-/- warning: continuous_linear_map.coe_add' -> ContinuousLinearMap.coe_add' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_add' ContinuousLinearMap.coe_add'ₓ'. -/
@[norm_cast]
theorem coe_add' (f g : M₁ →SL[σ₁₂] M₂) : ⇑(f + g) = f + g :=
rfl
@@ -1032,26 +823,17 @@ instance : AddCommMonoid (M₁ →SL[σ₁₂] M₂)
nsmul_zero f := by ext; simp
nsmul_succ n f := by ext; simp [Nat.succ_eq_one_add, add_smul]
-/- warning: continuous_linear_map.coe_sum -> ContinuousLinearMap.coe_sum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_sum ContinuousLinearMap.coe_sumₓ'. -/
@[simp, norm_cast]
theorem coe_sum {ι : Type _} (t : Finset ι) (f : ι → M₁ →SL[σ₁₂] M₂) :
↑(∑ d in t, f d) = (∑ d in t, f d : M₁ →ₛₗ[σ₁₂] M₂) :=
(AddMonoidHom.mk (coe : (M₁ →SL[σ₁₂] M₂) → M₁ →ₛₗ[σ₁₂] M₂) rfl fun _ _ => rfl).map_sum _ _
#align continuous_linear_map.coe_sum ContinuousLinearMap.coe_sum
-/- warning: continuous_linear_map.coe_sum' -> ContinuousLinearMap.coe_sum' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_sum' ContinuousLinearMap.coe_sum'ₓ'. -/
@[simp, norm_cast]
theorem coe_sum' {ι : Type _} (t : Finset ι) (f : ι → M₁ →SL[σ₁₂] M₂) :
⇑(∑ d in t, f d) = ∑ d in t, f d := by simp only [← coe_coe, coe_sum, LinearMap.coeFn_sum]
#align continuous_linear_map.coe_sum' ContinuousLinearMap.coe_sum'
-/- warning: continuous_linear_map.sum_apply -> ContinuousLinearMap.sum_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.sum_apply ContinuousLinearMap.sum_applyₓ'. -/
theorem sum_apply {ι : Type _} (t : Finset ι) (f : ι → M₁ →SL[σ₁₂] M₂) (b : M₁) :
(∑ d in t, f d) b = ∑ d in t, f d b := by simp only [coe_sum', Finset.sum_apply]
#align continuous_linear_map.sum_apply ContinuousLinearMap.sum_apply
@@ -1072,9 +854,6 @@ infixr:80 " ∘L " =>
@ContinuousLinearMap.comp _ _ _ _ _ _ (RingHom.id _) (RingHom.id _) (RingHom.id _) _ _ _ _ _ _ _ _
_ _ _ _ RingHomCompTriple.ids
-/- warning: continuous_linear_map.coe_comp -> ContinuousLinearMap.coe_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_comp ContinuousLinearMap.coe_compₓ'. -/
@[simp, norm_cast]
theorem coe_comp (h : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) :
(h.comp f : M₁ →ₛₗ[σ₁₃] M₃) = (h : M₂ →ₛₗ[σ₂₃] M₃).comp (f : M₁ →ₛₗ[σ₁₂] M₂) :=
@@ -1083,34 +862,22 @@ theorem coe_comp (h : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂)
include σ₁₃
-/- warning: continuous_linear_map.coe_comp' -> ContinuousLinearMap.coe_comp' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_comp' ContinuousLinearMap.coe_comp'ₓ'. -/
@[simp, norm_cast]
theorem coe_comp' (h : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) : ⇑(h.comp f) = h ∘ f :=
rfl
#align continuous_linear_map.coe_comp' ContinuousLinearMap.coe_comp'
-/- warning: continuous_linear_map.comp_apply -> ContinuousLinearMap.comp_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_apply ContinuousLinearMap.comp_applyₓ'. -/
theorem comp_apply (g : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) (x : M₁) : (g.comp f) x = g (f x) :=
rfl
#align continuous_linear_map.comp_apply ContinuousLinearMap.comp_apply
omit σ₁₃
-/- warning: continuous_linear_map.comp_id -> ContinuousLinearMap.comp_id is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_id ContinuousLinearMap.comp_idₓ'. -/
@[simp]
theorem comp_id (f : M₁ →SL[σ₁₂] M₂) : f.comp (id R₁ M₁) = f :=
ext fun x => rfl
#align continuous_linear_map.comp_id ContinuousLinearMap.comp_id
-/- warning: continuous_linear_map.id_comp -> ContinuousLinearMap.id_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.id_comp ContinuousLinearMap.id_compₓ'. -/
@[simp]
theorem id_comp (f : M₁ →SL[σ₁₂] M₂) : (id R₂ M₂).comp f = f :=
ext fun x => rfl
@@ -1118,31 +885,19 @@ theorem id_comp (f : M₁ →SL[σ₁₂] M₂) : (id R₂ M₂).comp f = f :=
include σ₁₃
-/- warning: continuous_linear_map.comp_zero -> ContinuousLinearMap.comp_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_zero ContinuousLinearMap.comp_zeroₓ'. -/
@[simp]
theorem comp_zero (g : M₂ →SL[σ₂₃] M₃) : g.comp (0 : M₁ →SL[σ₁₂] M₂) = 0 := by ext; simp
#align continuous_linear_map.comp_zero ContinuousLinearMap.comp_zero
-/- warning: continuous_linear_map.zero_comp -> ContinuousLinearMap.zero_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.zero_comp ContinuousLinearMap.zero_compₓ'. -/
@[simp]
theorem zero_comp (f : M₁ →SL[σ₁₂] M₂) : (0 : M₂ →SL[σ₂₃] M₃).comp f = 0 := by ext; simp
#align continuous_linear_map.zero_comp ContinuousLinearMap.zero_comp
-/- warning: continuous_linear_map.comp_add -> ContinuousLinearMap.comp_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_add ContinuousLinearMap.comp_addₓ'. -/
@[simp]
theorem comp_add [ContinuousAdd M₂] [ContinuousAdd M₃] (g : M₂ →SL[σ₂₃] M₃)
(f₁ f₂ : M₁ →SL[σ₁₂] M₂) : g.comp (f₁ + f₂) = g.comp f₁ + g.comp f₂ := by ext; simp
#align continuous_linear_map.comp_add ContinuousLinearMap.comp_add
-/- warning: continuous_linear_map.add_comp -> ContinuousLinearMap.add_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.add_comp ContinuousLinearMap.add_compₓ'. -/
@[simp]
theorem add_comp [ContinuousAdd M₃] (g₁ g₂ : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) :
(g₁ + g₂).comp f = g₁.comp f + g₂.comp f := by ext; simp
@@ -1150,9 +905,6 @@ theorem add_comp [ContinuousAdd M₃] (g₁ g₂ : M₂ →SL[σ₂₃] M₃) (f
omit σ₁₃
-/- warning: continuous_linear_map.comp_assoc -> ContinuousLinearMap.comp_assoc is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_assoc ContinuousLinearMap.comp_assocₓ'. -/
theorem comp_assoc {R₄ : Type _} [Semiring R₄] [Module R₄ M₄] {σ₁₄ : R₁ →+* R₄} {σ₂₄ : R₂ →+* R₄}
{σ₃₄ : R₃ →+* R₄} [RingHomCompTriple σ₁₃ σ₃₄ σ₁₄] [RingHomCompTriple σ₂₃ σ₃₄ σ₂₄]
[RingHomCompTriple σ₁₂ σ₂₄ σ₁₄] (h : M₃ →SL[σ₃₄] M₄) (g : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) :
@@ -1163,24 +915,15 @@ theorem comp_assoc {R₄ : Type _} [Semiring R₄] [Module R₄ M₄] {σ₁₄
instance : Mul (M₁ →L[R₁] M₁) :=
⟨comp⟩
-/- warning: continuous_linear_map.mul_def -> ContinuousLinearMap.mul_def is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.mul_def ContinuousLinearMap.mul_defₓ'. -/
theorem mul_def (f g : M₁ →L[R₁] M₁) : f * g = f.comp g :=
rfl
#align continuous_linear_map.mul_def ContinuousLinearMap.mul_def
-/- warning: continuous_linear_map.coe_mul -> ContinuousLinearMap.coe_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_mul ContinuousLinearMap.coe_mulₓ'. -/
@[simp]
theorem coe_mul (f g : M₁ →L[R₁] M₁) : ⇑(f * g) = f ∘ g :=
rfl
#align continuous_linear_map.coe_mul ContinuousLinearMap.coe_mul
-/- warning: continuous_linear_map.mul_apply -> ContinuousLinearMap.mul_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.mul_apply ContinuousLinearMap.mul_applyₓ'. -/
theorem mul_apply (f g : M₁ →L[R₁] M₁) (x : M₁) : (f * g) x = f (g x) :=
rfl
#align continuous_linear_map.mul_apply ContinuousLinearMap.mul_apply
@@ -1204,12 +947,6 @@ instance [ContinuousAdd M₁] : Semiring (M₁ →L[R₁] M₁) :=
left_distrib := fun f g h => ext fun x => map_add f (g x) (h x)
right_distrib := fun _ _ _ => ext fun _ => LinearMap.add_apply _ _ _ }
-/- warning: continuous_linear_map.to_linear_map_ring_hom -> ContinuousLinearMap.toLinearMapRingHom is a dubious translation:
-lean 3 declaration is
- forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : ContinuousAdd.{u2} M₁ _inst_4 (AddZeroClass.toHasAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)))], RingHom.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (LinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ M₁ _inst_5 _inst_5 _inst_14 _inst_14) (Semiring.toNonAssocSemiring.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.semiring.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19)) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ M₁ _inst_5 _inst_5 _inst_14 _inst_14) (Module.End.semiring.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.to_linear_map_ring_hom ContinuousLinearMap.toLinearMapRingHomₓ'. -/
/-- `continuous_linear_map.to_linear_map` as a `ring_hom`.-/
@[simps]
def toLinearMapRingHom [ContinuousAdd M₁] : (M₁ →L[R₁] M₁) →+* M₁ →ₗ[R₁] M₁
@@ -1225,12 +962,6 @@ section ApplyAction
variable [ContinuousAdd M₁]
-/- warning: continuous_linear_map.apply_module -> ContinuousLinearMap.applyModule is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.apply_module ContinuousLinearMap.applyModuleₓ'. -/
/-- The tautological action by `M₁ →L[R₁] M₁` on `M`.
This generalizes `function.End.apply_mul_action`. -/
@@ -1238,38 +969,20 @@ instance applyModule : Module (M₁ →L[R₁] M₁) M₁ :=
Module.compHom _ toLinearMapRingHom
#align continuous_linear_map.apply_module ContinuousLinearMap.applyModule
-/- warning: continuous_linear_map.smul_def -> ContinuousLinearMap.smul_def is a dubious translation:
-<too large>
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@[simp]
protected theorem smul_def (f : M₁ →L[R₁] M₁) (a : M₁) : f • a = f a :=
rfl
#align continuous_linear_map.smul_def ContinuousLinearMap.smul_def
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/-- `continuous_linear_map.apply_module` is faithful. -/
instance applyFaithfulSMul : FaithfulSMul (M₁ →L[R₁] M₁) M₁ :=
⟨fun _ _ => ContinuousLinearMap.ext⟩
#align continuous_linear_map.apply_has_faithful_smul ContinuousLinearMap.applyFaithfulSMul
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- forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : ContinuousAdd.{u2} M₁ _inst_4 (AddZeroClass.toHasAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)))], SMulCommClass.{u1, u2, u2} R₁ (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (SMulZeroClass.toHasSmul.{u1, u2} R₁ M₁ (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (SMulWithZero.toSmulZeroClass.{u1, u2} R₁ M₁ (MulZeroClass.toHasZero.{u1} R₁ (MulZeroOneClass.toMulZeroClass.{u1} R₁ (MonoidWithZero.toMulZeroOneClass.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)))) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (MulActionWithZero.toSMulWithZero.{u1, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (Module.toMulActionWithZero.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)))) (SMulZeroClass.toHasSmul.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (SMulWithZero.toSmulZeroClass.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (MulZeroClass.toHasZero.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (MulZeroOneClass.toMulZeroClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (MonoidWithZero.toMulZeroOneClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (Semiring.toMonoidWithZero.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.semiring.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19))))) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (MulActionWithZero.toSMulWithZero.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (Semiring.toMonoidWithZero.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.semiring.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19)) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (Module.toMulActionWithZero.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (ContinuousLinearMap.semiring.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19) _inst_5 (ContinuousLinearMap.applyModule.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19)))))
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-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.apply_smul_comm_class ContinuousLinearMap.applySMulCommClassₓ'. -/
instance applySMulCommClass : SMulCommClass R₁ (M₁ →L[R₁] M₁) M₁
where smul_comm r e m := (e.map_smul r m).symm
#align continuous_linear_map.apply_smul_comm_class ContinuousLinearMap.applySMulCommClass
-/- warning: continuous_linear_map.apply_smul_comm_class' -> ContinuousLinearMap.applySMulCommClass' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.apply_smul_comm_class' ContinuousLinearMap.applySMulCommClass'ₓ'. -/
instance applySMulCommClass' : SMulCommClass (M₁ →L[R₁] M₁) R₁ M₁
where smul_comm := ContinuousLinearMap.map_smul
#align continuous_linear_map.apply_smul_comm_class' ContinuousLinearMap.applySMulCommClass'
@@ -1279,30 +992,18 @@ instance : ContinuousConstSMul (M₁ →L[R₁] M₁) M₁ :=
end ApplyAction
-/- warning: continuous_linear_map.prod -> ContinuousLinearMap.prod is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.prod ContinuousLinearMap.prodₓ'. -/
/-- The cartesian product of two bounded linear maps, as a bounded linear map. -/
protected def prod [Module R₁ M₂] [Module R₁ M₃] (f₁ : M₁ →L[R₁] M₂) (f₂ : M₁ →L[R₁] M₃) :
M₁ →L[R₁] M₂ × M₃ :=
⟨(f₁ : M₁ →ₗ[R₁] M₂).Prod f₂, f₁.2.prod_mk f₂.2⟩
#align continuous_linear_map.prod ContinuousLinearMap.prod
-/- warning: continuous_linear_map.coe_prod -> ContinuousLinearMap.coe_prod is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_prod ContinuousLinearMap.coe_prodₓ'. -/
@[simp, norm_cast]
theorem coe_prod [Module R₁ M₂] [Module R₁ M₃] (f₁ : M₁ →L[R₁] M₂) (f₂ : M₁ →L[R₁] M₃) :
(f₁.Prod f₂ : M₁ →ₗ[R₁] M₂ × M₃) = LinearMap.prod f₁ f₂ :=
rfl
#align continuous_linear_map.coe_prod ContinuousLinearMap.coe_prod
-/- warning: continuous_linear_map.prod_apply -> ContinuousLinearMap.prod_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.prod_apply ContinuousLinearMap.prod_applyₓ'. -/
@[simp, norm_cast]
theorem prod_apply [Module R₁ M₂] [Module R₁ M₃] (f₁ : M₁ →L[R₁] M₂) (f₂ : M₁ →L[R₁] M₃) (x : M₁) :
f₁.Prod f₂ x = (f₁ x, f₂ x) :=
@@ -1313,23 +1014,11 @@ section
variable (R₁ M₁ M₂)
-/- warning: continuous_linear_map.inl -> ContinuousLinearMap.inl is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.inl ContinuousLinearMap.inlₓ'. -/
/-- The left injection into a product is a continuous linear map. -/
def inl [Module R₁ M₂] : M₁ →L[R₁] M₁ × M₂ :=
(id R₁ M₁).Prod 0
#align continuous_linear_map.inl ContinuousLinearMap.inl
-/- warning: continuous_linear_map.inr -> ContinuousLinearMap.inr is a dubious translation:
-lean 3 declaration is
- forall (R₁ : Type.{u1}) [_inst_1 : Semiring.{u1} R₁] (M₁ : Type.{u2}) [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] (M₂ : Type.{u3}) [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9], ContinuousLinearMap.{u1, u1, u3, max u2 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) _inst_19 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)
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-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.inr ContinuousLinearMap.inrₓ'. -/
/-- The right injection into a product is a continuous linear map. -/
def inr [Module R₁ M₂] : M₂ →L[R₁] M₁ × M₂ :=
(0 : M₂ →L[R₁] M₁).Prod (id R₁ M₂)
@@ -1339,49 +1028,31 @@ end
variable {F : Type _}
-/- warning: continuous_linear_map.inl_apply -> ContinuousLinearMap.inl_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.inl_apply ContinuousLinearMap.inl_applyₓ'. -/
@[simp]
theorem inl_apply [Module R₁ M₂] (x : M₁) : inl R₁ M₁ M₂ x = (x, 0) :=
rfl
#align continuous_linear_map.inl_apply ContinuousLinearMap.inl_apply
-/- warning: continuous_linear_map.inr_apply -> ContinuousLinearMap.inr_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.inr_apply ContinuousLinearMap.inr_applyₓ'. -/
@[simp]
theorem inr_apply [Module R₁ M₂] (x : M₂) : inr R₁ M₁ M₂ x = (0, x) :=
rfl
#align continuous_linear_map.inr_apply ContinuousLinearMap.inr_apply
-/- warning: continuous_linear_map.coe_inl -> ContinuousLinearMap.coe_inl is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_inl ContinuousLinearMap.coe_inlₓ'. -/
@[simp, norm_cast]
theorem coe_inl [Module R₁ M₂] : (inl R₁ M₁ M₂ : M₁ →ₗ[R₁] M₁ × M₂) = LinearMap.inl R₁ M₁ M₂ :=
rfl
#align continuous_linear_map.coe_inl ContinuousLinearMap.coe_inl
-/- warning: continuous_linear_map.coe_inr -> ContinuousLinearMap.coe_inr is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_inr ContinuousLinearMap.coe_inrₓ'. -/
@[simp, norm_cast]
theorem coe_inr [Module R₁ M₂] : (inr R₁ M₁ M₂ : M₂ →ₗ[R₁] M₁ × M₂) = LinearMap.inr R₁ M₁ M₂ :=
rfl
#align continuous_linear_map.coe_inr ContinuousLinearMap.coe_inr
-/- warning: continuous_linear_map.is_closed_ker -> ContinuousLinearMap.isClosed_ker is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.is_closed_ker ContinuousLinearMap.isClosed_kerₓ'. -/
theorem isClosed_ker [T1Space M₂] [ContinuousSemilinearMapClass F σ₁₂ M₁ M₂] (f : F) :
IsClosed (ker f : Set M₁) :=
continuous_iff_isClosed.1 (map_continuous f) _ isClosed_singleton
#align continuous_linear_map.is_closed_ker ContinuousLinearMap.isClosed_ker
-/- warning: continuous_linear_map.is_complete_ker -> ContinuousLinearMap.isComplete_ker is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.is_complete_ker ContinuousLinearMap.isComplete_kerₓ'. -/
theorem isComplete_ker {M' : Type _} [UniformSpace M'] [CompleteSpace M'] [AddCommMonoid M']
[Module R₁ M'] [T1Space M₂] [ContinuousSemilinearMapClass F σ₁₂ M' M₂] (f : F) :
IsComplete (ker f : Set M') :=
@@ -1396,18 +1067,12 @@ instance (priority := 100) completeSpace_ker {M' : Type _} [UniformSpace M'] [Co
#align continuous_linear_map.complete_space_ker ContinuousLinearMap.completeSpace_ker
-/
-/- warning: continuous_linear_map.ker_prod -> ContinuousLinearMap.ker_prod is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ker_prod ContinuousLinearMap.ker_prodₓ'. -/
@[simp]
theorem ker_prod [Module R₁ M₂] [Module R₁ M₃] (f : M₁ →L[R₁] M₂) (g : M₁ →L[R₁] M₃) :
ker (f.Prod g) = ker f ⊓ ker g :=
LinearMap.ker_prod f g
#align continuous_linear_map.ker_prod ContinuousLinearMap.ker_prod
-/- warning: continuous_linear_map.cod_restrict -> ContinuousLinearMap.codRestrict is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.cod_restrict ContinuousLinearMap.codRestrictₓ'. -/
/-- Restrict codomain of a continuous linear map. -/
def codRestrict (f : M₁ →SL[σ₁₂] M₂) (p : Submodule R₂ M₂) (h : ∀ x, f x ∈ p) : M₁ →SL[σ₁₂] p
where
@@ -1415,27 +1080,18 @@ def codRestrict (f : M₁ →SL[σ₁₂] M₂) (p : Submodule R₂ M₂) (h :
toLinearMap := (f : M₁ →ₛₗ[σ₁₂] M₂).codRestrict p h
#align continuous_linear_map.cod_restrict ContinuousLinearMap.codRestrict
-/- warning: continuous_linear_map.coe_cod_restrict -> ContinuousLinearMap.coe_codRestrict is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_cod_restrict ContinuousLinearMap.coe_codRestrictₓ'. -/
@[norm_cast]
theorem coe_codRestrict (f : M₁ →SL[σ₁₂] M₂) (p : Submodule R₂ M₂) (h : ∀ x, f x ∈ p) :
(f.codRestrict p h : M₁ →ₛₗ[σ₁₂] p) = (f : M₁ →ₛₗ[σ₁₂] M₂).codRestrict p h :=
rfl
#align continuous_linear_map.coe_cod_restrict ContinuousLinearMap.coe_codRestrict
-/- warning: continuous_linear_map.coe_cod_restrict_apply -> ContinuousLinearMap.coe_codRestrict_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_cod_restrict_apply ContinuousLinearMap.coe_codRestrict_applyₓ'. -/
@[simp]
theorem coe_codRestrict_apply (f : M₁ →SL[σ₁₂] M₂) (p : Submodule R₂ M₂) (h : ∀ x, f x ∈ p) (x) :
(f.codRestrict p h x : M₂) = f x :=
rfl
#align continuous_linear_map.coe_cod_restrict_apply ContinuousLinearMap.coe_codRestrict_apply
-/- warning: continuous_linear_map.ker_cod_restrict -> ContinuousLinearMap.ker_codRestrict is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ker_cod_restrict ContinuousLinearMap.ker_codRestrictₓ'. -/
@[simp]
theorem ker_codRestrict (f : M₁ →SL[σ₁₂] M₂) (p : Submodule R₂ M₂) (h : ∀ x, f x ∈ p) :
ker (f.codRestrict p h) = ker f :=
@@ -1451,41 +1107,26 @@ def Submodule.subtypeL (p : Submodule R₁ M₁) : p →L[R₁] M₁
#align submodule.subtypeL Submodule.subtypeL
-/
-/- warning: submodule.coe_subtypeL -> Submodule.coe_subtypeL is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.coe_subtypeL Submodule.coe_subtypeLₓ'. -/
@[simp, norm_cast]
theorem Submodule.coe_subtypeL (p : Submodule R₁ M₁) : (p.subtypeL : p →ₗ[R₁] M₁) = p.Subtype :=
rfl
#align submodule.coe_subtypeL Submodule.coe_subtypeL
-/- warning: submodule.coe_subtypeL' -> Submodule.coe_subtypeL' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.coe_subtypeL' Submodule.coe_subtypeL'ₓ'. -/
@[simp]
theorem Submodule.coe_subtypeL' (p : Submodule R₁ M₁) : ⇑p.subtypeL = p.Subtype :=
rfl
#align submodule.coe_subtypeL' Submodule.coe_subtypeL'
-/- warning: submodule.subtypeL_apply -> Submodule.subtypeL_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.subtypeL_apply Submodule.subtypeL_applyₓ'. -/
@[simp, norm_cast]
theorem Submodule.subtypeL_apply (p : Submodule R₁ M₁) (x : p) : p.subtypeL x = x :=
rfl
#align submodule.subtypeL_apply Submodule.subtypeL_apply
-/- warning: submodule.range_subtypeL -> Submodule.range_subtypeL is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.range_subtypeL Submodule.range_subtypeLₓ'. -/
@[simp]
theorem Submodule.range_subtypeL (p : Submodule R₁ M₁) : range p.subtypeL = p :=
Submodule.range_subtype _
#align submodule.range_subtypeL Submodule.range_subtypeL
-/- warning: submodule.ker_subtypeL -> Submodule.ker_subtypeL is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.ker_subtypeL Submodule.ker_subtypeLₓ'. -/
@[simp]
theorem Submodule.ker_subtypeL (p : Submodule R₁ M₁) : ker p.subtypeL = ⊥ :=
Submodule.ker_subtype _
@@ -1493,12 +1134,6 @@ theorem Submodule.ker_subtypeL (p : Submodule R₁ M₁) : ker p.subtypeL = ⊥
variable (R₁ M₁ M₂)
-/- warning: continuous_linear_map.fst -> ContinuousLinearMap.fst is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.fst ContinuousLinearMap.fstₓ'. -/
/-- `prod.fst` as a `continuous_linear_map`. -/
def fst [Module R₁ M₂] : M₁ × M₂ →L[R₁] M₁
where
@@ -1506,12 +1141,6 @@ def fst [Module R₁ M₂] : M₁ × M₂ →L[R₁] M₁
toLinearMap := LinearMap.fst R₁ M₁ M₂
#align continuous_linear_map.fst ContinuousLinearMap.fst
-/- warning: continuous_linear_map.snd -> ContinuousLinearMap.snd is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.snd ContinuousLinearMap.sndₓ'. -/
/-- `prod.snd` as a `continuous_linear_map`. -/
def snd [Module R₁ M₂] : M₁ × M₂ →L[R₁] M₂
where
@@ -1521,127 +1150,79 @@ def snd [Module R₁ M₂] : M₁ × M₂ →L[R₁] M₂
variable {R₁ M₁ M₂}
-/- warning: continuous_linear_map.coe_fst -> ContinuousLinearMap.coe_fst is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_fst ContinuousLinearMap.coe_fstₓ'. -/
@[simp, norm_cast]
theorem coe_fst [Module R₁ M₂] : ↑(fst R₁ M₁ M₂) = LinearMap.fst R₁ M₁ M₂ :=
rfl
#align continuous_linear_map.coe_fst ContinuousLinearMap.coe_fst
-/- warning: continuous_linear_map.coe_fst' -> ContinuousLinearMap.coe_fst' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_fst' ContinuousLinearMap.coe_fst'ₓ'. -/
@[simp, norm_cast]
theorem coe_fst' [Module R₁ M₂] : ⇑(fst R₁ M₁ M₂) = Prod.fst :=
rfl
#align continuous_linear_map.coe_fst' ContinuousLinearMap.coe_fst'
-/- warning: continuous_linear_map.coe_snd -> ContinuousLinearMap.coe_snd is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_snd ContinuousLinearMap.coe_sndₓ'. -/
@[simp, norm_cast]
theorem coe_snd [Module R₁ M₂] : ↑(snd R₁ M₁ M₂) = LinearMap.snd R₁ M₁ M₂ :=
rfl
#align continuous_linear_map.coe_snd ContinuousLinearMap.coe_snd
-/- warning: continuous_linear_map.coe_snd' -> ContinuousLinearMap.coe_snd' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_snd' ContinuousLinearMap.coe_snd'ₓ'. -/
@[simp, norm_cast]
theorem coe_snd' [Module R₁ M₂] : ⇑(snd R₁ M₁ M₂) = Prod.snd :=
rfl
#align continuous_linear_map.coe_snd' ContinuousLinearMap.coe_snd'
-/- warning: continuous_linear_map.fst_prod_snd -> ContinuousLinearMap.fst_prod_snd is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.fst_prod_snd ContinuousLinearMap.fst_prod_sndₓ'. -/
@[simp]
theorem fst_prod_snd [Module R₁ M₂] : (fst R₁ M₁ M₂).Prod (snd R₁ M₁ M₂) = id R₁ (M₁ × M₂) :=
ext fun ⟨x, y⟩ => rfl
#align continuous_linear_map.fst_prod_snd ContinuousLinearMap.fst_prod_snd
-/- warning: continuous_linear_map.fst_comp_prod -> ContinuousLinearMap.fst_comp_prod is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.fst_comp_prod ContinuousLinearMap.fst_comp_prodₓ'. -/
@[simp]
theorem fst_comp_prod [Module R₁ M₂] [Module R₁ M₃] (f : M₁ →L[R₁] M₂) (g : M₁ →L[R₁] M₃) :
(fst R₁ M₂ M₃).comp (f.Prod g) = f :=
ext fun x => rfl
#align continuous_linear_map.fst_comp_prod ContinuousLinearMap.fst_comp_prod
-/- warning: continuous_linear_map.snd_comp_prod -> ContinuousLinearMap.snd_comp_prod is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.snd_comp_prod ContinuousLinearMap.snd_comp_prodₓ'. -/
@[simp]
theorem snd_comp_prod [Module R₁ M₂] [Module R₁ M₃] (f : M₁ →L[R₁] M₂) (g : M₁ →L[R₁] M₃) :
(snd R₁ M₂ M₃).comp (f.Prod g) = g :=
ext fun x => rfl
#align continuous_linear_map.snd_comp_prod ContinuousLinearMap.snd_comp_prod
-/- warning: continuous_linear_map.prod_map -> ContinuousLinearMap.prodMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.prod_map ContinuousLinearMap.prodMapₓ'. -/
/-- `prod.map` of two continuous linear maps. -/
def prodMap [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (f₁ : M₁ →L[R₁] M₂) (f₂ : M₃ →L[R₁] M₄) :
M₁ × M₃ →L[R₁] M₂ × M₄ :=
(f₁.comp (fst R₁ M₁ M₃)).Prod (f₂.comp (snd R₁ M₁ M₃))
#align continuous_linear_map.prod_map ContinuousLinearMap.prodMap
-/- warning: continuous_linear_map.coe_prod_map -> ContinuousLinearMap.coe_prodMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_prod_map ContinuousLinearMap.coe_prodMapₓ'. -/
@[simp, norm_cast]
theorem coe_prodMap [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (f₁ : M₁ →L[R₁] M₂)
(f₂ : M₃ →L[R₁] M₄) : ↑(f₁.Prod_map f₂) = (f₁ : M₁ →ₗ[R₁] M₂).Prod_map (f₂ : M₃ →ₗ[R₁] M₄) :=
rfl
#align continuous_linear_map.coe_prod_map ContinuousLinearMap.coe_prodMap
-/- warning: continuous_linear_map.coe_prod_map' -> ContinuousLinearMap.coe_prodMap' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_prod_map' ContinuousLinearMap.coe_prodMap'ₓ'. -/
@[simp, norm_cast]
theorem coe_prodMap' [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (f₁ : M₁ →L[R₁] M₂)
(f₂ : M₃ →L[R₁] M₄) : ⇑(f₁.Prod_map f₂) = Prod.map f₁ f₂ :=
rfl
#align continuous_linear_map.coe_prod_map' ContinuousLinearMap.coe_prodMap'
-/- warning: continuous_linear_map.coprod -> ContinuousLinearMap.coprod is a dubious translation:
-lean 3 declaration is
- forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u4}} [_inst_10 : TopologicalSpace.{u4} M₃] [_inst_11 : AddCommMonoid.{u4} M₃] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u1, u4} R₁ M₃ _inst_1 _inst_11] [_inst_21 : ContinuousAdd.{u4} M₃ _inst_10 (AddZeroClass.toHasAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_11)))], (ContinuousLinearMap.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) -> (ContinuousLinearMap.{u1, u1, u3, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20) -> (ContinuousLinearMap.{u1, u1, max u2 u3, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) M₃ _inst_10 _inst_11 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) _inst_20)
-but is expected to have type
- forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u4}} [_inst_10 : TopologicalSpace.{u4} M₃] [_inst_11 : AddCommMonoid.{u4} M₃] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u1, u4} R₁ M₃ _inst_1 _inst_11] [_inst_21 : ContinuousAdd.{u4} M₃ _inst_10 (AddZeroClass.toAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_11)))], (ContinuousLinearMap.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) -> (ContinuousLinearMap.{u1, u1, u3, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20) -> (ContinuousLinearMap.{u1, u1, max u3 u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u3} M₁ M₂) (instTopologicalSpaceProd.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.instAddCommMonoidSum.{u2, u3} M₁ M₂ _inst_5 _inst_9) M₃ _inst_10 _inst_11 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) _inst_20)
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coprod ContinuousLinearMap.coprodₓ'. -/
/-- The continuous linear map given by `(x, y) ↦ f₁ x + f₂ y`. -/
def coprod [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃] (f₁ : M₁ →L[R₁] M₃)
(f₂ : M₂ →L[R₁] M₃) : M₁ × M₂ →L[R₁] M₃ :=
⟨LinearMap.coprod f₁ f₂, (f₁.cont.comp continuous_fst).add (f₂.cont.comp continuous_snd)⟩
#align continuous_linear_map.coprod ContinuousLinearMap.coprod
-/- warning: continuous_linear_map.coe_coprod -> ContinuousLinearMap.coe_coprod is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_coprod ContinuousLinearMap.coe_coprodₓ'. -/
@[norm_cast, simp]
theorem coe_coprod [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃] (f₁ : M₁ →L[R₁] M₃)
(f₂ : M₂ →L[R₁] M₃) : (f₁.coprod f₂ : M₁ × M₂ →ₗ[R₁] M₃) = LinearMap.coprod f₁ f₂ :=
rfl
#align continuous_linear_map.coe_coprod ContinuousLinearMap.coe_coprod
-/- warning: continuous_linear_map.coprod_apply -> ContinuousLinearMap.coprod_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coprod_apply ContinuousLinearMap.coprod_applyₓ'. -/
@[simp]
theorem coprod_apply [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃] (f₁ : M₁ →L[R₁] M₃)
(f₂ : M₂ →L[R₁] M₃) (x) : f₁.coprod f₂ x = f₁ x.1 + f₂ x.2 :=
rfl
#align continuous_linear_map.coprod_apply ContinuousLinearMap.coprod_apply
-/- warning: continuous_linear_map.range_coprod -> ContinuousLinearMap.range_coprod is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.range_coprod ContinuousLinearMap.range_coprodₓ'. -/
theorem range_coprod [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃] (f₁ : M₁ →L[R₁] M₃)
(f₂ : M₂ →L[R₁] M₃) : range (f₁.coprod f₂) = range f₁ ⊔ range f₂ :=
LinearMap.range_coprod _ _
@@ -1661,9 +1242,6 @@ def smulRight (c : M₁ →L[R] S) (f : M₂) : M₁ →L[R] M₂ :=
#align continuous_linear_map.smul_right ContinuousLinearMap.smulRight
-/
-/- warning: continuous_linear_map.smul_right_apply -> ContinuousLinearMap.smulRight_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_right_apply ContinuousLinearMap.smulRight_applyₓ'. -/
@[simp]
theorem smulRight_apply {c : M₁ →L[R] S} {f : M₂} {x : M₁} :
(smulRight c f : M₁ → M₂) x = c x • f :=
@@ -1674,26 +1252,17 @@ end
variable [Module R₁ M₂] [TopologicalSpace R₁] [ContinuousSMul R₁ M₂]
-/- warning: continuous_linear_map.smul_right_one_one -> ContinuousLinearMap.smulRight_one_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_right_one_one ContinuousLinearMap.smulRight_one_oneₓ'. -/
@[simp]
theorem smulRight_one_one (c : R₁ →L[R₁] M₂) : smulRight (1 : R₁ →L[R₁] R₁) (c 1) = c := by
ext <;> simp [← ContinuousLinearMap.map_smul_of_tower]
#align continuous_linear_map.smul_right_one_one ContinuousLinearMap.smulRight_one_one
-/- warning: continuous_linear_map.smul_right_one_eq_iff -> ContinuousLinearMap.smulRight_one_eq_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_right_one_eq_iff ContinuousLinearMap.smulRight_one_eq_iffₓ'. -/
@[simp]
theorem smulRight_one_eq_iff {f f' : M₂} :
smulRight (1 : R₁ →L[R₁] R₁) f = smulRight (1 : R₁ →L[R₁] R₁) f' ↔ f = f' := by
simp only [ext_ring_iff, smul_right_apply, one_apply, one_smul]
#align continuous_linear_map.smul_right_one_eq_iff ContinuousLinearMap.smulRight_one_eq_iff
-/- warning: continuous_linear_map.smul_right_comp -> ContinuousLinearMap.smulRight_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_right_comp ContinuousLinearMap.smulRight_compₓ'. -/
theorem smulRight_comp [ContinuousMul R₁] {x : M₂} {c : R₁} :
(smulRight (1 : R₁ →L[R₁] R₁) x).comp (smulRight (1 : R₁ →L[R₁] R₁) c) =
smulRight (1 : R₁ →L[R₁] R₁) (c • x) :=
@@ -1716,46 +1285,28 @@ def pi (f : ∀ i, M →L[R] φ i) : M →L[R] ∀ i, φ i :=
#align continuous_linear_map.pi ContinuousLinearMap.pi
-/
-/- warning: continuous_linear_map.coe_pi' -> ContinuousLinearMap.coe_pi' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_pi' ContinuousLinearMap.coe_pi'ₓ'. -/
@[simp]
theorem coe_pi' (f : ∀ i, M →L[R] φ i) : ⇑(pi f) = fun c i => f i c :=
rfl
#align continuous_linear_map.coe_pi' ContinuousLinearMap.coe_pi'
-/- warning: continuous_linear_map.coe_pi -> ContinuousLinearMap.coe_pi is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_pi ContinuousLinearMap.coe_piₓ'. -/
@[simp]
theorem coe_pi (f : ∀ i, M →L[R] φ i) : (pi f : M →ₗ[R] ∀ i, φ i) = LinearMap.pi fun i => f i :=
rfl
#align continuous_linear_map.coe_pi ContinuousLinearMap.coe_pi
-/- warning: continuous_linear_map.pi_apply -> ContinuousLinearMap.pi_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.pi_apply ContinuousLinearMap.pi_applyₓ'. -/
theorem pi_apply (f : ∀ i, M →L[R] φ i) (c : M) (i : ι) : pi f c i = f i c :=
rfl
#align continuous_linear_map.pi_apply ContinuousLinearMap.pi_apply
-/- warning: continuous_linear_map.pi_eq_zero -> ContinuousLinearMap.pi_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.pi_eq_zero ContinuousLinearMap.pi_eq_zeroₓ'. -/
theorem pi_eq_zero (f : ∀ i, M →L[R] φ i) : pi f = 0 ↔ ∀ i, f i = 0 := by
simp only [ext_iff, pi_apply, Function.funext_iff]; exact forall_swap
#align continuous_linear_map.pi_eq_zero ContinuousLinearMap.pi_eq_zero
-/- warning: continuous_linear_map.pi_zero -> ContinuousLinearMap.pi_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.pi_zero ContinuousLinearMap.pi_zeroₓ'. -/
theorem pi_zero : pi (fun i => 0 : ∀ i, M →L[R] φ i) = 0 :=
ext fun _ => rfl
#align continuous_linear_map.pi_zero ContinuousLinearMap.pi_zero
-/- warning: continuous_linear_map.pi_comp -> ContinuousLinearMap.pi_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.pi_comp ContinuousLinearMap.pi_compₓ'. -/
theorem pi_comp (f : ∀ i, M →L[R] φ i) (g : M₂ →L[R] M) :
(pi f).comp g = pi fun i => (f i).comp g :=
rfl
@@ -1768,33 +1319,21 @@ def proj (i : ι) : (∀ i, φ i) →L[R] φ i :=
#align continuous_linear_map.proj ContinuousLinearMap.proj
-/
-/- warning: continuous_linear_map.proj_apply -> ContinuousLinearMap.proj_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.proj_apply ContinuousLinearMap.proj_applyₓ'. -/
@[simp]
theorem proj_apply (i : ι) (b : ∀ i, φ i) : (proj i : (∀ i, φ i) →L[R] φ i) b = b i :=
rfl
#align continuous_linear_map.proj_apply ContinuousLinearMap.proj_apply
-/- warning: continuous_linear_map.proj_pi -> ContinuousLinearMap.proj_pi is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.proj_pi ContinuousLinearMap.proj_piₓ'. -/
theorem proj_pi (f : ∀ i, M₂ →L[R] φ i) (i : ι) : (proj i).comp (pi f) = f i :=
ext fun c => rfl
#align continuous_linear_map.proj_pi ContinuousLinearMap.proj_pi
-/- warning: continuous_linear_map.infi_ker_proj -> ContinuousLinearMap.iInf_ker_proj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.infi_ker_proj ContinuousLinearMap.iInf_ker_projₓ'. -/
theorem iInf_ker_proj : (⨅ i, ker (proj i : (∀ i, φ i) →L[R] φ i) : Submodule R (∀ i, φ i)) = ⊥ :=
LinearMap.iInf_ker_proj
#align continuous_linear_map.infi_ker_proj ContinuousLinearMap.iInf_ker_proj
variable (R φ)
-/- warning: continuous_linear_map.infi_ker_proj_equiv -> ContinuousLinearMap.iInfKerProjEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.infi_ker_proj_equiv ContinuousLinearMap.iInfKerProjEquivₓ'. -/
/-- If `I` and `J` are complementary index sets, the product of the kernels of the `J`th projections
of `φ` is linearly equivalent to the product over `I`. -/
def iInfKerProjEquiv {I J : Set ι} [DecidablePred fun i => i ∈ I] (hd : Disjoint I J)
@@ -1829,23 +1368,14 @@ variable {R : Type _} [Ring R] {R₂ : Type _} [Ring R₂] {R₃ : Type _} [Ring
section
-/- warning: continuous_linear_map.map_neg -> ContinuousLinearMap.map_neg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_neg ContinuousLinearMap.map_negₓ'. -/
protected theorem map_neg (f : M →SL[σ₁₂] M₂) (x : M) : f (-x) = -f x :=
map_neg _ _
#align continuous_linear_map.map_neg ContinuousLinearMap.map_neg
-/- warning: continuous_linear_map.map_sub -> ContinuousLinearMap.map_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_sub ContinuousLinearMap.map_subₓ'. -/
protected theorem map_sub (f : M →SL[σ₁₂] M₂) (x y : M) : f (x - y) = f x - f y :=
map_sub _ _ _
#align continuous_linear_map.map_sub ContinuousLinearMap.map_sub
-/- warning: continuous_linear_map.sub_apply' -> ContinuousLinearMap.sub_apply' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.sub_apply' ContinuousLinearMap.sub_apply'ₓ'. -/
@[simp]
theorem sub_apply' (f g : M →SL[σ₁₂] M₂) (x : M) : ((f : M →ₛₗ[σ₁₂] M₂) - g) x = f x - g x :=
rfl
@@ -1857,25 +1387,16 @@ section
variable [Module R M₂] [Module R M₃] [Module R M₄]
-/- warning: continuous_linear_map.range_prod_eq -> ContinuousLinearMap.range_prod_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.range_prod_eq ContinuousLinearMap.range_prod_eqₓ'. -/
theorem range_prod_eq {f : M →L[R] M₂} {g : M →L[R] M₃} (h : ker f ⊔ ker g = ⊤) :
range (f.Prod g) = (range f).Prod (range g) :=
LinearMap.range_prod_eq h
#align continuous_linear_map.range_prod_eq ContinuousLinearMap.range_prod_eq
-/- warning: continuous_linear_map.ker_prod_ker_le_ker_coprod -> ContinuousLinearMap.ker_prod_ker_le_ker_coprod is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ker_prod_ker_le_ker_coprod ContinuousLinearMap.ker_prod_ker_le_ker_coprodₓ'. -/
theorem ker_prod_ker_le_ker_coprod [ContinuousAdd M₃] (f : M →L[R] M₃) (g : M₂ →L[R] M₃) :
(LinearMap.ker f).Prod (LinearMap.ker g) ≤ LinearMap.ker (f.coprod g) :=
LinearMap.ker_prod_ker_le_ker_coprod f.toLinearMap g.toLinearMap
#align continuous_linear_map.ker_prod_ker_le_ker_coprod ContinuousLinearMap.ker_prod_ker_le_ker_coprod
-/- warning: continuous_linear_map.ker_coprod_of_disjoint_range -> ContinuousLinearMap.ker_coprod_of_disjoint_range is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ker_coprod_of_disjoint_range ContinuousLinearMap.ker_coprod_of_disjoint_rangeₓ'. -/
theorem ker_coprod_of_disjoint_range [ContinuousAdd M₃] (f : M →L[R] M₃) (g : M₂ →L[R] M₃)
(hd : Disjoint (range f) (range g)) :
LinearMap.ker (f.coprod g) = (LinearMap.ker f).Prod (LinearMap.ker g) :=
@@ -1891,25 +1412,16 @@ variable [TopologicalAddGroup M₂]
instance : Neg (M →SL[σ₁₂] M₂) :=
⟨fun f => ⟨-f, f.2.neg⟩⟩
-/- warning: continuous_linear_map.neg_apply -> ContinuousLinearMap.neg_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.neg_apply ContinuousLinearMap.neg_applyₓ'. -/
@[simp]
theorem neg_apply (f : M →SL[σ₁₂] M₂) (x : M) : (-f) x = -f x :=
rfl
#align continuous_linear_map.neg_apply ContinuousLinearMap.neg_apply
-/- warning: continuous_linear_map.coe_neg -> ContinuousLinearMap.coe_neg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_neg ContinuousLinearMap.coe_negₓ'. -/
@[simp, norm_cast]
theorem coe_neg (f : M →SL[σ₁₂] M₂) : (↑(-f) : M →ₛₗ[σ₁₂] M₂) = -f :=
rfl
#align continuous_linear_map.coe_neg ContinuousLinearMap.coe_neg
-/- warning: continuous_linear_map.coe_neg' -> ContinuousLinearMap.coe_neg' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_neg' ContinuousLinearMap.coe_neg'ₓ'. -/
@[norm_cast]
theorem coe_neg' (f : M →SL[σ₁₂] M₂) : ⇑(-f) = -f :=
rfl
@@ -1935,24 +1447,15 @@ instance : AddCommGroup (M →SL[σ₁₂] M₂) := by
ext <;>
apply_rules [zero_add, add_assoc, add_zero, add_left_neg, add_comm, sub_eq_add_neg]
-/- warning: continuous_linear_map.sub_apply -> ContinuousLinearMap.sub_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.sub_apply ContinuousLinearMap.sub_applyₓ'. -/
theorem sub_apply (f g : M →SL[σ₁₂] M₂) (x : M) : (f - g) x = f x - g x :=
rfl
#align continuous_linear_map.sub_apply ContinuousLinearMap.sub_apply
-/- warning: continuous_linear_map.coe_sub -> ContinuousLinearMap.coe_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_sub ContinuousLinearMap.coe_subₓ'. -/
@[simp, norm_cast]
theorem coe_sub (f g : M →SL[σ₁₂] M₂) : (↑(f - g) : M →ₛₗ[σ₁₂] M₂) = f - g :=
rfl
#align continuous_linear_map.coe_sub ContinuousLinearMap.coe_sub
-/- warning: continuous_linear_map.coe_sub' -> ContinuousLinearMap.coe_sub' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_sub' ContinuousLinearMap.coe_sub'ₓ'. -/
@[simp, norm_cast]
theorem coe_sub' (f g : M →SL[σ₁₂] M₂) : ⇑(f - g) = f - g :=
rfl
@@ -1960,34 +1463,22 @@ theorem coe_sub' (f g : M →SL[σ₁₂] M₂) : ⇑(f - g) = f - g :=
end
-/- warning: continuous_linear_map.comp_neg -> ContinuousLinearMap.comp_neg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_neg ContinuousLinearMap.comp_negₓ'. -/
@[simp]
theorem comp_neg [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₂] [TopologicalAddGroup M₃]
(g : M₂ →SL[σ₂₃] M₃) (f : M →SL[σ₁₂] M₂) : g.comp (-f) = -g.comp f := by ext; simp
#align continuous_linear_map.comp_neg ContinuousLinearMap.comp_neg
-/- warning: continuous_linear_map.neg_comp -> ContinuousLinearMap.neg_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.neg_comp ContinuousLinearMap.neg_compₓ'. -/
@[simp]
theorem neg_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₃] (g : M₂ →SL[σ₂₃] M₃)
(f : M →SL[σ₁₂] M₂) : (-g).comp f = -g.comp f := by ext; simp
#align continuous_linear_map.neg_comp ContinuousLinearMap.neg_comp
-/- warning: continuous_linear_map.comp_sub -> ContinuousLinearMap.comp_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_sub ContinuousLinearMap.comp_subₓ'. -/
@[simp]
theorem comp_sub [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₂] [TopologicalAddGroup M₃]
(g : M₂ →SL[σ₂₃] M₃) (f₁ f₂ : M →SL[σ₁₂] M₂) : g.comp (f₁ - f₂) = g.comp f₁ - g.comp f₂ := by
ext; simp
#align continuous_linear_map.comp_sub ContinuousLinearMap.comp_sub
-/- warning: continuous_linear_map.sub_comp -> ContinuousLinearMap.sub_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.sub_comp ContinuousLinearMap.sub_compₓ'. -/
@[simp]
theorem sub_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₃] (g₁ g₂ : M₂ →SL[σ₂₃] M₃)
(f : M →SL[σ₁₂] M₂) : (g₁ - g₂).comp f = g₁.comp f - g₂.comp f := by ext; simp
@@ -1999,9 +1490,6 @@ instance [TopologicalAddGroup M] : Ring (M →L[R] M) :=
mul := (· * ·)
one := 1 }
-/- warning: continuous_linear_map.smul_right_one_pow -> ContinuousLinearMap.smulRight_one_pow is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_right_one_pow ContinuousLinearMap.smulRight_one_powₓ'. -/
theorem smulRight_one_pow [TopologicalSpace R] [TopologicalRing R] (c : R) (n : ℕ) :
smulRight (1 : R →L[R] R) c ^ n = smulRight (1 : R →L[R] R) (c ^ n) :=
by
@@ -2014,9 +1502,6 @@ section
variable {σ₂₁ : R₂ →+* R} [RingHomInvPair σ₁₂ σ₂₁]
-/- warning: continuous_linear_map.proj_ker_of_right_inverse -> ContinuousLinearMap.projKerOfRightInverse is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.proj_ker_of_right_inverse ContinuousLinearMap.projKerOfRightInverseₓ'. -/
/-- Given a right inverse `f₂ : M₂ →L[R] M` to `f₁ : M →L[R] M₂`,
`proj_ker_of_right_inverse f₁ f₂ h` is the projection `M →L[R] f₁.ker` along `f₂.range`. -/
def projKerOfRightInverse [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂) (f₂ : M₂ →SL[σ₂₁] M)
@@ -2024,9 +1509,6 @@ def projKerOfRightInverse [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂
(id R M - f₂.comp f₁).codRestrict (LinearMap.ker f₁) fun x => by simp [h (f₁ x)]
#align continuous_linear_map.proj_ker_of_right_inverse ContinuousLinearMap.projKerOfRightInverse
-/- warning: continuous_linear_map.coe_proj_ker_of_right_inverse_apply -> ContinuousLinearMap.coe_projKerOfRightInverse_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_proj_ker_of_right_inverse_apply ContinuousLinearMap.coe_projKerOfRightInverse_applyₓ'. -/
@[simp]
theorem coe_projKerOfRightInverse_apply [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂)
(f₂ : M₂ →SL[σ₂₁] M) (h : Function.RightInverse f₂ f₁) (x : M) :
@@ -2034,9 +1516,6 @@ theorem coe_projKerOfRightInverse_apply [TopologicalAddGroup M] (f₁ : M →SL[
rfl
#align continuous_linear_map.coe_proj_ker_of_right_inverse_apply ContinuousLinearMap.coe_projKerOfRightInverse_apply
-/- warning: continuous_linear_map.proj_ker_of_right_inverse_apply_idem -> ContinuousLinearMap.projKerOfRightInverse_apply_idem is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.proj_ker_of_right_inverse_apply_idem ContinuousLinearMap.projKerOfRightInverse_apply_idemₓ'. -/
@[simp]
theorem projKerOfRightInverse_apply_idem [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂)
(f₂ : M₂ →SL[σ₂₁] M) (h : Function.RightInverse f₂ f₁) (x : LinearMap.ker f₁) :
@@ -2044,9 +1523,6 @@ theorem projKerOfRightInverse_apply_idem [TopologicalAddGroup M] (f₁ : M →SL
Subtype.ext_iff_val.2 <| by simp
#align continuous_linear_map.proj_ker_of_right_inverse_apply_idem ContinuousLinearMap.projKerOfRightInverse_apply_idem
-/- warning: continuous_linear_map.proj_ker_of_right_inverse_comp_inv -> ContinuousLinearMap.projKerOfRightInverse_comp_inv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.proj_ker_of_right_inverse_comp_inv ContinuousLinearMap.projKerOfRightInverse_comp_invₓ'. -/
@[simp]
theorem projKerOfRightInverse_comp_inv [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂)
(f₂ : M₂ →SL[σ₂₁] M) (h : Function.RightInverse f₂ f₁) (y : M₂) :
@@ -2062,9 +1538,6 @@ section DivisionMonoid
variable {R M : Type _}
-/- warning: continuous_linear_map.is_open_map_of_ne_zero -> ContinuousLinearMap.isOpenMap_of_ne_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.is_open_map_of_ne_zero ContinuousLinearMap.isOpenMap_of_ne_zeroₓ'. -/
/-- A nonzero continuous linear functional is open. -/
protected theorem isOpenMap_of_ne_zero [TopologicalSpace R] [DivisionRing R] [ContinuousSub R]
[AddCommGroup M] [TopologicalSpace M] [ContinuousAdd M] [Module R M] [ContinuousSMul R M]
@@ -2091,9 +1564,6 @@ variable {R R₂ R₃ S S₃ : Type _} [Semiring R] [Semiring R₂] [Semiring R
include σ₁₃
-/- warning: continuous_linear_map.smul_comp -> ContinuousLinearMap.smul_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_comp ContinuousLinearMap.smul_compₓ'. -/
@[simp]
theorem smul_comp (c : S₃) (h : M₂ →SL[σ₂₃] M₃) (f : M →SL[σ₁₂] M₂) :
(c • h).comp f = c • h.comp f :=
@@ -2106,9 +1576,6 @@ variable [DistribMulAction S₃ M₂] [ContinuousConstSMul S₃ M₂] [SMulCommC
variable [DistribMulAction S N₂] [ContinuousConstSMul S N₂] [SMulCommClass R S N₂]
-/- warning: continuous_linear_map.comp_smul -> ContinuousLinearMap.comp_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_smul ContinuousLinearMap.comp_smulₓ'. -/
@[simp]
theorem comp_smul [LinearMap.CompatibleSMul N₂ N₃ S R] (hₗ : N₂ →L[R] N₃) (c : S)
(fₗ : M →L[R] N₂) : hₗ.comp (c • fₗ) = c • hₗ.comp fₗ := by ext x;
@@ -2117,9 +1584,6 @@ theorem comp_smul [LinearMap.CompatibleSMul N₂ N₃ S R] (hₗ : N₂ →L[R]
include σ₁₃
-/- warning: continuous_linear_map.comp_smulₛₗ -> ContinuousLinearMap.comp_smulₛₗ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_smulₛₗ ContinuousLinearMap.comp_smulₛₗₓ'. -/
@[simp]
theorem comp_smulₛₗ [SMulCommClass R₂ R₂ M₂] [SMulCommClass R₃ R₃ M₃] [ContinuousConstSMul R₂ M₂]
[ContinuousConstSMul R₃ M₃] (h : M₂ →SL[σ₂₃] M₃) (c : R₂) (f : M →SL[σ₁₂] M₂) :
@@ -2150,9 +1614,6 @@ variable {R R₂ R₃ S S₃ : Type _} [Semiring R] [Semiring R₂] [Semiring R
{σ₁₂ : R →+* R₂} {σ₂₃ : R₂ →+* R₃} {σ₁₃ : R →+* R₃} [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] (c : S)
(h : M₂ →SL[σ₂₃] M₃) (f g : M →SL[σ₁₂] M₂) (x y z : M)
-/- warning: continuous_linear_map.prod_equiv -> ContinuousLinearMap.prodEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.prod_equiv ContinuousLinearMap.prodEquivₓ'. -/
/-- `continuous_linear_map.prod` as an `equiv`. -/
@[simps apply]
def prodEquiv : (M →L[R] N₂) × (M →L[R] N₃) ≃ (M →L[R] N₂ × N₃)
@@ -2163,17 +1624,11 @@ def prodEquiv : (M →L[R] N₂) × (M →L[R] N₃) ≃ (M →L[R] N₂ × N₃
right_inv f := by ext <;> rfl
#align continuous_linear_map.prod_equiv ContinuousLinearMap.prodEquiv
-/- warning: continuous_linear_map.prod_ext_iff -> ContinuousLinearMap.prod_ext_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.prod_ext_iff ContinuousLinearMap.prod_ext_iffₓ'. -/
theorem prod_ext_iff {f g : M × N₂ →L[R] N₃} :
f = g ↔ f.comp (inl _ _ _) = g.comp (inl _ _ _) ∧ f.comp (inr _ _ _) = g.comp (inr _ _ _) := by
simp only [← coe_inj, LinearMap.prod_ext_iff]; rfl
#align continuous_linear_map.prod_ext_iff ContinuousLinearMap.prod_ext_iff
-/- warning: continuous_linear_map.prod_ext -> ContinuousLinearMap.prod_ext is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.prod_ext ContinuousLinearMap.prod_extₓ'. -/
@[ext]
theorem prod_ext {f g : M × N₂ →L[R] N₃} (hl : f.comp (inl _ _ _) = g.comp (inl _ _ _))
(hr : f.comp (inr _ _ _) = g.comp (inr _ _ _)) : f = g :=
@@ -2192,9 +1647,6 @@ instance [Module S₃ᵐᵒᵖ M₃] [IsCentralScalar S₃ M₃] : IsCentralScal
variable (S) [ContinuousAdd N₃]
-/- warning: continuous_linear_map.prodₗ -> ContinuousLinearMap.prodₗ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.prodₗ ContinuousLinearMap.prodₗₓ'. -/
/-- `continuous_linear_map.prod` as a `linear_equiv`. -/
@[simps apply]
def prodₗ : ((M →L[R] N₂) × (M →L[R] N₃)) ≃ₗ[S] M →L[R] N₂ × N₃ :=
@@ -2203,9 +1655,6 @@ def prodₗ : ((M →L[R] N₂) × (M →L[R] N₃)) ≃ₗ[S] M →L[R] N₂ ×
map_smul' := fun c f => rfl }
#align continuous_linear_map.prodₗ ContinuousLinearMap.prodₗ
-/- warning: continuous_linear_map.coe_lm -> ContinuousLinearMap.coeLM is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_lm ContinuousLinearMap.coeLMₓ'. -/
/-- The coercion from `M →L[R] M₂` to `M →ₗ[R] M₂`, as a linear map. -/
@[simps]
def coeLM : (M →L[R] N₃) →ₗ[S] M →ₗ[R] N₃
@@ -2217,9 +1666,6 @@ def coeLM : (M →L[R] N₃) →ₗ[S] M →ₗ[R] N₃
variable {S} (σ₁₃)
-/- warning: continuous_linear_map.coe_lmₛₗ -> ContinuousLinearMap.coeLMₛₗ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_lmₛₗ ContinuousLinearMap.coeLMₛₗₓ'. -/
/-- The coercion from `M →SL[σ] M₂` to `M →ₛₗ[σ] M₂`, as a linear map. -/
@[simps]
def coeLMₛₗ : (M →SL[σ₁₃] M₃) →ₗ[S₃] M →ₛₗ[σ₁₃] M₃
@@ -2241,9 +1687,6 @@ variable {R S T M M₂ : Type _} [Semiring R] [Semiring S] [Semiring T] [Module
[ContinuousAdd M₂] [Module T M₂] [ContinuousConstSMul T M₂] [SMulCommClass R T M₂]
[SMulCommClass S T M₂]
-/- warning: continuous_linear_map.smul_rightₗ -> ContinuousLinearMap.smulRightₗ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_rightₗ ContinuousLinearMap.smulRightₗₓ'. -/
/-- Given `c : E →L[𝕜] 𝕜`, `c.smul_rightₗ` is the linear map from `F` to `E →L[𝕜] F`
sending `f` to `λ e, c e • f`. See also `continuous_linear_map.smul_rightL`. -/
def smulRightₗ (c : M →L[R] S) : M₂ →ₗ[T] M →L[R] M₂
@@ -2253,9 +1696,6 @@ def smulRightₗ (c : M →L[R] S) : M₂ →ₗ[T] M →L[R] M₂
map_smul' a x := by ext e; dsimp; apply smul_comm
#align continuous_linear_map.smul_rightₗ ContinuousLinearMap.smulRightₗ
-/- warning: continuous_linear_map.coe_smul_rightₗ -> ContinuousLinearMap.coe_smulRightₗ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_smul_rightₗ ContinuousLinearMap.coe_smulRightₗₓ'. -/
@[simp]
theorem coe_smulRightₗ (c : M →L[R] S) : ⇑(smulRightₗ c : M₂ →ₗ[T] M →L[R] M₂) = c.smul_right :=
rfl
@@ -2293,26 +1733,17 @@ def restrictScalars (f : M →L[A] M₂) : M →L[R] M₂ :=
variable {R}
-/- warning: continuous_linear_map.coe_restrict_scalars -> ContinuousLinearMap.coe_restrictScalars is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_restrict_scalars ContinuousLinearMap.coe_restrictScalarsₓ'. -/
@[simp, norm_cast]
theorem coe_restrictScalars (f : M →L[A] M₂) :
(f.restrictScalars R : M →ₗ[R] M₂) = (f : M →ₗ[A] M₂).restrictScalars R :=
rfl
#align continuous_linear_map.coe_restrict_scalars ContinuousLinearMap.coe_restrictScalars
-/- warning: continuous_linear_map.coe_restrict_scalars' -> ContinuousLinearMap.coe_restrictScalars' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_restrict_scalars' ContinuousLinearMap.coe_restrictScalars'ₓ'. -/
@[simp]
theorem coe_restrictScalars' (f : M →L[A] M₂) : ⇑(f.restrictScalars R) = f :=
rfl
#align continuous_linear_map.coe_restrict_scalars' ContinuousLinearMap.coe_restrictScalars'
-/- warning: continuous_linear_map.restrict_scalars_zero -> ContinuousLinearMap.restrictScalars_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.restrict_scalars_zero ContinuousLinearMap.restrictScalars_zeroₓ'. -/
@[simp]
theorem restrictScalars_zero : (0 : M →L[A] M₂).restrictScalars R = 0 :=
rfl
@@ -2322,18 +1753,12 @@ section
variable [TopologicalAddGroup M₂]
-/- warning: continuous_linear_map.restrict_scalars_add -> ContinuousLinearMap.restrictScalars_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.restrict_scalars_add ContinuousLinearMap.restrictScalars_addₓ'. -/
@[simp]
theorem restrictScalars_add (f g : M →L[A] M₂) :
(f + g).restrictScalars R = f.restrictScalars R + g.restrictScalars R :=
rfl
#align continuous_linear_map.restrict_scalars_add ContinuousLinearMap.restrictScalars_add
-/- warning: continuous_linear_map.restrict_scalars_neg -> ContinuousLinearMap.restrictScalars_neg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.restrict_scalars_neg ContinuousLinearMap.restrictScalars_negₓ'. -/
@[simp]
theorem restrictScalars_neg (f : M →L[A] M₂) : (-f).restrictScalars R = -f.restrictScalars R :=
rfl
@@ -2344,9 +1769,6 @@ end
variable {S : Type _} [Ring S] [Module S M₂] [ContinuousConstSMul S M₂] [SMulCommClass A S M₂]
[SMulCommClass R S M₂]
-/- warning: continuous_linear_map.restrict_scalars_smul -> ContinuousLinearMap.restrictScalars_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.restrict_scalars_smul ContinuousLinearMap.restrictScalars_smulₓ'. -/
@[simp]
theorem restrictScalars_smul (c : S) (f : M →L[A] M₂) :
(c • f).restrictScalars R = c • f.restrictScalars R :=
@@ -2368,9 +1790,6 @@ def restrictScalarsₗ : (M →L[A] M₂) →ₗ[S] M →L[R] M₂
variable {A M M₂ R S}
-/- warning: continuous_linear_map.coe_restrict_scalarsₗ -> ContinuousLinearMap.coe_restrictScalarsₗ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_restrict_scalarsₗ ContinuousLinearMap.coe_restrictScalarsₗₓ'. -/
@[simp]
theorem coe_restrictScalarsₗ : ⇑(restrictScalarsₗ A M M₂ R S) = restrictScalars R :=
rfl
@@ -2427,63 +1846,40 @@ instance : CoeFun (M₁ ≃SL[σ₁₂] M₂) fun _ => M₁ → M₂ :=
⟨fun f => f⟩
/- warning: continuous_linear_equiv.coe_def_rev clashes with [anonymous] -> [anonymous]
-warning: continuous_linear_equiv.coe_def_rev -> [anonymous] is a dubious translation:
-<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_def_rev [anonymous]ₓ'. -/
@[simp]
theorem [anonymous] (e : M₁ ≃SL[σ₁₂] M₂) : e.toContinuousLinearMap = e :=
rfl
#align continuous_linear_equiv.coe_def_rev [anonymous]
-/- warning: continuous_linear_equiv.coe_apply -> ContinuousLinearEquiv.coe_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_apply ContinuousLinearEquiv.coe_applyₓ'. -/
theorem coe_apply (e : M₁ ≃SL[σ₁₂] M₂) (b : M₁) : (e : M₁ →SL[σ₁₂] M₂) b = e b :=
rfl
#align continuous_linear_equiv.coe_apply ContinuousLinearEquiv.coe_apply
-/- warning: continuous_linear_equiv.coe_to_linear_equiv -> ContinuousLinearEquiv.coe_toLinearEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_to_linear_equiv ContinuousLinearEquiv.coe_toLinearEquivₓ'. -/
@[simp]
theorem coe_toLinearEquiv (f : M₁ ≃SL[σ₁₂] M₂) : ⇑f.toLinearEquiv = f :=
rfl
#align continuous_linear_equiv.coe_to_linear_equiv ContinuousLinearEquiv.coe_toLinearEquiv
-/- warning: continuous_linear_equiv.coe_coe -> ContinuousLinearEquiv.coe_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_coe ContinuousLinearEquiv.coe_coeₓ'. -/
@[simp, norm_cast]
theorem coe_coe (e : M₁ ≃SL[σ₁₂] M₂) : ⇑(e : M₁ →SL[σ₁₂] M₂) = e :=
rfl
#align continuous_linear_equiv.coe_coe ContinuousLinearEquiv.coe_coe
-/- warning: continuous_linear_equiv.to_linear_equiv_injective -> ContinuousLinearEquiv.toLinearEquiv_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.to_linear_equiv_injective ContinuousLinearEquiv.toLinearEquiv_injectiveₓ'. -/
theorem toLinearEquiv_injective :
Function.Injective (toLinearEquiv : (M₁ ≃SL[σ₁₂] M₂) → M₁ ≃ₛₗ[σ₁₂] M₂)
| ⟨e, _, _⟩, ⟨e', _, _⟩, rfl => rfl
#align continuous_linear_equiv.to_linear_equiv_injective ContinuousLinearEquiv.toLinearEquiv_injective
-/- warning: continuous_linear_equiv.ext -> ContinuousLinearEquiv.ext is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.ext ContinuousLinearEquiv.extₓ'. -/
@[ext]
theorem ext {f g : M₁ ≃SL[σ₁₂] M₂} (h : (f : M₁ → M₂) = g) : f = g :=
toLinearEquiv_injective <| LinearEquiv.ext <| congr_fun h
#align continuous_linear_equiv.ext ContinuousLinearEquiv.ext
-/- warning: continuous_linear_equiv.coe_injective -> ContinuousLinearEquiv.coe_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_injective ContinuousLinearEquiv.coe_injectiveₓ'. -/
theorem coe_injective : Function.Injective (coe : (M₁ ≃SL[σ₁₂] M₂) → M₁ →SL[σ₁₂] M₂) :=
fun e e' h => ext <| funext <| ContinuousLinearMap.ext_iff.1 h
#align continuous_linear_equiv.coe_injective ContinuousLinearEquiv.coe_injective
-/- warning: continuous_linear_equiv.coe_inj -> ContinuousLinearEquiv.coe_inj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_inj ContinuousLinearEquiv.coe_injₓ'. -/
@[simp, norm_cast]
theorem coe_inj {e e' : M₁ ≃SL[σ₁₂] M₂} : (e : M₁ →SL[σ₁₂] M₂) = e' ↔ e = e' :=
coe_injective.eq_iff
@@ -2496,63 +1892,39 @@ def toHomeomorph (e : M₁ ≃SL[σ₁₂] M₂) : M₁ ≃ₜ M₂ :=
#align continuous_linear_equiv.to_homeomorph ContinuousLinearEquiv.toHomeomorph
-/
-/- warning: continuous_linear_equiv.coe_to_homeomorph -> ContinuousLinearEquiv.coe_toHomeomorph is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_to_homeomorph ContinuousLinearEquiv.coe_toHomeomorphₓ'. -/
@[simp]
theorem coe_toHomeomorph (e : M₁ ≃SL[σ₁₂] M₂) : ⇑e.toHomeomorph = e :=
rfl
#align continuous_linear_equiv.coe_to_homeomorph ContinuousLinearEquiv.coe_toHomeomorph
-/- warning: continuous_linear_equiv.image_closure -> ContinuousLinearEquiv.image_closure is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.image_closure ContinuousLinearEquiv.image_closureₓ'. -/
theorem image_closure (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₁) : e '' closure s = closure (e '' s) :=
e.toHomeomorph.image_closure s
#align continuous_linear_equiv.image_closure ContinuousLinearEquiv.image_closure
-/- warning: continuous_linear_equiv.preimage_closure -> ContinuousLinearEquiv.preimage_closure is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.preimage_closure ContinuousLinearEquiv.preimage_closureₓ'. -/
theorem preimage_closure (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₂) : e ⁻¹' closure s = closure (e ⁻¹' s) :=
e.toHomeomorph.preimage_closure s
#align continuous_linear_equiv.preimage_closure ContinuousLinearEquiv.preimage_closure
-/- warning: continuous_linear_equiv.is_closed_image -> ContinuousLinearEquiv.isClosed_image is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.is_closed_image ContinuousLinearEquiv.isClosed_imageₓ'. -/
@[simp]
theorem isClosed_image (e : M₁ ≃SL[σ₁₂] M₂) {s : Set M₁} : IsClosed (e '' s) ↔ IsClosed s :=
e.toHomeomorph.isClosed_image
#align continuous_linear_equiv.is_closed_image ContinuousLinearEquiv.isClosed_image
-/- warning: continuous_linear_equiv.map_nhds_eq -> ContinuousLinearEquiv.map_nhds_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_nhds_eq ContinuousLinearEquiv.map_nhds_eqₓ'. -/
theorem map_nhds_eq (e : M₁ ≃SL[σ₁₂] M₂) (x : M₁) : map e (𝓝 x) = 𝓝 (e x) :=
e.toHomeomorph.map_nhds_eq x
#align continuous_linear_equiv.map_nhds_eq ContinuousLinearEquiv.map_nhds_eq
-/- warning: continuous_linear_equiv.map_zero -> ContinuousLinearEquiv.map_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_zero ContinuousLinearEquiv.map_zeroₓ'. -/
-- Make some straightforward lemmas available to `simp`.
@[simp]
theorem map_zero (e : M₁ ≃SL[σ₁₂] M₂) : e (0 : M₁) = 0 :=
(e : M₁ →SL[σ₁₂] M₂).map_zero
#align continuous_linear_equiv.map_zero ContinuousLinearEquiv.map_zero
-/- warning: continuous_linear_equiv.map_add -> ContinuousLinearEquiv.map_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_add ContinuousLinearEquiv.map_addₓ'. -/
@[simp]
theorem map_add (e : M₁ ≃SL[σ₁₂] M₂) (x y : M₁) : e (x + y) = e x + e y :=
(e : M₁ →SL[σ₁₂] M₂).map_add x y
#align continuous_linear_equiv.map_add ContinuousLinearEquiv.map_add
-/- warning: continuous_linear_equiv.map_smulₛₗ -> ContinuousLinearEquiv.map_smulₛₗ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_smulₛₗ ContinuousLinearEquiv.map_smulₛₗₓ'. -/
@[simp]
theorem map_smulₛₗ (e : M₁ ≃SL[σ₁₂] M₂) (c : R₁) (x : M₁) : e (c • x) = σ₁₂ c • e x :=
(e : M₁ →SL[σ₁₂] M₂).map_smulₛₗ c x
@@ -2560,9 +1932,6 @@ theorem map_smulₛₗ (e : M₁ ≃SL[σ₁₂] M₂) (c : R₁) (x : M₁) : e
omit σ₂₁
-/- warning: continuous_linear_equiv.map_smul -> ContinuousLinearEquiv.map_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_smul ContinuousLinearEquiv.map_smulₓ'. -/
@[simp]
theorem map_smul [Module R₁ M₂] (e : M₁ ≃L[R₁] M₂) (c : R₁) (x : M₁) : e (c • x) = c • e x :=
(e : M₁ →L[R₁] M₂).map_smul c x
@@ -2570,9 +1939,6 @@ theorem map_smul [Module R₁ M₂] (e : M₁ ≃L[R₁] M₂) (c : R₁) (x : M
include σ₂₁
-/- warning: continuous_linear_equiv.map_eq_zero_iff -> ContinuousLinearEquiv.map_eq_zero_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_eq_zero_iff ContinuousLinearEquiv.map_eq_zero_iffₓ'. -/
@[simp]
theorem map_eq_zero_iff (e : M₁ ≃SL[σ₁₂] M₂) {x : M₁} : e x = 0 ↔ x = 0 :=
e.toLinearEquiv.map_eq_zero_iff
@@ -2581,47 +1947,29 @@ theorem map_eq_zero_iff (e : M₁ ≃SL[σ₁₂] M₂) {x : M₁} : e x = 0 ↔
attribute [continuity]
ContinuousLinearEquiv.continuous_toFun ContinuousLinearEquiv.continuous_invFun
-/- warning: continuous_linear_equiv.continuous -> ContinuousLinearEquiv.continuous is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.continuous ContinuousLinearEquiv.continuousₓ'. -/
@[continuity]
protected theorem continuous (e : M₁ ≃SL[σ₁₂] M₂) : Continuous (e : M₁ → M₂) :=
e.continuous_toFun
#align continuous_linear_equiv.continuous ContinuousLinearEquiv.continuous
-/- warning: continuous_linear_equiv.continuous_on -> ContinuousLinearEquiv.continuousOn is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.continuous_on ContinuousLinearEquiv.continuousOnₓ'. -/
protected theorem continuousOn (e : M₁ ≃SL[σ₁₂] M₂) {s : Set M₁} : ContinuousOn (e : M₁ → M₂) s :=
e.Continuous.ContinuousOn
#align continuous_linear_equiv.continuous_on ContinuousLinearEquiv.continuousOn
-/- warning: continuous_linear_equiv.continuous_at -> ContinuousLinearEquiv.continuousAt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.continuous_at ContinuousLinearEquiv.continuousAtₓ'. -/
protected theorem continuousAt (e : M₁ ≃SL[σ₁₂] M₂) {x : M₁} : ContinuousAt (e : M₁ → M₂) x :=
e.Continuous.ContinuousAt
#align continuous_linear_equiv.continuous_at ContinuousLinearEquiv.continuousAt
-/- warning: continuous_linear_equiv.continuous_within_at -> ContinuousLinearEquiv.continuousWithinAt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.continuous_within_at ContinuousLinearEquiv.continuousWithinAtₓ'. -/
protected theorem continuousWithinAt (e : M₁ ≃SL[σ₁₂] M₂) {s : Set M₁} {x : M₁} :
ContinuousWithinAt (e : M₁ → M₂) s x :=
e.Continuous.ContinuousWithinAt
#align continuous_linear_equiv.continuous_within_at ContinuousLinearEquiv.continuousWithinAt
-/- warning: continuous_linear_equiv.comp_continuous_on_iff -> ContinuousLinearEquiv.comp_continuousOn_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.comp_continuous_on_iff ContinuousLinearEquiv.comp_continuousOn_iffₓ'. -/
theorem comp_continuousOn_iff {α : Type _} [TopologicalSpace α] (e : M₁ ≃SL[σ₁₂] M₂) {f : α → M₁}
{s : Set α} : ContinuousOn (e ∘ f) s ↔ ContinuousOn f s :=
e.toHomeomorph.comp_continuousOn_iff _ _
#align continuous_linear_equiv.comp_continuous_on_iff ContinuousLinearEquiv.comp_continuousOn_iff
-/- warning: continuous_linear_equiv.comp_continuous_iff -> ContinuousLinearEquiv.comp_continuous_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.comp_continuous_iff ContinuousLinearEquiv.comp_continuous_iffₓ'. -/
theorem comp_continuous_iff {α : Type _} [TopologicalSpace α] (e : M₁ ≃SL[σ₁₂] M₂) {f : α → M₁} :
Continuous (e ∘ f) ↔ Continuous f :=
e.toHomeomorph.comp_continuous_iff
@@ -2629,9 +1977,6 @@ theorem comp_continuous_iff {α : Type _} [TopologicalSpace α] (e : M₁ ≃SL[
omit σ₂₁
-/- warning: continuous_linear_equiv.ext₁ -> ContinuousLinearEquiv.ext₁ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.ext₁ ContinuousLinearEquiv.ext₁ₓ'. -/
/-- An extensionality lemma for `R ≃L[R] M`. -/
theorem ext₁ [TopologicalSpace R₁] {f g : R₁ ≃L[R₁] M₁} (h : f 1 = g 1) : f = g :=
ext <| funext fun x => mul_one x ▸ by rw [← smul_eq_mul, map_smul, h, map_smul]
@@ -2679,17 +2024,11 @@ protected def symm (e : M₁ ≃SL[σ₁₂] M₂) : M₂ ≃SL[σ₂₁] M₁ :
include σ₂₁
-/- warning: continuous_linear_equiv.symm_to_linear_equiv -> ContinuousLinearEquiv.symm_toLinearEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_to_linear_equiv ContinuousLinearEquiv.symm_toLinearEquivₓ'. -/
@[simp]
theorem symm_toLinearEquiv (e : M₁ ≃SL[σ₁₂] M₂) : e.symm.toLinearEquiv = e.toLinearEquiv.symm := by
ext; rfl
#align continuous_linear_equiv.symm_to_linear_equiv ContinuousLinearEquiv.symm_toLinearEquiv
-/- warning: continuous_linear_equiv.symm_to_homeomorph -> ContinuousLinearEquiv.symm_toHomeomorph is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_to_homeomorph ContinuousLinearEquiv.symm_toHomeomorphₓ'. -/
@[simp]
theorem symm_toHomeomorph (e : M₁ ≃SL[σ₁₂] M₂) : e.toHomeomorph.symm = e.symm.toHomeomorph :=
rfl
@@ -2713,9 +2052,6 @@ def Simps.symm_apply (h : M₁ ≃SL[σ₁₂] M₂) : M₂ → M₁ :=
initialize_simps_projections ContinuousLinearEquiv (to_linear_equiv_to_fun → apply,
to_linear_equiv_inv_fun → symm_apply)
-/- warning: continuous_linear_equiv.symm_map_nhds_eq -> ContinuousLinearEquiv.symm_map_nhds_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_map_nhds_eq ContinuousLinearEquiv.symm_map_nhds_eqₓ'. -/
theorem symm_map_nhds_eq (e : M₁ ≃SL[σ₁₂] M₂) (x : M₁) : map e.symm (𝓝 (e x)) = 𝓝 x :=
e.toHomeomorph.symm_map_nhds_eq x
#align continuous_linear_equiv.symm_map_nhds_eq ContinuousLinearEquiv.symm_map_nhds_eq
@@ -2738,9 +2074,6 @@ protected def trans (e₁ : M₁ ≃SL[σ₁₂] M₂) (e₂ : M₂ ≃SL[σ₂
include σ₁₃
-/- warning: continuous_linear_equiv.trans_to_linear_equiv -> ContinuousLinearEquiv.trans_toLinearEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.trans_to_linear_equiv ContinuousLinearEquiv.trans_toLinearEquivₓ'. -/
@[simp]
theorem trans_toLinearEquiv (e₁ : M₁ ≃SL[σ₁₂] M₂) (e₂ : M₂ ≃SL[σ₂₃] M₃) :
(e₁.trans e₂).toLinearEquiv = e₁.toLinearEquiv.trans e₂.toLinearEquiv := by ext; rfl
@@ -2748,9 +2081,6 @@ theorem trans_toLinearEquiv (e₁ : M₁ ≃SL[σ₁₂] M₂) (e₂ : M₂ ≃S
omit σ₁₃ σ₂₁ σ₃₂ σ₃₁
-/- warning: continuous_linear_equiv.prod -> ContinuousLinearEquiv.prod is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.prod ContinuousLinearEquiv.prodₓ'. -/
/-- Product of two continuous linear equivalences. The map comes from `equiv.prod_congr`. -/
def prod [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M₁ ≃L[R₁] M₂) (e' : M₃ ≃L[R₁] M₄) :
(M₁ × M₃) ≃L[R₁] M₂ × M₄ :=
@@ -2761,18 +2091,12 @@ def prod [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M₁ ≃L
continuous_invFun := e.continuous_invFun.Prod_map e'.continuous_invFun }
#align continuous_linear_equiv.prod ContinuousLinearEquiv.prod
-/- warning: continuous_linear_equiv.prod_apply -> ContinuousLinearEquiv.prod_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.prod_apply ContinuousLinearEquiv.prod_applyₓ'. -/
@[simp, norm_cast]
theorem prod_apply [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M₁ ≃L[R₁] M₂)
(e' : M₃ ≃L[R₁] M₄) (x) : e.Prod e' x = (e x.1, e' x.2) :=
rfl
#align continuous_linear_equiv.prod_apply ContinuousLinearEquiv.prod_apply
-/- warning: continuous_linear_equiv.coe_prod -> ContinuousLinearEquiv.coe_prod is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_prod ContinuousLinearEquiv.coe_prodₓ'. -/
@[simp, norm_cast]
theorem coe_prod [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M₁ ≃L[R₁] M₂)
(e' : M₃ ≃L[R₁] M₄) :
@@ -2780,9 +2104,6 @@ theorem coe_prod [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M
rfl
#align continuous_linear_equiv.coe_prod ContinuousLinearEquiv.coe_prod
-/- warning: continuous_linear_equiv.prod_symm -> ContinuousLinearEquiv.prod_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.prod_symm ContinuousLinearEquiv.prod_symmₓ'. -/
theorem prod_symm [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M₁ ≃L[R₁] M₂)
(e' : M₃ ≃L[R₁] M₄) : (e.Prod e').symm = e.symm.Prod e'.symm :=
rfl
@@ -2790,32 +2111,20 @@ theorem prod_symm [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e :
include σ₂₁
-/- warning: continuous_linear_equiv.bijective -> ContinuousLinearEquiv.bijective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.bijective ContinuousLinearEquiv.bijectiveₓ'. -/
protected theorem bijective (e : M₁ ≃SL[σ₁₂] M₂) : Function.Bijective e :=
e.toLinearEquiv.toEquiv.Bijective
#align continuous_linear_equiv.bijective ContinuousLinearEquiv.bijective
-/- warning: continuous_linear_equiv.injective -> ContinuousLinearEquiv.injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.injective ContinuousLinearEquiv.injectiveₓ'. -/
protected theorem injective (e : M₁ ≃SL[σ₁₂] M₂) : Function.Injective e :=
e.toLinearEquiv.toEquiv.Injective
#align continuous_linear_equiv.injective ContinuousLinearEquiv.injective
-/- warning: continuous_linear_equiv.surjective -> ContinuousLinearEquiv.surjective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.surjective ContinuousLinearEquiv.surjectiveₓ'. -/
protected theorem surjective (e : M₁ ≃SL[σ₁₂] M₂) : Function.Surjective e :=
e.toLinearEquiv.toEquiv.Surjective
#align continuous_linear_equiv.surjective ContinuousLinearEquiv.surjective
include σ₃₂ σ₃₁ σ₁₃
-/- warning: continuous_linear_equiv.trans_apply -> ContinuousLinearEquiv.trans_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.trans_apply ContinuousLinearEquiv.trans_applyₓ'. -/
@[simp]
theorem trans_apply (e₁ : M₁ ≃SL[σ₁₂] M₂) (e₂ : M₂ ≃SL[σ₂₃] M₃) (c : M₁) :
(e₁.trans e₂) c = e₂ (e₁ c) :=
@@ -2824,17 +2133,11 @@ theorem trans_apply (e₁ : M₁ ≃SL[σ₁₂] M₂) (e₂ : M₂ ≃SL[σ₂
omit σ₃₂ σ₃₁ σ₁₃
-/- warning: continuous_linear_equiv.apply_symm_apply -> ContinuousLinearEquiv.apply_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.apply_symm_apply ContinuousLinearEquiv.apply_symm_applyₓ'. -/
@[simp]
theorem apply_symm_apply (e : M₁ ≃SL[σ₁₂] M₂) (c : M₂) : e (e.symm c) = c :=
e.1.right_inv c
#align continuous_linear_equiv.apply_symm_apply ContinuousLinearEquiv.apply_symm_apply
-/- warning: continuous_linear_equiv.symm_apply_apply -> ContinuousLinearEquiv.symm_apply_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_apply_apply ContinuousLinearEquiv.symm_apply_applyₓ'. -/
@[simp]
theorem symm_apply_apply (e : M₁ ≃SL[σ₁₂] M₂) (b : M₁) : e.symm (e b) = b :=
e.1.left_inv b
@@ -2842,9 +2145,6 @@ theorem symm_apply_apply (e : M₁ ≃SL[σ₁₂] M₂) (b : M₁) : e.symm (e
include σ₁₂ σ₂₃ σ₁₃ σ₃₁
-/- warning: continuous_linear_equiv.symm_trans_apply -> ContinuousLinearEquiv.symm_trans_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_trans_apply ContinuousLinearEquiv.symm_trans_applyₓ'. -/
@[simp]
theorem symm_trans_apply (e₁ : M₂ ≃SL[σ₂₁] M₁) (e₂ : M₃ ≃SL[σ₃₂] M₂) (c : M₁) :
(e₂.trans e₁).symm c = e₂.symm (e₁.symm c) :=
@@ -2853,17 +2153,11 @@ theorem symm_trans_apply (e₁ : M₂ ≃SL[σ₂₁] M₁) (e₂ : M₃ ≃SL[
omit σ₁₂ σ₂₃ σ₁₃ σ₃₁
-/- warning: continuous_linear_equiv.symm_image_image -> ContinuousLinearEquiv.symm_image_image is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_image_image ContinuousLinearEquiv.symm_image_imageₓ'. -/
@[simp]
theorem symm_image_image (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₁) : e.symm '' (e '' s) = s :=
e.toLinearEquiv.toEquiv.symm_image_image s
#align continuous_linear_equiv.symm_image_image ContinuousLinearEquiv.symm_image_image
-/- warning: continuous_linear_equiv.image_symm_image -> ContinuousLinearEquiv.image_symm_image is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.image_symm_image ContinuousLinearEquiv.image_symm_imageₓ'. -/
@[simp]
theorem image_symm_image (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₂) : e '' (e.symm '' s) = s :=
e.symm.symm_image_image s
@@ -2871,9 +2165,6 @@ theorem image_symm_image (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₂) : e '' (
include σ₃₂ σ₃₁
-/- warning: continuous_linear_equiv.comp_coe -> ContinuousLinearEquiv.comp_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.comp_coe ContinuousLinearEquiv.comp_coeₓ'. -/
@[simp, norm_cast]
theorem comp_coe (f : M₁ ≃SL[σ₁₂] M₂) (f' : M₂ ≃SL[σ₂₃] M₃) :
(f' : M₂ →SL[σ₂₃] M₃).comp (f : M₁ →SL[σ₁₂] M₂) = (f.trans f' : M₁ →SL[σ₁₃] M₃) :=
@@ -2882,18 +2173,12 @@ theorem comp_coe (f : M₁ ≃SL[σ₁₂] M₂) (f' : M₂ ≃SL[σ₂₃] M₃
omit σ₃₂ σ₃₁ σ₂₁
-/- warning: continuous_linear_equiv.coe_comp_coe_symm -> ContinuousLinearEquiv.coe_comp_coe_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_comp_coe_symm ContinuousLinearEquiv.coe_comp_coe_symmₓ'. -/
@[simp]
theorem coe_comp_coe_symm (e : M₁ ≃SL[σ₁₂] M₂) :
(e : M₁ →SL[σ₁₂] M₂).comp (e.symm : M₂ →SL[σ₂₁] M₁) = ContinuousLinearMap.id R₂ M₂ :=
ContinuousLinearMap.ext e.apply_symm_apply
#align continuous_linear_equiv.coe_comp_coe_symm ContinuousLinearEquiv.coe_comp_coe_symm
-/- warning: continuous_linear_equiv.coe_symm_comp_coe -> ContinuousLinearEquiv.coe_symm_comp_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_symm_comp_coe ContinuousLinearEquiv.coe_symm_comp_coeₓ'. -/
@[simp]
theorem coe_symm_comp_coe (e : M₁ ≃SL[σ₁₂] M₂) :
(e.symm : M₂ →SL[σ₂₁] M₁).comp (e : M₁ →SL[σ₁₂] M₂) = ContinuousLinearMap.id R₁ M₁ :=
@@ -2902,25 +2187,16 @@ theorem coe_symm_comp_coe (e : M₁ ≃SL[σ₁₂] M₂) :
include σ₂₁
-/- warning: continuous_linear_equiv.symm_comp_self -> ContinuousLinearEquiv.symm_comp_self is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_comp_self ContinuousLinearEquiv.symm_comp_selfₓ'. -/
@[simp]
theorem symm_comp_self (e : M₁ ≃SL[σ₁₂] M₂) : (e.symm : M₂ → M₁) ∘ (e : M₁ → M₂) = id := by ext x;
exact symm_apply_apply e x
#align continuous_linear_equiv.symm_comp_self ContinuousLinearEquiv.symm_comp_self
-/- warning: continuous_linear_equiv.self_comp_symm -> ContinuousLinearEquiv.self_comp_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.self_comp_symm ContinuousLinearEquiv.self_comp_symmₓ'. -/
@[simp]
theorem self_comp_symm (e : M₁ ≃SL[σ₁₂] M₂) : (e : M₁ → M₂) ∘ (e.symm : M₂ → M₁) = id := by ext x;
exact apply_symm_apply e x
#align continuous_linear_equiv.self_comp_symm ContinuousLinearEquiv.self_comp_symm
-/- warning: continuous_linear_equiv.symm_symm -> ContinuousLinearEquiv.symm_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_symm ContinuousLinearEquiv.symm_symmₓ'. -/
@[simp]
theorem symm_symm (e : M₁ ≃SL[σ₁₂] M₂) : e.symm.symm = e := by ext x; rfl
#align continuous_linear_equiv.symm_symm ContinuousLinearEquiv.symm_symm
@@ -2936,62 +2212,38 @@ theorem refl_symm : (ContinuousLinearEquiv.refl R₁ M₁).symm = ContinuousLine
include σ₂₁
-/- warning: continuous_linear_equiv.symm_symm_apply -> ContinuousLinearEquiv.symm_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_symm_apply ContinuousLinearEquiv.symm_symm_applyₓ'. -/
theorem symm_symm_apply (e : M₁ ≃SL[σ₁₂] M₂) (x : M₁) : e.symm.symm x = e x :=
rfl
#align continuous_linear_equiv.symm_symm_apply ContinuousLinearEquiv.symm_symm_apply
-/- warning: continuous_linear_equiv.symm_apply_eq -> ContinuousLinearEquiv.symm_apply_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_apply_eq ContinuousLinearEquiv.symm_apply_eqₓ'. -/
theorem symm_apply_eq (e : M₁ ≃SL[σ₁₂] M₂) {x y} : e.symm x = y ↔ x = e y :=
e.toLinearEquiv.symm_apply_eq
#align continuous_linear_equiv.symm_apply_eq ContinuousLinearEquiv.symm_apply_eq
-/- warning: continuous_linear_equiv.eq_symm_apply -> ContinuousLinearEquiv.eq_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.eq_symm_apply ContinuousLinearEquiv.eq_symm_applyₓ'. -/
theorem eq_symm_apply (e : M₁ ≃SL[σ₁₂] M₂) {x y} : y = e.symm x ↔ e y = x :=
e.toLinearEquiv.eq_symm_apply
#align continuous_linear_equiv.eq_symm_apply ContinuousLinearEquiv.eq_symm_apply
-/- warning: continuous_linear_equiv.image_eq_preimage -> ContinuousLinearEquiv.image_eq_preimage is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.image_eq_preimage ContinuousLinearEquiv.image_eq_preimageₓ'. -/
protected theorem image_eq_preimage (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₁) : e '' s = e.symm ⁻¹' s :=
e.toLinearEquiv.toEquiv.image_eq_preimage s
#align continuous_linear_equiv.image_eq_preimage ContinuousLinearEquiv.image_eq_preimage
-/- warning: continuous_linear_equiv.image_symm_eq_preimage -> ContinuousLinearEquiv.image_symm_eq_preimage is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.image_symm_eq_preimage ContinuousLinearEquiv.image_symm_eq_preimageₓ'. -/
protected theorem image_symm_eq_preimage (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₂) :
e.symm '' s = e ⁻¹' s := by rw [e.symm.image_eq_preimage, e.symm_symm]
#align continuous_linear_equiv.image_symm_eq_preimage ContinuousLinearEquiv.image_symm_eq_preimage
-/- warning: continuous_linear_equiv.symm_preimage_preimage -> ContinuousLinearEquiv.symm_preimage_preimage is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_preimage_preimage ContinuousLinearEquiv.symm_preimage_preimageₓ'. -/
@[simp]
protected theorem symm_preimage_preimage (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₂) :
e.symm ⁻¹' (e ⁻¹' s) = s :=
e.toLinearEquiv.toEquiv.symm_preimage_preimage s
#align continuous_linear_equiv.symm_preimage_preimage ContinuousLinearEquiv.symm_preimage_preimage
-/- warning: continuous_linear_equiv.preimage_symm_preimage -> ContinuousLinearEquiv.preimage_symm_preimage is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.preimage_symm_preimage ContinuousLinearEquiv.preimage_symm_preimageₓ'. -/
@[simp]
protected theorem preimage_symm_preimage (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₁) :
e ⁻¹' (e.symm ⁻¹' s) = s :=
e.symm.symm_preimage_preimage s
#align continuous_linear_equiv.preimage_symm_preimage ContinuousLinearEquiv.preimage_symm_preimage
-/- warning: continuous_linear_equiv.uniform_embedding -> ContinuousLinearEquiv.uniformEmbedding is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.uniform_embedding ContinuousLinearEquiv.uniformEmbeddingₓ'. -/
protected theorem uniformEmbedding {E₁ E₂ : Type _} [UniformSpace E₁] [UniformSpace E₂]
[AddCommGroup E₁] [AddCommGroup E₂] [Module R₁ E₁] [Module R₂ E₂] [UniformAddGroup E₁]
[UniformAddGroup E₂] (e : E₁ ≃SL[σ₁₂] E₂) : UniformEmbedding e :=
@@ -2999,9 +2251,6 @@ protected theorem uniformEmbedding {E₁ E₂ : Type _} [UniformSpace E₁] [Uni
e.symm.toContinuousLinearMap.UniformContinuous
#align continuous_linear_equiv.uniform_embedding ContinuousLinearEquiv.uniformEmbedding
-/- warning: linear_equiv.uniform_embedding -> LinearEquiv.uniformEmbedding is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_equiv.uniform_embedding LinearEquiv.uniformEmbeddingₓ'. -/
protected theorem LinearEquiv.uniformEmbedding {E₁ E₂ : Type _} [UniformSpace E₁] [UniformSpace E₂]
[AddCommGroup E₁] [AddCommGroup E₂] [Module R₁ E₁] [Module R₂ E₂] [UniformAddGroup E₁]
[UniformAddGroup E₂] (e : E₁ ≃ₛₗ[σ₁₂] E₂) (h₁ : Continuous e) (h₂ : Continuous e.symm) :
@@ -3015,9 +2264,6 @@ protected theorem LinearEquiv.uniformEmbedding {E₁ E₂ : Type _} [UniformSpac
omit σ₂₁
-/- warning: continuous_linear_equiv.equiv_of_inverse -> ContinuousLinearEquiv.equivOfInverse is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.equiv_of_inverse ContinuousLinearEquiv.equivOfInverseₓ'. -/
/-- Create a `continuous_linear_equiv` from two `continuous_linear_map`s that are
inverse of each other. -/
def equivOfInverse (f₁ : M₁ →SL[σ₁₂] M₂) (f₂ : M₂ →SL[σ₂₁] M₁) (h₁ : Function.LeftInverse f₂ f₁)
@@ -3033,18 +2279,12 @@ def equivOfInverse (f₁ : M₁ →SL[σ₁₂] M₂) (f₂ : M₂ →SL[σ₂
include σ₂₁
-/- warning: continuous_linear_equiv.equiv_of_inverse_apply -> ContinuousLinearEquiv.equivOfInverse_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.equiv_of_inverse_apply ContinuousLinearEquiv.equivOfInverse_applyₓ'. -/
@[simp]
theorem equivOfInverse_apply (f₁ : M₁ →SL[σ₁₂] M₂) (f₂ h₁ h₂ x) :
equivOfInverse f₁ f₂ h₁ h₂ x = f₁ x :=
rfl
#align continuous_linear_equiv.equiv_of_inverse_apply ContinuousLinearEquiv.equivOfInverse_apply
-/- warning: continuous_linear_equiv.symm_equiv_of_inverse -> ContinuousLinearEquiv.symm_equivOfInverse is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_equiv_of_inverse ContinuousLinearEquiv.symm_equivOfInverseₓ'. -/
@[simp]
theorem symm_equivOfInverse (f₁ : M₁ →SL[σ₁₂] M₂) (f₂ h₁ h₂) :
(equivOfInverse f₁ f₂ h₁ h₂).symm = equivOfInverse f₂ f₁ h₂ h₁ :=
@@ -3115,9 +2355,6 @@ variable {R : Type _} [Semiring R] {M : Type _} [TopologicalSpace M] [AddCommGro
variable [TopologicalAddGroup M₄]
-/- warning: continuous_linear_equiv.skew_prod -> ContinuousLinearEquiv.skewProd is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.skew_prod ContinuousLinearEquiv.skewProdₓ'. -/
/-- Equivalence given by a block lower diagonal matrix. `e` and `e'` are diagonal square blocks,
and `f` is a rectangular block below the diagonal. -/
def skewProd (e : M ≃L[R] M₂) (e' : M₃ ≃L[R] M₄) (f : M →L[R] M₄) : (M × M₃) ≃L[R] M₂ × M₄ :=
@@ -3133,18 +2370,12 @@ def skewProd (e : M ≃L[R] M₂) (e' : M₃ ≃L[R] M₄) (f : M →L[R] M₄)
continuous_snd.sub <| f.Continuous.comp <| e.continuous_invFun.comp continuous_fst) }
#align continuous_linear_equiv.skew_prod ContinuousLinearEquiv.skewProd
-/- warning: continuous_linear_equiv.skew_prod_apply -> ContinuousLinearEquiv.skewProd_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.skew_prod_apply ContinuousLinearEquiv.skewProd_applyₓ'. -/
@[simp]
theorem skewProd_apply (e : M ≃L[R] M₂) (e' : M₃ ≃L[R] M₄) (f : M →L[R] M₄) (x) :
e.skewProd e' f x = (e x.1, e' x.2 + f x.1) :=
rfl
#align continuous_linear_equiv.skew_prod_apply ContinuousLinearEquiv.skewProd_apply
-/- warning: continuous_linear_equiv.skew_prod_symm_apply -> ContinuousLinearEquiv.skewProd_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.skew_prod_symm_apply ContinuousLinearEquiv.skewProd_symm_applyₓ'. -/
@[simp]
theorem skewProd_symm_apply (e : M ≃L[R] M₂) (e' : M₃ ≃L[R] M₄) (f : M →L[R] M₄) (x) :
(e.skewProd e' f).symm x = (e.symm x.1, e'.symm (x.2 - f (e.symm x.1))) :=
@@ -3162,17 +2393,11 @@ variable {σ₁₂ : R →+* R₂} {σ₂₁ : R₂ →+* R} [RingHomInvPair σ
include σ₂₁
-/- warning: continuous_linear_equiv.map_sub -> ContinuousLinearEquiv.map_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_sub ContinuousLinearEquiv.map_subₓ'. -/
@[simp]
theorem map_sub (e : M ≃SL[σ₁₂] M₂) (x y : M) : e (x - y) = e x - e y :=
(e : M →SL[σ₁₂] M₂).map_sub x y
#align continuous_linear_equiv.map_sub ContinuousLinearEquiv.map_sub
-/- warning: continuous_linear_equiv.map_neg -> ContinuousLinearEquiv.map_neg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_neg ContinuousLinearEquiv.map_negₓ'. -/
@[simp]
theorem map_neg (e : M ≃SL[σ₁₂] M₂) (x : M) : e (-x) = -e x :=
(e : M →SL[σ₁₂] M₂).map_neg x
@@ -3188,12 +2413,6 @@ section
variable [TopologicalAddGroup M]
-/- warning: continuous_linear_equiv.of_unit -> ContinuousLinearEquiv.ofUnit is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_11 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)], (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) -> (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.ofUnit._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.ofUnit._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.of_unit ContinuousLinearEquiv.ofUnitₓ'. -/
/-- An invertible continuous linear map `f` determines a continuous equivalence from `M` to itself.
-/
def ofUnit (f : (M →L[R] M)ˣ) : M ≃L[R] M
@@ -3209,12 +2428,6 @@ def ofUnit (f : (M →L[R] M)ˣ) : M ≃L[R] M
continuous_invFun := f.inv.Continuous
#align continuous_linear_equiv.of_unit ContinuousLinearEquiv.ofUnit
-/- warning: continuous_linear_equiv.to_unit -> ContinuousLinearEquiv.toUnit is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_11 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)], (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.toUnit._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.toUnit._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) -> (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11)))
-but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)], (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) -> (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.to_unit ContinuousLinearEquiv.toUnitₓ'. -/
/-- A continuous equivalence from `M` to itself determines an invertible continuous linear map. -/
def toUnit (f : M ≃L[R] M) : (M →L[R] M)ˣ where
val := f
@@ -3225,9 +2438,6 @@ def toUnit (f : M ≃L[R] M) : (M →L[R] M)ˣ where
variable (R M)
-/- warning: continuous_linear_equiv.units_equiv -> ContinuousLinearEquiv.unitsEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv ContinuousLinearEquiv.unitsEquivₓ'. -/
/-- The units of the algebra of continuous `R`-linear endomorphisms of `M` is multiplicatively
equivalent to the type of continuous linear equivalences between `M` and itself. -/
def unitsEquiv : (M →L[R] M)ˣ ≃* M ≃L[R] M
@@ -3239,9 +2449,6 @@ def unitsEquiv : (M →L[R] M)ˣ ≃* M ≃L[R] M
map_mul' x y := by ext; rfl
#align continuous_linear_equiv.units_equiv ContinuousLinearEquiv.unitsEquiv
-/- warning: continuous_linear_equiv.units_equiv_apply -> ContinuousLinearEquiv.unitsEquiv_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv_apply ContinuousLinearEquiv.unitsEquiv_applyₓ'. -/
@[simp]
theorem unitsEquiv_apply (f : (M →L[R] M)ˣ) (x : M) : unitsEquiv R M f x = f x :=
rfl
@@ -3253,12 +2460,6 @@ section
variable (R) [TopologicalSpace R] [ContinuousMul R]
-/- warning: continuous_linear_equiv.units_equiv_aut -> ContinuousLinearEquiv.unitsEquivAut is a dubious translation:
-lean 3 declaration is
- forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))], Equiv.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))
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-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv_aut ContinuousLinearEquiv.unitsEquivAutₓ'. -/
/-- Continuous linear equivalences `R ≃L[R] R` are enumerated by `Rˣ`. -/
def unitsEquivAut : Rˣ ≃ R ≃L[R] R
where
@@ -3274,25 +2475,16 @@ def unitsEquivAut : Rˣ ≃ R ≃L[R] R
variable {R}
-/- warning: continuous_linear_equiv.units_equiv_aut_apply -> ContinuousLinearEquiv.unitsEquivAut_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv_aut_apply ContinuousLinearEquiv.unitsEquivAut_applyₓ'. -/
@[simp]
theorem unitsEquivAut_apply (u : Rˣ) (x : R) : unitsEquivAut R u x = x * u :=
rfl
#align continuous_linear_equiv.units_equiv_aut_apply ContinuousLinearEquiv.unitsEquivAut_apply
-/- warning: continuous_linear_equiv.units_equiv_aut_apply_symm -> ContinuousLinearEquiv.unitsEquivAut_apply_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv_aut_apply_symm ContinuousLinearEquiv.unitsEquivAut_apply_symmₓ'. -/
@[simp]
theorem unitsEquivAut_apply_symm (u : Rˣ) (x : R) : (unitsEquivAut R u).symm x = x * ↑u⁻¹ :=
rfl
#align continuous_linear_equiv.units_equiv_aut_apply_symm ContinuousLinearEquiv.unitsEquivAut_apply_symm
-/- warning: continuous_linear_equiv.units_equiv_aut_symm_apply -> ContinuousLinearEquiv.unitsEquivAut_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv_aut_symm_apply ContinuousLinearEquiv.unitsEquivAut_symm_applyₓ'. -/
@[simp]
theorem unitsEquivAut_symm_apply (e : R ≃L[R] R) : ↑((unitsEquivAut R).symm e) = e 1 :=
rfl
@@ -3306,9 +2498,6 @@ open _Root_.ContinuousLinearMap (id fst snd)
open _Root_.LinearMap (mem_ker)
-/- warning: continuous_linear_equiv.equiv_of_right_inverse -> ContinuousLinearEquiv.equivOfRightInverse is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.equiv_of_right_inverse ContinuousLinearEquiv.equivOfRightInverseₓ'. -/
/-- A pair of continuous linear maps such that `f₁ ∘ f₂ = id` generates a continuous
linear equivalence `e` between `M` and `M₂ × f₁.ker` such that `(e x).2 = x` for `x ∈ f₁.ker`,
`(e x).1 = f₁ x`, and `(e (f₂ y)).2 = 0`. The map is given by `e x = (f₁ x, x - f₂ (f₁ x))`. -/
@@ -3318,18 +2507,12 @@ def equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M) (h : Fun
(fun x => by simp) fun ⟨x, y⟩ => by simp [h x]
#align continuous_linear_equiv.equiv_of_right_inverse ContinuousLinearEquiv.equivOfRightInverse
-/- warning: continuous_linear_equiv.fst_equiv_of_right_inverse -> ContinuousLinearEquiv.fst_equivOfRightInverse is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.fst_equiv_of_right_inverse ContinuousLinearEquiv.fst_equivOfRightInverseₓ'. -/
@[simp]
theorem fst_equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
(h : Function.RightInverse f₂ f₁) (x : M) : (equivOfRightInverse f₁ f₂ h x).1 = f₁ x :=
rfl
#align continuous_linear_equiv.fst_equiv_of_right_inverse ContinuousLinearEquiv.fst_equivOfRightInverse
-/- warning: continuous_linear_equiv.snd_equiv_of_right_inverse -> ContinuousLinearEquiv.snd_equivOfRightInverse is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.snd_equiv_of_right_inverse ContinuousLinearEquiv.snd_equivOfRightInverseₓ'. -/
@[simp]
theorem snd_equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
(h : Function.RightInverse f₂ f₁) (x : M) :
@@ -3337,9 +2520,6 @@ theorem snd_equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
rfl
#align continuous_linear_equiv.snd_equiv_of_right_inverse ContinuousLinearEquiv.snd_equivOfRightInverse
-/- warning: continuous_linear_equiv.equiv_of_right_inverse_symm_apply -> ContinuousLinearEquiv.equivOfRightInverse_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.equiv_of_right_inverse_symm_apply ContinuousLinearEquiv.equivOfRightInverse_symm_applyₓ'. -/
@[simp]
theorem equivOfRightInverse_symm_apply (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
(h : Function.RightInverse f₂ f₁) (y : M₂ × ker f₁) :
@@ -3363,17 +2543,11 @@ def funUnique : (ι → M) ≃L[R] M :=
variable {ι R M}
-/- warning: continuous_linear_equiv.coe_fun_unique -> ContinuousLinearEquiv.coe_funUnique is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_fun_unique ContinuousLinearEquiv.coe_funUniqueₓ'. -/
@[simp]
theorem coe_funUnique : ⇑(funUnique ι R M) = Function.eval default :=
rfl
#align continuous_linear_equiv.coe_fun_unique ContinuousLinearEquiv.coe_funUnique
-/- warning: continuous_linear_equiv.coe_fun_unique_symm -> ContinuousLinearEquiv.coe_funUnique_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_fun_unique_symm ContinuousLinearEquiv.coe_funUnique_symmₓ'. -/
@[simp]
theorem coe_funUnique_symm : ⇑(funUnique ι R M).symm = Function.const ι :=
rfl
@@ -3381,9 +2555,6 @@ theorem coe_funUnique_symm : ⇑(funUnique ι R M).symm = Function.const ι :=
variable (R M)
-/- warning: continuous_linear_equiv.pi_fin_two -> ContinuousLinearEquiv.piFinTwo is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.pi_fin_two ContinuousLinearEquiv.piFinTwoₓ'. -/
/-- Continuous linear equivalence between dependent functions `Π i : fin 2, M i` and `M 0 × M 1`. -/
@[simps (config := { fullyApplied := false })]
def piFinTwo (M : Fin 2 → Type _) [∀ i, AddCommMonoid (M i)] [∀ i, Module R (M i)]
@@ -3391,12 +2562,6 @@ def piFinTwo (M : Fin 2 → Type _) [∀ i, AddCommMonoid (M i)] [∀ i, Module
{ Homeomorph.piFinTwo M with toLinearEquiv := LinearEquiv.piFinTwo R M }
#align continuous_linear_equiv.pi_fin_two ContinuousLinearEquiv.piFinTwo
-/- warning: continuous_linear_equiv.fin_two_arrow -> ContinuousLinearEquiv.finTwoArrow is a dubious translation:
-lean 3 declaration is
- forall (R : Type.{u1}) (M : Type.{u2}) [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], ContinuousLinearEquiv.{u1, u1, u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) ((Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> M) (Pi.topologicalSpace.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => M) (fun (a : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => _inst_5)) (Pi.addCommMonoid.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => M) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => _inst_3)) (Prod.{u2, u2} M M) (Prod.topologicalSpace.{u2, u2} M M _inst_5 _inst_5) (Prod.addCommMonoid.{u2, u2} M M _inst_3 _inst_3) (Pi.Function.module.{0, u1, u2} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) R M _inst_2 _inst_3 _inst_4) (Prod.module.{u1, u2, u2} R M M _inst_2 _inst_3 _inst_3 _inst_4 _inst_4)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.fin_two_arrow ContinuousLinearEquiv.finTwoArrowₓ'. -/
/-- Continuous linear equivalence between vectors in `M² = fin 2 → M` and `M × M`. -/
@[simps (config := { fullyApplied := false })]
def finTwoArrow : (Fin 2 → M) ≃L[R] M × M :=
@@ -3431,9 +2596,6 @@ noncomputable def inverse : (M →L[R] M₂) → M₂ →L[R] M := fun f =>
#align continuous_linear_map.inverse ContinuousLinearMap.inverse
-/
-/- warning: continuous_linear_map.inverse_equiv -> ContinuousLinearMap.inverse_equiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.inverse_equiv ContinuousLinearMap.inverse_equivₓ'. -/
/-- By definition, if `f` is invertible then `inverse f = f.symm`. -/
@[simp]
theorem inverse_equiv (e : M ≃L[R] M₂) : inverse (e : M →L[R] M₂) = e.symm :=
@@ -3444,9 +2606,6 @@ theorem inverse_equiv (e : M ≃L[R] M₂) : inverse (e : M →L[R] M₂) = e.sy
exact_mod_cast Classical.choose_spec h
#align continuous_linear_map.inverse_equiv ContinuousLinearMap.inverse_equiv
-/- warning: continuous_linear_map.inverse_non_equiv -> ContinuousLinearMap.inverse_non_equiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.inverse_non_equiv ContinuousLinearMap.inverse_non_equivₓ'. -/
/-- By definition, if `f` is not invertible then `inverse f = 0`. -/
@[simp]
theorem inverse_non_equiv (f : M →L[R] M₂) (h : ¬∃ e' : M ≃L[R] M₂, ↑e' = f) : inverse f = 0 :=
@@ -3463,9 +2622,6 @@ variable [AddCommGroup M] [TopologicalAddGroup M] [Module R M]
variable [AddCommGroup M₂] [Module R M₂]
-/- warning: continuous_linear_map.ring_inverse_equiv -> ContinuousLinearMap.ring_inverse_equiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ring_inverse_equiv ContinuousLinearMap.ring_inverse_equivₓ'. -/
@[simp]
theorem ring_inverse_equiv (e : M ≃L[R] M) : Ring.inverse ↑e = inverse (e : M →L[R] M) :=
by
@@ -3475,9 +2631,6 @@ theorem ring_inverse_equiv (e : M ≃L[R] M) : Ring.inverse ↑e = inverse (e :
rfl
#align continuous_linear_map.ring_inverse_equiv ContinuousLinearMap.ring_inverse_equiv
-/- warning: continuous_linear_map.to_ring_inverse -> ContinuousLinearMap.to_ring_inverse is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.to_ring_inverse ContinuousLinearMap.to_ring_inverseₓ'. -/
/-- The function `continuous_linear_equiv.inverse` can be written in terms of `ring.inverse` for the
ring of self-maps of the domain. -/
theorem to_ring_inverse (e : M ≃L[R] M₂) (f : M →L[R] M₂) :
@@ -3497,12 +2650,6 @@ theorem to_ring_inverse (e : M ≃L[R] M₂) (f : M →L[R] M₂) :
dsimp; rw [coeFn_coe_base' F, hF]; simp
#align continuous_linear_map.to_ring_inverse ContinuousLinearMap.to_ring_inverse
-/- warning: continuous_linear_map.ring_inverse_eq_map_inverse -> ContinuousLinearMap.ring_inverse_eq_map_inverse is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} M] [_inst_3 : Ring.{u1} R] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : TopologicalAddGroup.{u2} M _inst_1 (AddCommGroup.toAddGroup.{u2} M _inst_4)] [_inst_6 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)], Eq.{succ u2} ((ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) -> (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6)) (Ring.inverse.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_3) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6)) (ContinuousLinearMap.inverse.{u1, u2, u2} R M M _inst_1 _inst_1 (Ring.toSemiring.{u1} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6)
-but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} M] [_inst_3 : Ring.{u1} R] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)], Eq.{succ u2} ((ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) -> (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5)) (Ring.inverse.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_3) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) (ContinuousLinearMap.inverse.{u1, u2, u2} R M M _inst_1 _inst_1 (Ring.toSemiring.{u1} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ring_inverse_eq_map_inverse ContinuousLinearMap.ring_inverse_eq_map_inverseₓ'. -/
theorem ring_inverse_eq_map_inverse : Ring.inverse = @inverse R M M _ _ _ _ _ _ _ :=
by
ext
@@ -3527,12 +2674,6 @@ def ClosedComplemented (p : Submodule R M) : Prop :=
#align submodule.closed_complemented Submodule.ClosedComplemented
-/
-/- warning: submodule.closed_complemented.has_closed_complement -> Submodule.ClosedComplemented.has_closed_complement is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align submodule.closed_complemented.has_closed_complement Submodule.ClosedComplemented.has_closed_complementₓ'. -/
theorem ClosedComplemented.has_closed_complement {p : Submodule R M} [T1Space p]
(h : ClosedComplemented p) : ∃ (q : Submodule R M)(hq : IsClosed (q : Set M)), IsCompl p q :=
Exists.elim h fun f hf => ⟨ker f, f.isClosed_ker, LinearMap.isCompl_of_proj hf⟩
@@ -3548,23 +2689,11 @@ protected theorem ClosedComplemented.isClosed [TopologicalAddGroup M] [T1Space M
#align submodule.closed_complemented.is_closed Submodule.ClosedComplemented.isClosed
-/
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@[simp]
theorem closedComplemented_bot : ClosedComplemented (⊥ : Submodule R M) :=
⟨0, fun x => by simp only [zero_apply, eq_zero_of_bot_submodule x]⟩
#align submodule.closed_complemented_bot Submodule.closedComplemented_bot
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-Case conversion may be inaccurate. Consider using '#align submodule.closed_complemented_top Submodule.closedComplemented_topₓ'. -/
@[simp]
theorem closedComplemented_top : ClosedComplemented (⊤ : Submodule R M) :=
⟨(id R M).codRestrict ⊤ fun x => trivial, fun x => Subtype.ext_iff_val.2 <| by simp⟩
@@ -3572,9 +2701,6 @@ theorem closedComplemented_top : ClosedComplemented (⊤ : Submodule R M) :=
end Submodule
-/- warning: continuous_linear_map.closed_complemented_ker_of_right_inverse -> ContinuousLinearMap.closedComplemented_ker_of_rightInverse is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.closed_complemented_ker_of_right_inverse ContinuousLinearMap.closedComplemented_ker_of_rightInverseₓ'. -/
theorem ContinuousLinearMap.closedComplemented_ker_of_rightInverse {R : Type _} [Ring R]
{M : Type _} [TopologicalSpace M] [AddCommGroup M] {M₂ : Type _} [TopologicalSpace M₂]
[AddCommGroup M₂] [Module R M] [Module R M₂] [TopologicalAddGroup M] (f₁ : M →L[R] M₂)
@@ -3589,12 +2715,6 @@ namespace Submodule
variable {R M : Type _} [Ring R] [AddCommGroup M] [Module R M] [TopologicalSpace M]
(S : Submodule R M)
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- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : TopologicalSpace.{u2} M] (S : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : TopologicalAddGroup.{u2} M _inst_4 (AddCommGroup.toAddGroup.{u2} M _inst_2)], IsOpenMap.{u2, u2} M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) _inst_4 (Quotient.topologicalSpace.{u2} M (Submodule.quotientRel.{u1, u2} R M _inst_1 _inst_2 _inst_3 S) _inst_4) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) => M -> (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 S))
-but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : TopologicalSpace.{u2} M] (S : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : TopologicalAddGroup.{u2} M _inst_4 (AddCommGroup.toAddGroup.{u2} M _inst_2)], IsOpenMap.{u2, u2} M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) _inst_4 (QuotientModule.Quotient.topologicalSpace.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 S) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 S))
-Case conversion may be inaccurate. Consider using '#align submodule.is_open_map_mkq Submodule.isOpenMap_mkQₓ'. -/
theorem isOpenMap_mkQ [TopologicalAddGroup M] : IsOpenMap S.mkQ :=
QuotientAddGroup.isOpenMap_coe S.toAddSubgroup
#align submodule.is_open_map_mkq Submodule.isOpenMap_mkQ
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -65,16 +65,11 @@ theorem ContinuousSMul.of_nhds_zero [TopologicalRing R] [TopologicalAddGroup M]
rintro ⟨a, m⟩
simp [sub_smul, smul_sub]
abel
- rw [funext key]
- clear key
+ rw [funext key]; clear key
refine' tendsto_const_nhds.add (tendsto.add (tendsto.add _ _) _)
· rw [sub_self, zero_smul]
apply (hmulleft m₀).comp
- rw [show (fun p : R × M => p.1 - a₀) = (fun a => a - a₀) ∘ Prod.fst
- by
- ext
- rfl,
- nhds_prod_eq]
+ rw [show (fun p : R × M => p.1 - a₀) = (fun a => a - a₀) ∘ Prod.fst by ext; rfl, nhds_prod_eq]
have : tendsto (fun a => a - a₀) (𝓝 a₀) (𝓝 0) :=
by
rw [← sub_self a₀]
@@ -82,11 +77,7 @@ theorem ContinuousSMul.of_nhds_zero [TopologicalRing R] [TopologicalAddGroup M]
exact this.comp tendsto_fst
· rw [sub_self, smul_zero]
apply (hmulright a₀).comp
- rw [show (fun p : R × M => p.2 - m₀) = (fun m => m - m₀) ∘ Prod.snd
- by
- ext
- rfl,
- nhds_prod_eq]
+ rw [show (fun p : R × M => p.2 - m₀) = (fun m => m - m₀) ∘ Prod.snd by ext; rfl, nhds_prod_eq]
have : tendsto (fun m => m - m₀) (𝓝 m₀) (𝓝 0) :=
by
rw [← sub_self m₀]
@@ -96,9 +87,7 @@ theorem ContinuousSMul.of_nhds_zero [TopologicalRing R] [TopologicalAddGroup M]
show
(fun p : R × M => (p.fst - a₀) • (p.snd - m₀)) =
(fun p : R × M => p.1 • p.2) ∘ Prod.map (fun a => a - a₀) fun m => m - m₀
- by
- ext
- rfl]
+ by ext; rfl]
apply hmul.comp (tendsto.prod_map _ _) <;>
· rw [← sub_self]
exact tendsto_id.sub tendsto_const_nhds⟩
@@ -326,10 +315,8 @@ but is expected to have type
Case conversion may be inaccurate. Consider using '#align submodule.dense_iff_topological_closure_eq_top Submodule.dense_iff_topologicalClosure_eq_topₓ'. -/
/-- A subspace is dense iff its topological closure is the entire space. -/
theorem Submodule.dense_iff_topologicalClosure_eq_top {s : Submodule R M} :
- Dense (s : Set M) ↔ s.topologicalClosure = ⊤ :=
- by
- rw [← SetLike.coe_set_eq, dense_iff_closure_eq]
- simp
+ Dense (s : Set M) ↔ s.topologicalClosure = ⊤ := by
+ rw [← SetLike.coe_set_eq, dense_iff_closure_eq]; simp
#align submodule.dense_iff_topological_closure_eq_top Submodule.dense_iff_topologicalClosure_eq_top
instance {M' : Type _} [AddCommMonoid M'] [Module R M'] [UniformSpace M'] [ContinuousAdd M']
@@ -369,10 +356,8 @@ theorem LinearMap.continuous_on_pi {ι : Type _} {R : Type _} {M : Type _} [Fini
classical
-- for the proof, write `f` in the standard basis, and use that each coordinate is a continuous
-- function.
- have : (f : (ι → R) → M) = fun x => ∑ i : ι, x i • f fun j => if i = j then 1 else 0 :=
- by
- ext x
- exact f.pi_apply_eq_sum_univ x
+ have : (f : (ι → R) → M) = fun x => ∑ i : ι, x i • f fun j => if i = j then 1 else 0 := by
+ ext x; exact f.pi_apply_eq_sum_univ x
rw [this]
refine' continuous_finset_sum _ fun i hi => _
exact (continuous_apply i).smul continuous_const
@@ -589,12 +574,8 @@ theorem [anonymous] (f : M₁ →SL[σ₁₂] M₂) : f.toLinearMap = f :=
/- warning: continuous_linear_map.coe_injective -> ContinuousLinearMap.coe_injective is a dubious translation:
<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_injective ContinuousLinearMap.coe_injectiveₓ'. -/
-theorem coe_injective : Function.Injective (coe : (M₁ →SL[σ₁₂] M₂) → M₁ →ₛₗ[σ₁₂] M₂) :=
- by
- intro f g H
- cases f
- cases g
- congr
+theorem coe_injective : Function.Injective (coe : (M₁ →SL[σ₁₂] M₂) → M₁ →ₛₗ[σ₁₂] M₂) := by
+ intro f g H; cases f; cases g; congr
#align continuous_linear_map.coe_injective ContinuousLinearMap.coe_injective
instance : ContinuousSemilinearMapClass (M₁ →SL[σ₁₂] M₂) σ₁₂ M₁ M₂
@@ -940,9 +921,7 @@ instance uniqueOfRight [Subsingleton M₂] : Unique (M₁ →SL[σ₁₂] M₂)
/- warning: continuous_linear_map.exists_ne_zero -> ContinuousLinearMap.exists_ne_zero is a dubious translation:
<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.exists_ne_zero ContinuousLinearMap.exists_ne_zeroₓ'. -/
-theorem exists_ne_zero {f : M₁ →SL[σ₁₂] M₂} (hf : f ≠ 0) : ∃ x, f x ≠ 0 :=
- by
- by_contra' h
+theorem exists_ne_zero {f : M₁ →SL[σ₁₂] M₂} (hf : f ≠ 0) : ∃ x, f x ≠ 0 := by by_contra' h;
exact hf (ContinuousLinearMap.ext h)
#align continuous_linear_map.exists_ne_zero ContinuousLinearMap.exists_ne_zero
@@ -1050,12 +1029,8 @@ instance : AddCommMonoid (M₁ →SL[σ₁₂] M₂)
add_assoc := by
intros <;> ext <;> apply_rules [zero_add, add_assoc, add_zero, add_left_neg, add_comm]
nsmul := (· • ·)
- nsmul_zero f := by
- ext
- simp
- nsmul_succ n f := by
- ext
- simp [Nat.succ_eq_one_add, add_smul]
+ nsmul_zero f := by ext; simp
+ nsmul_succ n f := by ext; simp [Nat.succ_eq_one_add, add_smul]
/- warning: continuous_linear_map.coe_sum -> ContinuousLinearMap.coe_sum is a dubious translation:
<too large>
@@ -1147,20 +1122,14 @@ include σ₁₃
<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_zero ContinuousLinearMap.comp_zeroₓ'. -/
@[simp]
-theorem comp_zero (g : M₂ →SL[σ₂₃] M₃) : g.comp (0 : M₁ →SL[σ₁₂] M₂) = 0 :=
- by
- ext
- simp
+theorem comp_zero (g : M₂ →SL[σ₂₃] M₃) : g.comp (0 : M₁ →SL[σ₁₂] M₂) = 0 := by ext; simp
#align continuous_linear_map.comp_zero ContinuousLinearMap.comp_zero
/- warning: continuous_linear_map.zero_comp -> ContinuousLinearMap.zero_comp is a dubious translation:
<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.zero_comp ContinuousLinearMap.zero_compₓ'. -/
@[simp]
-theorem zero_comp (f : M₁ →SL[σ₁₂] M₂) : (0 : M₂ →SL[σ₂₃] M₃).comp f = 0 :=
- by
- ext
- simp
+theorem zero_comp (f : M₁ →SL[σ₁₂] M₂) : (0 : M₂ →SL[σ₂₃] M₃).comp f = 0 := by ext; simp
#align continuous_linear_map.zero_comp ContinuousLinearMap.zero_comp
/- warning: continuous_linear_map.comp_add -> ContinuousLinearMap.comp_add is a dubious translation:
@@ -1168,10 +1137,7 @@ theorem zero_comp (f : M₁ →SL[σ₁₂] M₂) : (0 : M₂ →SL[σ₂₃] M
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_add ContinuousLinearMap.comp_addₓ'. -/
@[simp]
theorem comp_add [ContinuousAdd M₂] [ContinuousAdd M₃] (g : M₂ →SL[σ₂₃] M₃)
- (f₁ f₂ : M₁ →SL[σ₁₂] M₂) : g.comp (f₁ + f₂) = g.comp f₁ + g.comp f₂ :=
- by
- ext
- simp
+ (f₁ f₂ : M₁ →SL[σ₁₂] M₂) : g.comp (f₁ + f₂) = g.comp f₁ + g.comp f₂ := by ext; simp
#align continuous_linear_map.comp_add ContinuousLinearMap.comp_add
/- warning: continuous_linear_map.add_comp -> ContinuousLinearMap.add_comp is a dubious translation:
@@ -1179,9 +1145,7 @@ theorem comp_add [ContinuousAdd M₂] [ContinuousAdd M₃] (g : M₂ →SL[σ₂
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.add_comp ContinuousLinearMap.add_compₓ'. -/
@[simp]
theorem add_comp [ContinuousAdd M₃] (g₁ g₂ : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) :
- (g₁ + g₂).comp f = g₁.comp f + g₂.comp f := by
- ext
- simp
+ (g₁ + g₂).comp f = g₁.comp f + g₂.comp f := by ext; simp
#align continuous_linear_map.add_comp ContinuousLinearMap.add_comp
omit σ₁₃
@@ -1733,9 +1697,7 @@ Case conversion may be inaccurate. Consider using '#align continuous_linear_map.
theorem smulRight_comp [ContinuousMul R₁] {x : M₂} {c : R₁} :
(smulRight (1 : R₁ →L[R₁] R₁) x).comp (smulRight (1 : R₁ →L[R₁] R₁) c) =
smulRight (1 : R₁ →L[R₁] R₁) (c • x) :=
- by
- ext
- simp [mul_smul]
+ by ext; simp [mul_smul]
#align continuous_linear_map.smul_right_comp ContinuousLinearMap.smulRight_comp
end Semiring
@@ -1780,10 +1742,8 @@ theorem pi_apply (f : ∀ i, M →L[R] φ i) (c : M) (i : ι) : pi f c i = f i c
/- warning: continuous_linear_map.pi_eq_zero -> ContinuousLinearMap.pi_eq_zero is a dubious translation:
<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.pi_eq_zero ContinuousLinearMap.pi_eq_zeroₓ'. -/
-theorem pi_eq_zero (f : ∀ i, M →L[R] φ i) : pi f = 0 ↔ ∀ i, f i = 0 :=
- by
- simp only [ext_iff, pi_apply, Function.funext_iff]
- exact forall_swap
+theorem pi_eq_zero (f : ∀ i, M →L[R] φ i) : pi f = 0 ↔ ∀ i, f i = 0 := by
+ simp only [ext_iff, pi_apply, Function.funext_iff]; exact forall_swap
#align continuous_linear_map.pi_eq_zero ContinuousLinearMap.pi_eq_zero
/- warning: continuous_linear_map.pi_zero -> ContinuousLinearMap.pi_zero is a dubious translation:
@@ -1968,15 +1928,9 @@ instance : AddCommGroup (M →SL[σ₁₂] M₂) := by
sub_eq_add_neg := _
nsmul := (· • ·)
zsmul := (· • ·)
- zsmul_zero' := fun f => by
- ext
- simp
- zsmul_succ' := fun n f => by
- ext
- simp [add_smul, add_comm]
- zsmul_neg' := fun n f => by
- ext
- simp [Nat.succ_eq_add_one, add_smul].. } <;>
+ zsmul_zero' := fun f => by ext; simp
+ zsmul_succ' := fun n f => by ext; simp [add_smul, add_comm]
+ zsmul_neg' := fun n f => by ext; simp [Nat.succ_eq_add_one, add_smul].. } <;>
intros <;>
ext <;>
apply_rules [zero_add, add_assoc, add_zero, add_left_neg, add_comm, sub_eq_add_neg]
@@ -2011,10 +1965,7 @@ end
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_neg ContinuousLinearMap.comp_negₓ'. -/
@[simp]
theorem comp_neg [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₂] [TopologicalAddGroup M₃]
- (g : M₂ →SL[σ₂₃] M₃) (f : M →SL[σ₁₂] M₂) : g.comp (-f) = -g.comp f :=
- by
- ext
- simp
+ (g : M₂ →SL[σ₂₃] M₃) (f : M →SL[σ₁₂] M₂) : g.comp (-f) = -g.comp f := by ext; simp
#align continuous_linear_map.comp_neg ContinuousLinearMap.comp_neg
/- warning: continuous_linear_map.neg_comp -> ContinuousLinearMap.neg_comp is a dubious translation:
@@ -2022,10 +1973,7 @@ theorem comp_neg [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddG
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.neg_comp ContinuousLinearMap.neg_compₓ'. -/
@[simp]
theorem neg_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₃] (g : M₂ →SL[σ₂₃] M₃)
- (f : M →SL[σ₁₂] M₂) : (-g).comp f = -g.comp f :=
- by
- ext
- simp
+ (f : M →SL[σ₁₂] M₂) : (-g).comp f = -g.comp f := by ext; simp
#align continuous_linear_map.neg_comp ContinuousLinearMap.neg_comp
/- warning: continuous_linear_map.comp_sub -> ContinuousLinearMap.comp_sub is a dubious translation:
@@ -2033,10 +1981,8 @@ theorem neg_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddG
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_sub ContinuousLinearMap.comp_subₓ'. -/
@[simp]
theorem comp_sub [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₂] [TopologicalAddGroup M₃]
- (g : M₂ →SL[σ₂₃] M₃) (f₁ f₂ : M →SL[σ₁₂] M₂) : g.comp (f₁ - f₂) = g.comp f₁ - g.comp f₂ :=
- by
- ext
- simp
+ (g : M₂ →SL[σ₂₃] M₃) (f₁ f₂ : M →SL[σ₁₂] M₂) : g.comp (f₁ - f₂) = g.comp f₁ - g.comp f₂ := by
+ ext; simp
#align continuous_linear_map.comp_sub ContinuousLinearMap.comp_sub
/- warning: continuous_linear_map.sub_comp -> ContinuousLinearMap.sub_comp is a dubious translation:
@@ -2044,10 +1990,7 @@ theorem comp_sub [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddG
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.sub_comp ContinuousLinearMap.sub_compₓ'. -/
@[simp]
theorem sub_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₃] (g₁ g₂ : M₂ →SL[σ₂₃] M₃)
- (f : M →SL[σ₁₂] M₂) : (g₁ - g₂).comp f = g₁.comp f - g₂.comp f :=
- by
- ext
- simp
+ (f : M →SL[σ₁₂] M₂) : (g₁ - g₂).comp f = g₁.comp f - g₂.comp f := by ext; simp
#align continuous_linear_map.sub_comp ContinuousLinearMap.sub_comp
instance [TopologicalAddGroup M] : Ring (M →L[R] M) :=
@@ -2063,8 +2006,7 @@ theorem smulRight_one_pow [TopologicalSpace R] [TopologicalRing R] (c : R) (n :
smulRight (1 : R →L[R] R) c ^ n = smulRight (1 : R →L[R] R) (c ^ n) :=
by
induction' n with n ihn
- · ext
- simp
+ · ext; simp
· rw [pow_succ, ihn, mul_def, smul_right_comp, smul_eq_mul, pow_succ']
#align continuous_linear_map.smul_right_one_pow ContinuousLinearMap.smulRight_one_pow
@@ -2169,9 +2111,7 @@ variable [DistribMulAction S N₂] [ContinuousConstSMul S N₂] [SMulCommClass R
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_smul ContinuousLinearMap.comp_smulₓ'. -/
@[simp]
theorem comp_smul [LinearMap.CompatibleSMul N₂ N₃ S R] (hₗ : N₂ →L[R] N₃) (c : S)
- (fₗ : M →L[R] N₂) : hₗ.comp (c • fₗ) = c • hₗ.comp fₗ :=
- by
- ext x
+ (fₗ : M →L[R] N₂) : hₗ.comp (c • fₗ) = c • hₗ.comp fₗ := by ext x;
exact hₗ.map_smul_of_tower c (fₗ x)
#align continuous_linear_map.comp_smul ContinuousLinearMap.comp_smul
@@ -2183,8 +2123,7 @@ Case conversion may be inaccurate. Consider using '#align continuous_linear_map.
@[simp]
theorem comp_smulₛₗ [SMulCommClass R₂ R₂ M₂] [SMulCommClass R₃ R₃ M₃] [ContinuousConstSMul R₂ M₂]
[ContinuousConstSMul R₃ M₃] (h : M₂ →SL[σ₂₃] M₃) (c : R₂) (f : M →SL[σ₁₂] M₂) :
- h.comp (c • f) = σ₂₃ c • h.comp f := by
- ext x
+ h.comp (c • f) = σ₂₃ c • h.comp f := by ext x;
simp only [coe_smul', coe_comp', Function.comp_apply, Pi.smul_apply,
ContinuousLinearMap.map_smulₛₗ]
#align continuous_linear_map.comp_smulₛₗ ContinuousLinearMap.comp_smulₛₗ
@@ -2228,10 +2167,8 @@ def prodEquiv : (M →L[R] N₂) × (M →L[R] N₃) ≃ (M →L[R] N₂ × N₃
<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.prod_ext_iff ContinuousLinearMap.prod_ext_iffₓ'. -/
theorem prod_ext_iff {f g : M × N₂ →L[R] N₃} :
- f = g ↔ f.comp (inl _ _ _) = g.comp (inl _ _ _) ∧ f.comp (inr _ _ _) = g.comp (inr _ _ _) :=
- by
- simp only [← coe_inj, LinearMap.prod_ext_iff]
- rfl
+ f = g ↔ f.comp (inl _ _ _) = g.comp (inl _ _ _) ∧ f.comp (inr _ _ _) = g.comp (inr _ _ _) := by
+ simp only [← coe_inj, LinearMap.prod_ext_iff]; rfl
#align continuous_linear_map.prod_ext_iff ContinuousLinearMap.prod_ext_iff
/- warning: continuous_linear_map.prod_ext -> ContinuousLinearMap.prod_ext is a dubious translation:
@@ -2312,13 +2249,8 @@ sending `f` to `λ e, c e • f`. See also `continuous_linear_map.smul_rightL`.
def smulRightₗ (c : M →L[R] S) : M₂ →ₗ[T] M →L[R] M₂
where
toFun := c.smul_right
- map_add' x y := by
- ext e
- apply smul_add
- map_smul' a x := by
- ext e
- dsimp
- apply smul_comm
+ map_add' x y := by ext e; apply smul_add
+ map_smul' a x := by ext e; dsimp; apply smul_comm
#align continuous_linear_map.smul_rightₗ ContinuousLinearMap.smulRightₗ
/- warning: continuous_linear_map.coe_smul_rightₗ -> ContinuousLinearMap.coe_smulRightₗ is a dubious translation:
@@ -2480,10 +2412,7 @@ instance : ContinuousSemilinearEquivClass (M₁ ≃SL[σ₁₂] M₂) σ₁₂ M
coe f := f
inv f := f.invFun
coe_injective' f g h₁ h₂ := by
- cases' f with f' _
- cases' g with g' _
- cases f'
- cases g'
+ cases' f with f' _; cases' g with g' _; cases f'; cases g'
congr
left_inv f := f.left_inv
right_inv f := f.right_inv
@@ -2754,10 +2683,8 @@ include σ₂₁
<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_to_linear_equiv ContinuousLinearEquiv.symm_toLinearEquivₓ'. -/
@[simp]
-theorem symm_toLinearEquiv (e : M₁ ≃SL[σ₁₂] M₂) : e.symm.toLinearEquiv = e.toLinearEquiv.symm :=
- by
- ext
- rfl
+theorem symm_toLinearEquiv (e : M₁ ≃SL[σ₁₂] M₂) : e.symm.toLinearEquiv = e.toLinearEquiv.symm := by
+ ext; rfl
#align continuous_linear_equiv.symm_to_linear_equiv ContinuousLinearEquiv.symm_toLinearEquiv
/- warning: continuous_linear_equiv.symm_to_homeomorph -> ContinuousLinearEquiv.symm_toHomeomorph is a dubious translation:
@@ -2816,10 +2743,7 @@ include σ₁₃
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.trans_to_linear_equiv ContinuousLinearEquiv.trans_toLinearEquivₓ'. -/
@[simp]
theorem trans_toLinearEquiv (e₁ : M₁ ≃SL[σ₁₂] M₂) (e₂ : M₂ ≃SL[σ₂₃] M₃) :
- (e₁.trans e₂).toLinearEquiv = e₁.toLinearEquiv.trans e₂.toLinearEquiv :=
- by
- ext
- rfl
+ (e₁.trans e₂).toLinearEquiv = e₁.toLinearEquiv.trans e₂.toLinearEquiv := by ext; rfl
#align continuous_linear_equiv.trans_to_linear_equiv ContinuousLinearEquiv.trans_toLinearEquiv
omit σ₁₃ σ₂₁ σ₃₂ σ₃₁
@@ -2982,9 +2906,7 @@ include σ₂₁
<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_comp_self ContinuousLinearEquiv.symm_comp_selfₓ'. -/
@[simp]
-theorem symm_comp_self (e : M₁ ≃SL[σ₁₂] M₂) : (e.symm : M₂ → M₁) ∘ (e : M₁ → M₂) = id :=
- by
- ext x
+theorem symm_comp_self (e : M₁ ≃SL[σ₁₂] M₂) : (e.symm : M₂ → M₁) ∘ (e : M₁ → M₂) = id := by ext x;
exact symm_apply_apply e x
#align continuous_linear_equiv.symm_comp_self ContinuousLinearEquiv.symm_comp_self
@@ -2992,9 +2914,7 @@ theorem symm_comp_self (e : M₁ ≃SL[σ₁₂] M₂) : (e.symm : M₂ → M₁
<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.self_comp_symm ContinuousLinearEquiv.self_comp_symmₓ'. -/
@[simp]
-theorem self_comp_symm (e : M₁ ≃SL[σ₁₂] M₂) : (e : M₁ → M₂) ∘ (e.symm : M₂ → M₁) = id :=
- by
- ext x
+theorem self_comp_symm (e : M₁ ≃SL[σ₁₂] M₂) : (e : M₁ → M₂) ∘ (e.symm : M₂ → M₁) = id := by ext x;
exact apply_symm_apply e x
#align continuous_linear_equiv.self_comp_symm ContinuousLinearEquiv.self_comp_symm
@@ -3002,10 +2922,7 @@ theorem self_comp_symm (e : M₁ ≃SL[σ₁₂] M₂) : (e : M₁ → M₂) ∘
<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_symm ContinuousLinearEquiv.symm_symmₓ'. -/
@[simp]
-theorem symm_symm (e : M₁ ≃SL[σ₁₂] M₂) : e.symm.symm = e :=
- by
- ext x
- rfl
+theorem symm_symm (e : M₁ ≃SL[σ₁₂] M₂) : e.symm.symm = e := by ext x; rfl
#align continuous_linear_equiv.symm_symm ContinuousLinearEquiv.symm_symm
omit σ₂₁
@@ -3145,18 +3062,10 @@ instance automorphismGroup : Group (M₁ ≃L[R₁] M₁)
mul f g := g.trans f
one := ContinuousLinearEquiv.refl R₁ M₁
inv f := f.symm
- mul_assoc f g h := by
- ext
- rfl
- mul_one f := by
- ext
- rfl
- one_mul f := by
- ext
- rfl
- mul_left_inv f := by
- ext
- exact f.left_inv x
+ mul_assoc f g h := by ext; rfl
+ mul_one f := by ext; rfl
+ one_mul f := by ext; rfl
+ mul_left_inv f := by ext; exact f.left_inv x
#align continuous_linear_equiv.automorphism_group ContinuousLinearEquiv.automorphismGroup
-/
@@ -3294,14 +3203,8 @@ def ofUnit (f : (M →L[R] M)ˣ) : M ≃L[R] M
map_add' := by simp
map_smul' := by simp
invFun := f.inv
- left_inv := fun x =>
- show (f.inv * f.val) x = x by
- rw [f.inv_val]
- simp
- right_inv := fun x =>
- show (f.val * f.inv) x = x by
- rw [f.val_inv]
- simp }
+ left_inv := fun x => show (f.inv * f.val) x = x by rw [f.inv_val]; simp
+ right_inv := fun x => show (f.val * f.inv) x = x by rw [f.val_inv]; simp }
continuous_toFun := f.val.Continuous
continuous_invFun := f.inv.Continuous
#align continuous_linear_equiv.of_unit ContinuousLinearEquiv.ofUnit
@@ -3316,12 +3219,8 @@ Case conversion may be inaccurate. Consider using '#align continuous_linear_equi
def toUnit (f : M ≃L[R] M) : (M →L[R] M)ˣ where
val := f
inv := f.symm
- val_inv := by
- ext
- simp
- inv_val := by
- ext
- simp
+ val_inv := by ext; simp
+ inv_val := by ext; simp
#align continuous_linear_equiv.to_unit ContinuousLinearEquiv.toUnit
variable (R M)
@@ -3335,15 +3234,9 @@ def unitsEquiv : (M →L[R] M)ˣ ≃* M ≃L[R] M
where
toFun := ofUnit
invFun := toUnit
- left_inv f := by
- ext
- rfl
- right_inv f := by
- ext
- rfl
- map_mul' x y := by
- ext
- rfl
+ left_inv f := by ext; rfl
+ right_inv f := by ext; rfl
+ map_mul' x y := by ext; rfl
#align continuous_linear_equiv.units_equiv ContinuousLinearEquiv.unitsEquiv
/- warning: continuous_linear_equiv.units_equiv_apply -> ContinuousLinearEquiv.unitsEquiv_apply is a dubious translation:
@@ -3601,9 +3494,7 @@ theorem to_ring_inverse (e : M ≃L[R] M₂) (f : M →L[R] M₂) :
rcases h₁ with ⟨F, hF⟩
use (ContinuousLinearEquiv.unitsEquiv _ _ F).trans e
ext
- dsimp
- rw [coeFn_coe_base' F, hF]
- simp
+ dsimp; rw [coeFn_coe_base' F, hF]; simp
#align continuous_linear_map.to_ring_inverse ContinuousLinearMap.to_ring_inverse
/- warning: continuous_linear_map.ring_inverse_eq_map_inverse -> ContinuousLinearMap.ring_inverse_eq_map_inverse is a dubious translation:
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -49,10 +49,7 @@ variable {R : Type _} {M : Type _} [Ring R] [TopologicalSpace R] [TopologicalSpa
[AddCommGroup M] [Module R M]
/- warning: has_continuous_smul.of_nhds_zero -> ContinuousSMul.of_nhds_zero is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_6 : TopologicalRing.{u1} R _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))] [_inst_7 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)], (Filter.Tendsto.{max u1 u2, u2} (Prod.{u1, u2} R M) M (fun (p : Prod.{u1, u2} R M) => SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))) (Prod.fst.{u1, u2} R M p) (Prod.snd.{u1, u2} R M p)) (Filter.prod.{u1, u2} R M (nhds.{u1} R _inst_2 (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))))))) (nhds.{u2} M _inst_3 (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_4)))))))))) (nhds.{u2} M _inst_3 (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_4)))))))))) -> (forall (m : M), Filter.Tendsto.{u1, u2} R M (fun (a : R) => SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))) a m) (nhds.{u1} R _inst_2 (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))))))) (nhds.{u2} M _inst_3 (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_4)))))))))) -> (forall (a : R), Filter.Tendsto.{u2, u2} M M (fun (m : M) => SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))) a m) (nhds.{u2} M _inst_3 (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_4))))))))) (nhds.{u2} M _inst_3 (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_4)))))))))) -> (ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))) _inst_2 _inst_3)
-but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : TopologicalSpace.{u2} R] [_inst_3 : TopologicalSpace.{u1} M] [_inst_4 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4)] [_inst_6 : TopologicalRing.{u2} R _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))] [_inst_7 : TopologicalAddGroup.{u1} M _inst_3 (AddCommGroup.toAddGroup.{u1} M _inst_4)], (Filter.Tendsto.{max u2 u1, u1} (Prod.{u2, u1} R M) M (fun (p : Prod.{u2, u1} R M) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5))))) (Prod.fst.{u2, u1} R M p) (Prod.snd.{u2, u1} R M p)) (Filter.prod.{u2, u1} R M (nhds.{u2} R _inst_2 (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) (nhds.{u1} M _inst_3 (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))))))) (nhds.{u1} M _inst_3 (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))))))) -> (forall (m : M), Filter.Tendsto.{u2, u1} R M (fun (a : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5))))) a m) (nhds.{u2} R _inst_2 (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) (nhds.{u1} M _inst_3 (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))))))) -> (forall (a : R), Filter.Tendsto.{u1, u1} M M (fun (m : M) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5))))) a m) (nhds.{u1} M _inst_3 (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4)))))))) (nhds.{u1} M _inst_3 (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))))))) -> (ContinuousSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5)))) _inst_2 _inst_3)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_continuous_smul.of_nhds_zero ContinuousSMul.of_nhds_zeroₓ'. -/
theorem ContinuousSMul.of_nhds_zero [TopologicalRing R] [TopologicalAddGroup M]
(hmul : Tendsto (fun p : R × M => p.1 • p.2) (𝓝 0 ×ᶠ 𝓝 0) (𝓝 0))
@@ -176,10 +173,7 @@ variable {ι R M₁ M₂ : Type _} [Semiring R] [AddCommMonoid M₁] [AddCommMon
(f : M₁ →ₗ[R] M₂)
/- warning: has_continuous_smul_induced -> continuousSMul_induced is a dubious translation:
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- forall {R : Type.{u1}} {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : AddCommMonoid.{u3} M₂] [_inst_4 : Module.{u1, u2} R M₁ _inst_1 _inst_2] [_inst_5 : Module.{u1, u3} R M₂ _inst_1 _inst_3] [u : TopologicalSpace.{u1} R] {t : TopologicalSpace.{u3} M₂} [_inst_6 : ContinuousSMul.{u1, u3} R M₂ (SMulZeroClass.toHasSmul.{u1, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M₂ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_3))) (Module.toMulActionWithZero.{u1, u3} R M₂ _inst_1 _inst_3 _inst_5)))) u t] (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5), ContinuousSMul.{u1, u2} R M₁ (SMulZeroClass.toHasSmul.{u1, u2} R M₁ (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M₁ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M₁ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2))) (Module.toMulActionWithZero.{u1, u2} R M₁ _inst_1 _inst_2 _inst_4)))) u (TopologicalSpace.induced.{u2, u3} M₁ M₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M₁ M₂ _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f) t)
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- forall {R : Type.{u3}} {M₁ : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : AddCommMonoid.{u1} M₂] [_inst_4 : Module.{u3, u2} R M₁ _inst_1 _inst_2] [_inst_5 : Module.{u3, u1} R M₂ _inst_1 _inst_3] [u : TopologicalSpace.{u3} R] {t : TopologicalSpace.{u1} M₂} [_inst_6 : ContinuousSMul.{u3, u1} R M₂ (SMulZeroClass.toSMul.{u3, u1} R M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u1} R M₂ (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u1} R M₂ (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_3)) (Module.toMulActionWithZero.{u3, u1} R M₂ _inst_1 _inst_3 _inst_5)))) u t] (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5), ContinuousSMul.{u3, u2} R M₁ (SMulZeroClass.toSMul.{u3, u2} R M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M₁ (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M₁ (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (Module.toMulActionWithZero.{u3, u2} R M₁ _inst_1 _inst_2 _inst_4)))) u (TopologicalSpace.induced.{u2, u1} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M₁ M₂ _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) t)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_continuous_smul_induced continuousSMul_inducedₓ'. -/
theorem continuousSMul_induced : @ContinuousSMul R M₁ _ u (t.induced f) :=
{
@@ -526,10 +520,7 @@ end
variable [ContinuousAdd M₂] {σ : R →+* S} {l : Filter α}
/- warning: linear_map_of_mem_closure_range_coe -> linearMapOfMemClosureRangeCoe is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align linear_map_of_mem_closure_range_coe linearMapOfMemClosureRangeCoeₓ'. -/
/-- Constructs a bundled linear map from a function and a proof that this function belongs to the
closure of the set of linear maps. -/
@@ -544,10 +535,7 @@ def linearMapOfMemClosureRangeCoe (f : M₁ → M₂)
#align linear_map_of_mem_closure_range_coe linearMapOfMemClosureRangeCoe
/- warning: linear_map_of_tendsto -> linearMapOfTendsto is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align linear_map_of_tendsto linearMapOfTendstoₓ'. -/
/-- Construct a bundled linear map from a pointwise limit of linear maps -/
@[simps (config := { fullyApplied := false })]
@@ -560,10 +548,7 @@ def linearMapOfTendsto (f : M₁ → M₂) (g : α → M₁ →ₛₗ[σ] M₂)
variable (M₁ M₂ σ)
/- warning: linear_map.is_closed_range_coe -> LinearMap.isClosed_range_coe is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align linear_map.is_closed_range_coe LinearMap.isClosed_range_coeₓ'. -/
theorem LinearMap.isClosed_range_coe : IsClosed (Set.range (coeFn : (M₁ →ₛₗ[σ] M₂) → M₁ → M₂)) :=
isClosed_of_closure_subset fun f hf => ⟨linearMapOfMemClosureRangeCoe f hf, rfl⟩
@@ -593,10 +578,7 @@ instance : Coe (M₁ →SL[σ₁₂] M₂) (M₁ →ₛₗ[σ₁₂] M₂) :=
/- warning: continuous_linear_map.to_linear_map_eq_coe clashes with [anonymous] -> [anonymous]
warning: continuous_linear_map.to_linear_map_eq_coe -> [anonymous] is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.to_linear_map_eq_coe [anonymous]ₓ'. -/
-- make the coercion the preferred form
@[simp]
@@ -605,10 +587,7 @@ theorem [anonymous] (f : M₁ →SL[σ₁₂] M₂) : f.toLinearMap = f :=
#align continuous_linear_map.to_linear_map_eq_coe [anonymous]
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theorem coe_injective : Function.Injective (coe : (M₁ →SL[σ₁₂] M₂) → M₁ →ₛₗ[σ₁₂] M₂) :=
by
@@ -633,10 +612,7 @@ instance toFun : CoeFun (M₁ →SL[σ₁₂] M₂) fun _ => M₁ → M₂ :=
#align continuous_linear_map.to_fun ContinuousLinearMap.toFun
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_mk ContinuousLinearMap.coe_mkₓ'. -/
@[simp]
theorem coe_mk (f : M₁ →ₛₗ[σ₁₂] M₂) (h) : (mk f h : M₁ →ₛₗ[σ₁₂] M₂) = f :=
@@ -644,10 +620,7 @@ theorem coe_mk (f : M₁ →ₛₗ[σ₁₂] M₂) (h) : (mk f h : M₁ →ₛ
#align continuous_linear_map.coe_mk ContinuousLinearMap.coe_mk
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_mk' ContinuousLinearMap.coe_mk'ₓ'. -/
@[simp]
theorem coe_mk' (f : M₁ →ₛₗ[σ₁₂] M₂) (h) : (mk f h : M₁ → M₂) = f :=
@@ -655,10 +628,7 @@ theorem coe_mk' (f : M₁ →ₛₗ[σ₁₂] M₂) (h) : (mk f h : M₁ → M
#align continuous_linear_map.coe_mk' ContinuousLinearMap.coe_mk'
/- warning: continuous_linear_map.continuous -> ContinuousLinearMap.continuous is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.continuous ContinuousLinearMap.continuousₓ'. -/
@[continuity]
protected theorem continuous (f : M₁ →SL[σ₁₂] M₂) : Continuous f :=
@@ -666,10 +636,7 @@ protected theorem continuous (f : M₁ →SL[σ₁₂] M₂) : Continuous f :=
#align continuous_linear_map.continuous ContinuousLinearMap.continuous
/- warning: continuous_linear_map.uniform_continuous -> ContinuousLinearMap.uniformContinuous is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.uniform_continuous ContinuousLinearMap.uniformContinuousₓ'. -/
protected theorem uniformContinuous {E₁ E₂ : Type _} [UniformSpace E₁] [UniformSpace E₂]
[AddCommGroup E₁] [AddCommGroup E₂] [Module R₁ E₁] [Module R₂ E₂] [UniformAddGroup E₁]
@@ -678,10 +645,7 @@ protected theorem uniformContinuous {E₁ E₂ : Type _} [UniformSpace E₁] [Un
#align continuous_linear_map.uniform_continuous ContinuousLinearMap.uniformContinuous
/- warning: continuous_linear_map.coe_inj -> ContinuousLinearMap.coe_inj is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_inj ContinuousLinearMap.coe_injₓ'. -/
@[simp, norm_cast]
theorem coe_inj {f g : M₁ →SL[σ₁₂] M₂} : (f : M₁ →ₛₗ[σ₁₂] M₂) = g ↔ f = g :=
@@ -689,10 +653,7 @@ theorem coe_inj {f g : M₁ →SL[σ₁₂] M₂} : (f : M₁ →ₛₗ[σ₁₂
#align continuous_linear_map.coe_inj ContinuousLinearMap.coe_inj
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_fn_injective ContinuousLinearMap.coeFn_injectiveₓ'. -/
theorem coeFn_injective : @Function.Injective (M₁ →SL[σ₁₂] M₂) (M₁ → M₂) coeFn :=
FunLike.coe_injective
@@ -716,10 +677,7 @@ def Simps.coe (h : M₁ →SL[σ₁₂] M₂) : M₁ →ₛₗ[σ₁₂] M₂ :=
initialize_simps_projections ContinuousLinearMap (to_linear_map_to_fun → apply, toLinearMap → coe)
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ext ContinuousLinearMap.extₓ'. -/
@[ext]
theorem ext {f g : M₁ →SL[σ₁₂] M₂} (h : ∀ x, f x = g x) : f = g :=
@@ -727,20 +685,14 @@ theorem ext {f g : M₁ →SL[σ₁₂] M₂} (h : ∀ x, f x = g x) : f = g :=
#align continuous_linear_map.ext ContinuousLinearMap.ext
/- warning: continuous_linear_map.ext_iff -> ContinuousLinearMap.ext_iff is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ext_iff ContinuousLinearMap.ext_iffₓ'. -/
theorem ext_iff {f g : M₁ →SL[σ₁₂] M₂} : f = g ↔ ∀ x, f x = g x :=
FunLike.ext_iff
#align continuous_linear_map.ext_iff ContinuousLinearMap.ext_iff
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.copy ContinuousLinearMap.copyₓ'. -/
/-- Copy of a `continuous_linear_map` with a new `to_fun` equal to the old one. Useful to fix
definitional equalities. -/
@@ -751,10 +703,7 @@ protected def copy (f : M₁ →SL[σ₁₂] M₂) (f' : M₁ → M₂) (h : f'
#align continuous_linear_map.copy ContinuousLinearMap.copy
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_copy ContinuousLinearMap.coe_copyₓ'. -/
@[simp]
theorem coe_copy (f : M₁ →SL[σ₁₂] M₂) (f' : M₁ → M₂) (h : f' = ⇑f) : ⇑(f.copy f' h) = f' :=
@@ -762,20 +711,14 @@ theorem coe_copy (f : M₁ →SL[σ₁₂] M₂) (f' : M₁ → M₂) (h : f' =
#align continuous_linear_map.coe_copy ContinuousLinearMap.coe_copy
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.copy_eq ContinuousLinearMap.copy_eqₓ'. -/
theorem copy_eq (f : M₁ →SL[σ₁₂] M₂) (f' : M₁ → M₂) (h : f' = ⇑f) : f.copy f' h = f :=
FunLike.ext' h
#align continuous_linear_map.copy_eq ContinuousLinearMap.copy_eq
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_zero ContinuousLinearMap.map_zeroₓ'. -/
-- make some straightforward lemmas available to `simp`.
protected theorem map_zero (f : M₁ →SL[σ₁₂] M₂) : f (0 : M₁) = 0 :=
@@ -783,20 +726,14 @@ protected theorem map_zero (f : M₁ →SL[σ₁₂] M₂) : f (0 : M₁) = 0 :=
#align continuous_linear_map.map_zero ContinuousLinearMap.map_zero
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_add ContinuousLinearMap.map_addₓ'. -/
protected theorem map_add (f : M₁ →SL[σ₁₂] M₂) (x y : M₁) : f (x + y) = f x + f y :=
map_add f x y
#align continuous_linear_map.map_add ContinuousLinearMap.map_add
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_smulₛₗ ContinuousLinearMap.map_smulₛₗₓ'. -/
@[simp]
protected theorem map_smulₛₗ (f : M₁ →SL[σ₁₂] M₂) (c : R₁) (x : M₁) : f (c • x) = σ₁₂ c • f x :=
@@ -804,10 +741,7 @@ protected theorem map_smulₛₗ (f : M₁ →SL[σ₁₂] M₂) (c : R₁) (x :
#align continuous_linear_map.map_smulₛₗ ContinuousLinearMap.map_smulₛₗ
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_smul ContinuousLinearMap.map_smulₓ'. -/
@[simp]
protected theorem map_smul [Module R₁ M₂] (f : M₁ →L[R₁] M₂) (c : R₁) (x : M₁) :
@@ -815,10 +749,7 @@ protected theorem map_smul [Module R₁ M₂] (f : M₁ →L[R₁] M₂) (c : R
#align continuous_linear_map.map_smul ContinuousLinearMap.map_smul
/- warning: continuous_linear_map.map_smul_of_tower -> ContinuousLinearMap.map_smul_of_tower is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_smul_of_tower ContinuousLinearMap.map_smul_of_towerₓ'. -/
@[simp]
theorem map_smul_of_tower {R S : Type _} [Semiring S] [SMul R M₁] [Module S M₁] [SMul R M₂]
@@ -828,10 +759,7 @@ theorem map_smul_of_tower {R S : Type _} [Semiring S] [SMul R M₁] [Module S M
#align continuous_linear_map.map_smul_of_tower ContinuousLinearMap.map_smul_of_tower
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_sum ContinuousLinearMap.map_sumₓ'. -/
protected theorem map_sum {ι : Type _} (f : M₁ →SL[σ₁₂] M₂) (s : Finset ι) (g : ι → M₁) :
f (∑ i in s, g i) = ∑ i in s, f (g i) :=
@@ -839,10 +767,7 @@ protected theorem map_sum {ι : Type _} (f : M₁ →SL[σ₁₂] M₂) (s : Fin
#align continuous_linear_map.map_sum ContinuousLinearMap.map_sum
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_coe ContinuousLinearMap.coe_coeₓ'. -/
@[simp, norm_cast]
theorem coe_coe (f : M₁ →SL[σ₁₂] M₂) : ⇑(f : M₁ →ₛₗ[σ₁₂] M₂) = f :=
@@ -850,10 +775,7 @@ theorem coe_coe (f : M₁ →SL[σ₁₂] M₂) : ⇑(f : M₁ →ₛₗ[σ₁
#align continuous_linear_map.coe_coe ContinuousLinearMap.coe_coe
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ext_ring ContinuousLinearMap.ext_ringₓ'. -/
@[ext]
theorem ext_ring [TopologicalSpace R₁] {f g : R₁ →L[R₁] M₁} (h : f 1 = g 1) : f = g :=
@@ -861,20 +783,14 @@ theorem ext_ring [TopologicalSpace R₁] {f g : R₁ →L[R₁] M₁} (h : f 1 =
#align continuous_linear_map.ext_ring ContinuousLinearMap.ext_ring
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ext_ring_iff ContinuousLinearMap.ext_ring_iffₓ'. -/
theorem ext_ring_iff [TopologicalSpace R₁] {f g : R₁ →L[R₁] M₁} : f = g ↔ f 1 = g 1 :=
⟨fun h => h ▸ rfl, ext_ring⟩
#align continuous_linear_map.ext_ring_iff ContinuousLinearMap.ext_ring_iff
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.eq_on_closure_span ContinuousLinearMap.eqOn_closure_spanₓ'. -/
/-- If two continuous linear maps are equal on a set `s`, then they are equal on the closure
of the `submodule.span` of this set. -/
@@ -884,10 +800,7 @@ theorem eqOn_closure_span [T2Space M₂] {s : Set M₁} {f g : M₁ →SL[σ₁
#align continuous_linear_map.eq_on_closure_span ContinuousLinearMap.eqOn_closure_span
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ext_on ContinuousLinearMap.ext_onₓ'. -/
/-- If the submodule generated by a set `s` is dense in the ambient module, then two continuous
linear maps equal on `s` are equal. -/
@@ -897,10 +810,7 @@ theorem ext_on [T2Space M₂] {s : Set M₁} (hs : Dense (Submodule.span R₁ s
#align continuous_linear_map.ext_on ContinuousLinearMap.ext_on
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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.topological_closure_map Submodule.topologicalClosure_mapₓ'. -/
/-- Under a continuous linear map, the image of the `topological_closure` of a submodule is
contained in the `topological_closure` of its image. -/
@@ -913,10 +823,7 @@ theorem Submodule.topologicalClosure_map [RingHomSurjective σ₁₂] [Topologic
#align submodule.topological_closure_map Submodule.topologicalClosure_map
/- warning: dense_range.topological_closure_map_submodule -> DenseRange.topologicalClosure_map_submodule is a dubious translation:
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(Semiring.toMonoidWithZero.{u1} R₁ _inst_1)))) (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5))) (MulActionWithZero.toSMulWithZero.{u1, u3} R₁ M₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5))) (Module.toMulActionWithZero.{u1, u3} R₁ M₁ _inst_1 _inst_5 _inst_14)))) _inst_19 _inst_4] [_inst_22 : ContinuousAdd.{u3} M₁ _inst_4 (AddZeroClass.toHasAdd.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5)))] [_inst_23 : ContinuousSMul.{u2, u4} R₂ M₂ (SMulZeroClass.toHasSmul.{u2, u4} R₂ M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (SMulWithZero.toSmulZeroClass.{u2, u4} R₂ M₂ (MulZeroClass.toHasZero.{u2} R₂ (MulZeroOneClass.toMulZeroClass.{u2} R₂ (MonoidWithZero.toMulZeroOneClass.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)))) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (MulActionWithZero.toSMulWithZero.{u2, u4} R₂ M₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (Module.toMulActionWithZero.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)))) _inst_20 _inst_8] [_inst_24 : ContinuousAdd.{u4} M₂ _inst_8 (AddZeroClass.toHasAdd.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9)))] {f : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16}, (DenseRange.{u4, u3} M₂ _inst_8 M₁ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 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u2} R₁ M₁ _inst_1 _inst_5 _inst_14)))) _inst_21) _inst_22 s) (Top.top.{u2} (Submodule.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) (Submodule.instTopSubmodule.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14))) -> (Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (Submodule.topologicalClosure.{u3, u1} R₂ M₂ _inst_2 _inst_8 _inst_9 _inst_16 (ContinuousSMul.continuousConstSMul.{u3, u1} R₂ M₂ _inst_20 _inst_8 (SMulZeroClass.toSMul.{u3, u1} R₂ M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u3, u1} R₂ M₂ (MonoidWithZero.toZero.{u3} R₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u3, u1} R₂ M₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16)))) _inst_23) _inst_24 (Submodule.map.{u4, u3, u2, u1, max u2 u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂ _inst_18 (LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f) s)) (Top.top.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (Submodule.instTopSubmodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16))))
+<too large>
Case conversion may be inaccurate. Consider using '#align dense_range.topological_closure_map_submodule DenseRange.topologicalClosure_map_submoduleₓ'. -/
/-- Under a dense continuous linear map, a submodule whose `topological_closure` is `⊤` is sent to
another such submodule. That is, the image of a dense set under a map with dense range is dense.
@@ -946,20 +853,14 @@ instance : MulAction S₂ (M₁ →SL[σ₁₂] M₂)
mul_smul a b f := ext fun x => mul_smul _ _ _
/- warning: continuous_linear_map.smul_apply -> ContinuousLinearMap.smul_apply is a dubious translation:
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(ContinuousLinearMap.continuousSemilinearMapClass.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) f x))
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_apply ContinuousLinearMap.smul_applyₓ'. -/
theorem smul_apply (c : S₂) (f : M₁ →SL[σ₁₂] M₂) (x : M₁) : (c • f) x = c • f x :=
rfl
#align continuous_linear_map.smul_apply ContinuousLinearMap.smul_apply
/- warning: continuous_linear_map.coe_smul -> ContinuousLinearMap.coe_smul is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_smul ContinuousLinearMap.coe_smulₓ'. -/
@[simp, norm_cast]
theorem coe_smul (c : S₂) (f : M₁ →SL[σ₁₂] M₂) : (↑(c • f) : M₁ →ₛₗ[σ₁₂] M₂) = c • f :=
@@ -967,10 +868,7 @@ theorem coe_smul (c : S₂) (f : M₁ →SL[σ₁₂] M₂) : (↑(c • f) : M
#align continuous_linear_map.coe_smul ContinuousLinearMap.coe_smul
/- warning: continuous_linear_map.coe_smul' -> ContinuousLinearMap.coe_smul' is a dubious translation:
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(MulActionWithZero.toSMulWithZero.{u4, u2} R₂ M₂ (Semiring.toMonoidWithZero.{u4} R₂ _inst_2) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (Module.toMulActionWithZero.{u4, u2} R₂ M₂ _inst_2 _inst_9 _inst_16)))) (SMulZeroClass.toSMul.{u1, u2} S₂ M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (DistribSMul.toSMulZeroClass.{u1, u2} S₂ M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S₂ M₂ _inst_18 (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9) _inst_20)))] [_inst_22 : ContinuousConstSMul.{u1, u2} S₂ M₂ _inst_8 (SMulZeroClass.toSMul.{u1, u2} S₂ M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (DistribSMul.toSMulZeroClass.{u1, u2} S₂ M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S₂ M₂ _inst_18 (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9) _inst_20)))] (c : S₂) (f : 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_inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) f))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_smul' ContinuousLinearMap.coe_smul'ₓ'. -/
@[simp, norm_cast]
theorem coe_smul' (c : S₂) (f : M₁ →SL[σ₁₂] M₂) : ⇑(c • f) = c • f :=
@@ -993,10 +891,7 @@ instance : Inhabited (M₁ →SL[σ₁₂] M₂) :=
⟨0⟩
/- warning: continuous_linear_map.default_def -> ContinuousLinearMap.default_def is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.default_def ContinuousLinearMap.default_defₓ'. -/
@[simp]
theorem default_def : (default : M₁ →SL[σ₁₂] M₂) = 0 :=
@@ -1004,10 +899,7 @@ theorem default_def : (default : M₁ →SL[σ₁₂] M₂) = 0 :=
#align continuous_linear_map.default_def ContinuousLinearMap.default_def
/- warning: continuous_linear_map.zero_apply -> ContinuousLinearMap.zero_apply is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.zero_apply ContinuousLinearMap.zero_applyₓ'. -/
@[simp]
theorem zero_apply (x : M₁) : (0 : M₁ →SL[σ₁₂] M₂) x = 0 :=
@@ -1015,10 +907,7 @@ theorem zero_apply (x : M₁) : (0 : M₁ →SL[σ₁₂] M₂) x = 0 :=
#align continuous_linear_map.zero_apply ContinuousLinearMap.zero_apply
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_zero ContinuousLinearMap.coe_zeroₓ'. -/
@[simp, norm_cast]
theorem coe_zero : ((0 : M₁ →SL[σ₁₂] M₂) : M₁ →ₛₗ[σ₁₂] M₂) = 0 :=
@@ -1026,10 +915,7 @@ theorem coe_zero : ((0 : M₁ →SL[σ₁₂] M₂) : M₁ →ₛₗ[σ₁₂] M
#align continuous_linear_map.coe_zero ContinuousLinearMap.coe_zero
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_zero' ContinuousLinearMap.coe_zero'ₓ'. -/
/- no simp attribute on the next line as simp does not always simplify `0 x` to `0`
when `0` is the zero function, while it does for the zero continuous linear map,
@@ -1052,10 +938,7 @@ instance uniqueOfRight [Subsingleton M₂] : Unique (M₁ →SL[σ₁₂] M₂)
-/
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.exists_ne_zero ContinuousLinearMap.exists_ne_zeroₓ'. -/
theorem exists_ne_zero {f : M₁ →SL[σ₁₂] M₂} (hf : f ≠ 0) : ∃ x, f x ≠ 0 :=
by
@@ -1086,10 +969,7 @@ theorem one_def : (1 : M₁ →L[R₁] M₁) = id R₁ M₁ :=
-/
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.id_apply ContinuousLinearMap.id_applyₓ'. -/
theorem id_apply (x : M₁) : id R₁ M₁ x = x :=
rfl
@@ -1103,10 +983,7 @@ theorem coe_id : (id R₁ M₁ : M₁ →ₗ[R₁] M₁) = LinearMap.id :=
-/
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_id' ContinuousLinearMap.coe_id'ₓ'. -/
@[simp, norm_cast]
theorem coe_id' : ⇑(id R₁ M₁) = id :=
@@ -1114,10 +991,7 @@ theorem coe_id' : ⇑(id R₁ M₁) = id :=
#align continuous_linear_map.coe_id' ContinuousLinearMap.coe_id'
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_eq_id ContinuousLinearMap.coe_eq_idₓ'. -/
@[simp, norm_cast]
theorem coe_eq_id {f : M₁ →L[R₁] M₁} : (f : M₁ →ₗ[R₁] M₁) = LinearMap.id ↔ f = id _ _ := by
@@ -1125,10 +999,7 @@ theorem coe_eq_id {f : M₁ →L[R₁] M₁} : (f : M₁ →ₗ[R₁] M₁) = Li
#align continuous_linear_map.coe_eq_id ContinuousLinearMap.coe_eq_id
/- warning: continuous_linear_map.one_apply -> ContinuousLinearMap.one_apply is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.one_apply ContinuousLinearMap.one_applyₓ'. -/
@[simp]
theorem one_apply (x : M₁) : (1 : M₁ →L[R₁] M₁) x = x :=
@@ -1143,10 +1014,7 @@ instance : Add (M₁ →SL[σ₁₂] M₂) :=
⟨fun f g => ⟨f + g, f.2.add g.2⟩⟩
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.add_apply ContinuousLinearMap.add_applyₓ'. -/
@[simp]
theorem add_apply (f g : M₁ →SL[σ₁₂] M₂) (x : M₁) : (f + g) x = f x + g x :=
@@ -1154,10 +1022,7 @@ theorem add_apply (f g : M₁ →SL[σ₁₂] M₂) (x : M₁) : (f + g) x = f x
#align continuous_linear_map.add_apply ContinuousLinearMap.add_apply
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_add ContinuousLinearMap.coe_addₓ'. -/
@[simp, norm_cast]
theorem coe_add (f g : M₁ →SL[σ₁₂] M₂) : (↑(f + g) : M₁ →ₛₗ[σ₁₂] M₂) = f + g :=
@@ -1165,10 +1030,7 @@ theorem coe_add (f g : M₁ →SL[σ₁₂] M₂) : (↑(f + g) : M₁ →ₛₗ
#align continuous_linear_map.coe_add ContinuousLinearMap.coe_add
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_add' ContinuousLinearMap.coe_add'ₓ'. -/
@[norm_cast]
theorem coe_add' (f g : M₁ →SL[σ₁₂] M₂) : ⇑(f + g) = f + g :=
@@ -1196,10 +1058,7 @@ instance : AddCommMonoid (M₁ →SL[σ₁₂] M₂)
simp [Nat.succ_eq_one_add, add_smul]
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_sum ContinuousLinearMap.coe_sumₓ'. -/
@[simp, norm_cast]
theorem coe_sum {ι : Type _} (t : Finset ι) (f : ι → M₁ →SL[σ₁₂] M₂) :
@@ -1208,10 +1067,7 @@ theorem coe_sum {ι : Type _} (t : Finset ι) (f : ι → M₁ →SL[σ₁₂] M
#align continuous_linear_map.coe_sum ContinuousLinearMap.coe_sum
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_sum' ContinuousLinearMap.coe_sum'ₓ'. -/
@[simp, norm_cast]
theorem coe_sum' {ι : Type _} (t : Finset ι) (f : ι → M₁ →SL[σ₁₂] M₂) :
@@ -1219,10 +1075,7 @@ theorem coe_sum' {ι : Type _} (t : Finset ι) (f : ι → M₁ →SL[σ₁₂]
#align continuous_linear_map.coe_sum' ContinuousLinearMap.coe_sum'
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.sum_apply ContinuousLinearMap.sum_applyₓ'. -/
theorem sum_apply {ι : Type _} (t : Finset ι) (f : ι → M₁ →SL[σ₁₂] M₂) (b : M₁) :
(∑ d in t, f d) b = ∑ d in t, f d b := by simp only [coe_sum', Finset.sum_apply]
@@ -1245,10 +1098,7 @@ infixr:80 " ∘L " =>
_ _ _ _ RingHomCompTriple.ids
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_comp ContinuousLinearMap.coe_compₓ'. -/
@[simp, norm_cast]
theorem coe_comp (h : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) :
@@ -1259,10 +1109,7 @@ theorem coe_comp (h : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂)
include σ₁₃
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_comp' ContinuousLinearMap.coe_comp'ₓ'. -/
@[simp, norm_cast]
theorem coe_comp' (h : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) : ⇑(h.comp f) = h ∘ f :=
@@ -1270,10 +1117,7 @@ theorem coe_comp' (h : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂
#align continuous_linear_map.coe_comp' ContinuousLinearMap.coe_comp'
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_apply ContinuousLinearMap.comp_applyₓ'. -/
theorem comp_apply (g : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) (x : M₁) : (g.comp f) x = g (f x) :=
rfl
@@ -1282,10 +1126,7 @@ theorem comp_apply (g : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M
omit σ₁₃
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_id ContinuousLinearMap.comp_idₓ'. -/
@[simp]
theorem comp_id (f : M₁ →SL[σ₁₂] M₂) : f.comp (id R₁ M₁) = f :=
@@ -1293,10 +1134,7 @@ theorem comp_id (f : M₁ →SL[σ₁₂] M₂) : f.comp (id R₁ M₁) = f :=
#align continuous_linear_map.comp_id ContinuousLinearMap.comp_id
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.id_comp ContinuousLinearMap.id_compₓ'. -/
@[simp]
theorem id_comp (f : M₁ →SL[σ₁₂] M₂) : (id R₂ M₂).comp f = f :=
@@ -1306,10 +1144,7 @@ theorem id_comp (f : M₁ →SL[σ₁₂] M₂) : (id R₂ M₂).comp f = f :=
include σ₁₃
/- warning: continuous_linear_map.comp_zero -> ContinuousLinearMap.comp_zero is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_zero ContinuousLinearMap.comp_zeroₓ'. -/
@[simp]
theorem comp_zero (g : M₂ →SL[σ₂₃] M₃) : g.comp (0 : M₁ →SL[σ₁₂] M₂) = 0 :=
@@ -1319,10 +1154,7 @@ theorem comp_zero (g : M₂ →SL[σ₂₃] M₃) : g.comp (0 : M₁ →SL[σ₁
#align continuous_linear_map.comp_zero ContinuousLinearMap.comp_zero
/- warning: continuous_linear_map.zero_comp -> ContinuousLinearMap.zero_comp is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.zero_comp ContinuousLinearMap.zero_compₓ'. -/
@[simp]
theorem zero_comp (f : M₁ →SL[σ₁₂] M₂) : (0 : M₂ →SL[σ₂₃] M₃).comp f = 0 :=
@@ -1332,10 +1164,7 @@ theorem zero_comp (f : M₁ →SL[σ₁₂] M₂) : (0 : M₂ →SL[σ₂₃] M
#align continuous_linear_map.zero_comp ContinuousLinearMap.zero_comp
/- warning: continuous_linear_map.comp_add -> ContinuousLinearMap.comp_add is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_add ContinuousLinearMap.comp_addₓ'. -/
@[simp]
theorem comp_add [ContinuousAdd M₂] [ContinuousAdd M₃] (g : M₂ →SL[σ₂₃] M₃)
@@ -1346,10 +1175,7 @@ theorem comp_add [ContinuousAdd M₂] [ContinuousAdd M₃] (g : M₂ →SL[σ₂
#align continuous_linear_map.comp_add ContinuousLinearMap.comp_add
/- warning: continuous_linear_map.add_comp -> ContinuousLinearMap.add_comp is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.add_comp ContinuousLinearMap.add_compₓ'. -/
@[simp]
theorem add_comp [ContinuousAdd M₃] (g₁ g₂ : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) :
@@ -1361,10 +1187,7 @@ theorem add_comp [ContinuousAdd M₃] (g₁ g₂ : M₂ →SL[σ₂₃] M₃) (f
omit σ₁₃
/- warning: continuous_linear_map.comp_assoc -> ContinuousLinearMap.comp_assoc is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_assoc ContinuousLinearMap.comp_assocₓ'. -/
theorem comp_assoc {R₄ : Type _} [Semiring R₄] [Module R₄ M₄] {σ₁₄ : R₁ →+* R₄} {σ₂₄ : R₂ →+* R₄}
{σ₃₄ : R₃ →+* R₄} [RingHomCompTriple σ₁₃ σ₃₄ σ₁₄] [RingHomCompTriple σ₂₃ σ₃₄ σ₂₄]
@@ -1377,20 +1200,14 @@ instance : Mul (M₁ →L[R₁] M₁) :=
⟨comp⟩
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.mul_def ContinuousLinearMap.mul_defₓ'. -/
theorem mul_def (f g : M₁ →L[R₁] M₁) : f * g = f.comp g :=
rfl
#align continuous_linear_map.mul_def ContinuousLinearMap.mul_def
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_mul ContinuousLinearMap.coe_mulₓ'. -/
@[simp]
theorem coe_mul (f g : M₁ →L[R₁] M₁) : ⇑(f * g) = f ∘ g :=
@@ -1398,10 +1215,7 @@ theorem coe_mul (f g : M₁ →L[R₁] M₁) : ⇑(f * g) = f ∘ g :=
#align continuous_linear_map.coe_mul ContinuousLinearMap.coe_mul
/- warning: continuous_linear_map.mul_apply -> ContinuousLinearMap.mul_apply is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.mul_apply ContinuousLinearMap.mul_applyₓ'. -/
theorem mul_apply (f g : M₁ →L[R₁] M₁) (x : M₁) : (f * g) x = f (g x) :=
rfl
@@ -1461,10 +1275,7 @@ instance applyModule : Module (M₁ →L[R₁] M₁) M₁ :=
#align continuous_linear_map.apply_module ContinuousLinearMap.applyModule
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_def ContinuousLinearMap.smul_defₓ'. -/
@[simp]
protected theorem smul_def (f : M₁ →L[R₁] M₁) (a : M₁) : f • a = f a :=
@@ -1493,10 +1304,7 @@ instance applySMulCommClass : SMulCommClass R₁ (M₁ →L[R₁] M₁) M₁
#align continuous_linear_map.apply_smul_comm_class ContinuousLinearMap.applySMulCommClass
/- warning: continuous_linear_map.apply_smul_comm_class' -> ContinuousLinearMap.applySMulCommClass' is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.apply_smul_comm_class' ContinuousLinearMap.applySMulCommClass'ₓ'. -/
instance applySMulCommClass' : SMulCommClass (M₁ →L[R₁] M₁) R₁ M₁
where smul_comm := ContinuousLinearMap.map_smul
@@ -1520,10 +1328,7 @@ protected def prod [Module R₁ M₂] [Module R₁ M₃] (f₁ : M₁ →L[R₁]
#align continuous_linear_map.prod ContinuousLinearMap.prod
/- warning: continuous_linear_map.coe_prod -> ContinuousLinearMap.coe_prod is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_prod ContinuousLinearMap.coe_prodₓ'. -/
@[simp, norm_cast]
theorem coe_prod [Module R₁ M₂] [Module R₁ M₃] (f₁ : M₁ →L[R₁] M₂) (f₂ : M₁ →L[R₁] M₃) :
@@ -1532,10 +1337,7 @@ theorem coe_prod [Module R₁ M₂] [Module R₁ M₃] (f₁ : M₁ →L[R₁] M
#align continuous_linear_map.coe_prod ContinuousLinearMap.coe_prod
/- warning: continuous_linear_map.prod_apply -> ContinuousLinearMap.prod_apply is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.prod_apply ContinuousLinearMap.prod_applyₓ'. -/
@[simp, norm_cast]
theorem prod_apply [Module R₁ M₂] [Module R₁ M₃] (f₁ : M₁ →L[R₁] M₂) (f₂ : M₁ →L[R₁] M₃) (x : M₁) :
@@ -1574,10 +1376,7 @@ end
variable {F : Type _}
/- warning: continuous_linear_map.inl_apply -> ContinuousLinearMap.inl_apply is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.inl_apply ContinuousLinearMap.inl_applyₓ'. -/
@[simp]
theorem inl_apply [Module R₁ M₂] (x : M₁) : inl R₁ M₁ M₂ x = (x, 0) :=
@@ -1585,10 +1384,7 @@ theorem inl_apply [Module R₁ M₂] (x : M₁) : inl R₁ M₁ M₂ x = (x, 0)
#align continuous_linear_map.inl_apply ContinuousLinearMap.inl_apply
/- warning: continuous_linear_map.inr_apply -> ContinuousLinearMap.inr_apply is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.inr_apply ContinuousLinearMap.inr_applyₓ'. -/
@[simp]
theorem inr_apply [Module R₁ M₂] (x : M₂) : inr R₁ M₁ M₂ x = (0, x) :=
@@ -1596,10 +1392,7 @@ theorem inr_apply [Module R₁ M₂] (x : M₂) : inr R₁ M₁ M₂ x = (0, x)
#align continuous_linear_map.inr_apply ContinuousLinearMap.inr_apply
/- warning: continuous_linear_map.coe_inl -> ContinuousLinearMap.coe_inl is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_inl ContinuousLinearMap.coe_inlₓ'. -/
@[simp, norm_cast]
theorem coe_inl [Module R₁ M₂] : (inl R₁ M₁ M₂ : M₁ →ₗ[R₁] M₁ × M₂) = LinearMap.inl R₁ M₁ M₂ :=
@@ -1607,10 +1400,7 @@ theorem coe_inl [Module R₁ M₂] : (inl R₁ M₁ M₂ : M₁ →ₗ[R₁] M
#align continuous_linear_map.coe_inl ContinuousLinearMap.coe_inl
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_inr ContinuousLinearMap.coe_inrₓ'. -/
@[simp, norm_cast]
theorem coe_inr [Module R₁ M₂] : (inr R₁ M₁ M₂ : M₂ →ₗ[R₁] M₁ × M₂) = LinearMap.inr R₁ M₁ M₂ :=
@@ -1618,10 +1408,7 @@ theorem coe_inr [Module R₁ M₂] : (inr R₁ M₁ M₂ : M₂ →ₗ[R₁] M
#align continuous_linear_map.coe_inr ContinuousLinearMap.coe_inr
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.is_closed_ker ContinuousLinearMap.isClosed_kerₓ'. -/
theorem isClosed_ker [T1Space M₂] [ContinuousSemilinearMapClass F σ₁₂ M₁ M₂] (f : F) :
IsClosed (ker f : Set M₁) :=
@@ -1629,10 +1416,7 @@ theorem isClosed_ker [T1Space M₂] [ContinuousSemilinearMapClass F σ₁₂ M
#align continuous_linear_map.is_closed_ker ContinuousLinearMap.isClosed_ker
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.is_complete_ker ContinuousLinearMap.isComplete_kerₓ'. -/
theorem isComplete_ker {M' : Type _} [UniformSpace M'] [CompleteSpace M'] [AddCommMonoid M']
[Module R₁ M'] [T1Space M₂] [ContinuousSemilinearMapClass F σ₁₂ M' M₂] (f : F) :
@@ -1649,10 +1433,7 @@ instance (priority := 100) completeSpace_ker {M' : Type _} [UniformSpace M'] [Co
-/
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ker_prod ContinuousLinearMap.ker_prodₓ'. -/
@[simp]
theorem ker_prod [Module R₁ M₂] [Module R₁ M₃] (f : M₁ →L[R₁] M₂) (g : M₁ →L[R₁] M₃) :
@@ -1661,10 +1442,7 @@ theorem ker_prod [Module R₁ M₂] [Module R₁ M₃] (f : M₁ →L[R₁] M₂
#align continuous_linear_map.ker_prod ContinuousLinearMap.ker_prod
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.cod_restrict ContinuousLinearMap.codRestrictₓ'. -/
/-- Restrict codomain of a continuous linear map. -/
def codRestrict (f : M₁ →SL[σ₁₂] M₂) (p : Submodule R₂ M₂) (h : ∀ x, f x ∈ p) : M₁ →SL[σ₁₂] p
@@ -1674,10 +1452,7 @@ def codRestrict (f : M₁ →SL[σ₁₂] M₂) (p : Submodule R₂ M₂) (h :
#align continuous_linear_map.cod_restrict ContinuousLinearMap.codRestrict
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_cod_restrict ContinuousLinearMap.coe_codRestrictₓ'. -/
@[norm_cast]
theorem coe_codRestrict (f : M₁ →SL[σ₁₂] M₂) (p : Submodule R₂ M₂) (h : ∀ x, f x ∈ p) :
@@ -1686,10 +1461,7 @@ theorem coe_codRestrict (f : M₁ →SL[σ₁₂] M₂) (p : Submodule R₂ M₂
#align continuous_linear_map.coe_cod_restrict ContinuousLinearMap.coe_codRestrict
/- warning: continuous_linear_map.coe_cod_restrict_apply -> ContinuousLinearMap.coe_codRestrict_apply is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_cod_restrict_apply ContinuousLinearMap.coe_codRestrict_applyₓ'. -/
@[simp]
theorem coe_codRestrict_apply (f : M₁ →SL[σ₁₂] M₂) (p : Submodule R₂ M₂) (h : ∀ x, f x ∈ p) (x) :
@@ -1698,10 +1470,7 @@ theorem coe_codRestrict_apply (f : M₁ →SL[σ₁₂] M₂) (p : Submodule R
#align continuous_linear_map.coe_cod_restrict_apply ContinuousLinearMap.coe_codRestrict_apply
/- warning: continuous_linear_map.ker_cod_restrict -> ContinuousLinearMap.ker_codRestrict is a dubious translation:
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_inst_9 _inst_16) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)) x p) _inst_8) (Submodule.addCommMonoid.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16 p) _inst_14 (Submodule.module.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16 p) (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 (coeSort.{succ u4, succ (succ u4)} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)) p) (Subtype.topologicalSpace.{u4} M₂ (fun (x : M₂) => Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)) x p) _inst_8) (Submodule.addCommMonoid.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16 p) _inst_14 (Submodule.module.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16 p))) (ContinuousLinearMap.codRestrict.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f p h)) (LinearMap.ker.{u1, u2, u3, u4, max u3 u4} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂ (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u4, u1, u2, u3, u4} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16)) f)
-but is expected to have type
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_inst_16)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) f x) p), Eq.{succ u2} (Submodule.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) 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(ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16)) f)
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ker_cod_restrict ContinuousLinearMap.ker_codRestrictₓ'. -/
@[simp]
theorem ker_codRestrict (f : M₁ →SL[σ₁₂] M₂) (p : Submodule R₂ M₂) (h : ∀ x, f x ∈ p) :
@@ -1719,10 +1488,7 @@ def Submodule.subtypeL (p : Submodule R₁ M₁) : p →L[R₁] M₁
-/
/- warning: submodule.coe_subtypeL -> Submodule.coe_subtypeL is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align submodule.coe_subtypeL Submodule.coe_subtypeLₓ'. -/
@[simp, norm_cast]
theorem Submodule.coe_subtypeL (p : Submodule R₁ M₁) : (p.subtypeL : p →ₗ[R₁] M₁) = p.Subtype :=
@@ -1730,10 +1496,7 @@ theorem Submodule.coe_subtypeL (p : Submodule R₁ M₁) : (p.subtypeL : p →
#align submodule.coe_subtypeL Submodule.coe_subtypeL
/- warning: submodule.coe_subtypeL' -> Submodule.coe_subtypeL' is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align submodule.coe_subtypeL' Submodule.coe_subtypeL'ₓ'. -/
@[simp]
theorem Submodule.coe_subtypeL' (p : Submodule R₁ M₁) : ⇑p.subtypeL = p.Subtype :=
@@ -1741,10 +1504,7 @@ theorem Submodule.coe_subtypeL' (p : Submodule R₁ M₁) : ⇑p.subtypeL = p.Su
#align submodule.coe_subtypeL' Submodule.coe_subtypeL'
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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.subtypeL_apply Submodule.subtypeL_applyₓ'. -/
@[simp, norm_cast]
theorem Submodule.subtypeL_apply (p : Submodule R₁ M₁) (x : p) : p.subtypeL x = x :=
@@ -1752,10 +1512,7 @@ theorem Submodule.subtypeL_apply (p : Submodule R₁ M₁) (x : p) : p.subtypeL
#align submodule.subtypeL_apply Submodule.subtypeL_apply
/- warning: submodule.range_subtypeL -> Submodule.range_subtypeL is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align submodule.range_subtypeL Submodule.range_subtypeLₓ'. -/
@[simp]
theorem Submodule.range_subtypeL (p : Submodule R₁ M₁) : range p.subtypeL = p :=
@@ -1763,10 +1520,7 @@ theorem Submodule.range_subtypeL (p : Submodule R₁ M₁) : range p.subtypeL =
#align submodule.range_subtypeL Submodule.range_subtypeL
/- warning: submodule.ker_subtypeL -> Submodule.ker_subtypeL is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align submodule.ker_subtypeL Submodule.ker_subtypeLₓ'. -/
@[simp]
theorem Submodule.ker_subtypeL (p : Submodule R₁ M₁) : ker p.subtypeL = ⊥ :=
@@ -1804,10 +1558,7 @@ def snd [Module R₁ M₂] : M₁ × M₂ →L[R₁] M₂
variable {R₁ M₁ M₂}
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@[simp, norm_cast]
theorem coe_fst [Module R₁ M₂] : ↑(fst R₁ M₁ M₂) = LinearMap.fst R₁ M₁ M₂ :=
@@ -1815,10 +1566,7 @@ theorem coe_fst [Module R₁ M₂] : ↑(fst R₁ M₁ M₂) = LinearMap.fst R
#align continuous_linear_map.coe_fst ContinuousLinearMap.coe_fst
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_fst' ContinuousLinearMap.coe_fst'ₓ'. -/
@[simp, norm_cast]
theorem coe_fst' [Module R₁ M₂] : ⇑(fst R₁ M₁ M₂) = Prod.fst :=
@@ -1826,10 +1574,7 @@ theorem coe_fst' [Module R₁ M₂] : ⇑(fst R₁ M₁ M₂) = Prod.fst :=
#align continuous_linear_map.coe_fst' ContinuousLinearMap.coe_fst'
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_snd ContinuousLinearMap.coe_sndₓ'. -/
@[simp, norm_cast]
theorem coe_snd [Module R₁ M₂] : ↑(snd R₁ M₁ M₂) = LinearMap.snd R₁ M₁ M₂ :=
@@ -1837,10 +1582,7 @@ theorem coe_snd [Module R₁ M₂] : ↑(snd R₁ M₁ M₂) = LinearMap.snd R
#align continuous_linear_map.coe_snd ContinuousLinearMap.coe_snd
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_snd' ContinuousLinearMap.coe_snd'ₓ'. -/
@[simp, norm_cast]
theorem coe_snd' [Module R₁ M₂] : ⇑(snd R₁ M₁ M₂) = Prod.snd :=
@@ -1859,10 +1601,7 @@ theorem fst_prod_snd [Module R₁ M₂] : (fst R₁ M₁ M₂).Prod (snd R₁ M
#align continuous_linear_map.fst_prod_snd ContinuousLinearMap.fst_prod_snd
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.fst_comp_prod ContinuousLinearMap.fst_comp_prodₓ'. -/
@[simp]
theorem fst_comp_prod [Module R₁ M₂] [Module R₁ M₃] (f : M₁ →L[R₁] M₂) (g : M₁ →L[R₁] M₃) :
@@ -1871,10 +1610,7 @@ theorem fst_comp_prod [Module R₁ M₂] [Module R₁ M₃] (f : M₁ →L[R₁]
#align continuous_linear_map.fst_comp_prod ContinuousLinearMap.fst_comp_prod
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.snd_comp_prod ContinuousLinearMap.snd_comp_prodₓ'. -/
@[simp]
theorem snd_comp_prod [Module R₁ M₂] [Module R₁ M₃] (f : M₁ →L[R₁] M₂) (g : M₁ →L[R₁] M₃) :
@@ -1883,10 +1619,7 @@ theorem snd_comp_prod [Module R₁ M₂] [Module R₁ M₃] (f : M₁ →L[R₁]
#align continuous_linear_map.snd_comp_prod ContinuousLinearMap.snd_comp_prod
/- warning: continuous_linear_map.prod_map -> ContinuousLinearMap.prodMap is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.prod_map ContinuousLinearMap.prodMapₓ'. -/
/-- `prod.map` of two continuous linear maps. -/
def prodMap [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (f₁ : M₁ →L[R₁] M₂) (f₂ : M₃ →L[R₁] M₄) :
@@ -1895,10 +1628,7 @@ def prodMap [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (f₁ : M
#align continuous_linear_map.prod_map ContinuousLinearMap.prodMap
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_prod_map ContinuousLinearMap.coe_prodMapₓ'. -/
@[simp, norm_cast]
theorem coe_prodMap [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (f₁ : M₁ →L[R₁] M₂)
@@ -1907,10 +1637,7 @@ theorem coe_prodMap [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (f
#align continuous_linear_map.coe_prod_map ContinuousLinearMap.coe_prodMap
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_prod_map' ContinuousLinearMap.coe_prodMap'ₓ'. -/
@[simp, norm_cast]
theorem coe_prodMap' [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (f₁ : M₁ →L[R₁] M₂)
@@ -1931,10 +1658,7 @@ def coprod [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃] (f₁ : M
#align continuous_linear_map.coprod ContinuousLinearMap.coprod
/- warning: continuous_linear_map.coe_coprod -> ContinuousLinearMap.coe_coprod is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_coprod ContinuousLinearMap.coe_coprodₓ'. -/
@[norm_cast, simp]
theorem coe_coprod [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃] (f₁ : M₁ →L[R₁] M₃)
@@ -1943,10 +1667,7 @@ theorem coe_coprod [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃] (f
#align continuous_linear_map.coe_coprod ContinuousLinearMap.coe_coprod
/- warning: continuous_linear_map.coprod_apply -> ContinuousLinearMap.coprod_apply is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coprod_apply ContinuousLinearMap.coprod_applyₓ'. -/
@[simp]
theorem coprod_apply [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃] (f₁ : M₁ →L[R₁] M₃)
@@ -1955,10 +1676,7 @@ theorem coprod_apply [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃]
#align continuous_linear_map.coprod_apply ContinuousLinearMap.coprod_apply
/- warning: continuous_linear_map.range_coprod -> ContinuousLinearMap.range_coprod is a dubious translation:
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- forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u4}} [_inst_10 : TopologicalSpace.{u4} M₃] [_inst_11 : AddCommMonoid.{u4} M₃] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u1, u4} R₁ M₃ _inst_1 _inst_11] [_inst_21 : ContinuousAdd.{u4} M₃ _inst_10 (AddZeroClass.toHasAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_11)))] (f₁ : ContinuousLinearMap.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) (f₂ : ContinuousLinearMap.{u1, u1, u3, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.range_coprod ContinuousLinearMap.range_coprodₓ'. -/
theorem range_coprod [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃] (f₁ : M₁ →L[R₁] M₃)
(f₂ : M₂ →L[R₁] M₃) : range (f₁.coprod f₂) = range f₁ ⊔ range f₂ :=
@@ -1980,10 +1698,7 @@ def smulRight (c : M₁ →L[R] S) (f : M₂) : M₁ →L[R] M₂ :=
-/
/- warning: continuous_linear_map.smul_right_apply -> ContinuousLinearMap.smulRight_apply is a dubious translation:
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- forall {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] {M₂ : Type.{u2}} [_inst_8 : TopologicalSpace.{u2} M₂] [_inst_9 : AddCommMonoid.{u2} M₂] {R : Type.{u3}} {S : Type.{u4}} [_inst_19 : Semiring.{u3} R] [_inst_20 : Semiring.{u4} S] [_inst_21 : Module.{u3, u1} R M₁ _inst_19 _inst_5] [_inst_22 : Module.{u3, u2} R M₂ _inst_19 _inst_9] [_inst_23 : Module.{u3, u4} R S _inst_19 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_20)))] [_inst_24 : Module.{u4, u2} S M₂ _inst_20 _inst_9] [_inst_25 : IsScalarTower.{u3, u4, u2} R S M₂ (SMulZeroClass.toHasSmul.{u3, u4} R S (AddZeroClass.toHasZero.{u4} S (AddMonoid.toAddZeroClass.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_20)))))) (SMulWithZero.toSmulZeroClass.{u3, u4} R S 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_inst_23) => M₁ -> S) (ContinuousLinearMap.toFun.{u3, u3, u1, u4} R R _inst_19 _inst_19 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_19)) M₁ _inst_4 _inst_5 S _inst_26 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_20))) _inst_21 _inst_23) c x) f)
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(MulActionWithZero.toSMulWithZero.{u4, u2} R S (Semiring.toMonoidWithZero.{u4} R _inst_19) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_20)) (Module.toMulActionWithZero.{u4, u2} R S _inst_19 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_20))) _inst_23)))) (SMulZeroClass.toSMul.{u2, u1} S M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u2, u1} S M₂ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_20)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u2, u1} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_20) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u2, u1} S M₂ _inst_20 _inst_9 _inst_24)))) (SMulZeroClass.toSMul.{u4, u1} R M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u4, u1} R M₂ (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_19)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u4, u1} R M₂ (Semiring.toMonoidWithZero.{u4} R _inst_19) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u4, u1} R M₂ _inst_19 _inst_9 _inst_22))))] [_inst_26 : TopologicalSpace.{u2} S] [_inst_27 : ContinuousSMul.{u2, u1} S M₂ (SMulZeroClass.toSMul.{u2, u1} S M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u2, u1} S M₂ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_20)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u2, u1} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_20) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u2, u1} S M₂ _inst_20 _inst_9 _inst_24)))) _inst_26 _inst_8] {c : ContinuousLinearMap.{u4, u4, u3, u2} R R _inst_19 _inst_19 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_19)) M₁ _inst_4 _inst_5 S _inst_26 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_20))) _inst_21 _inst_23} {f : M₂} {x : M₁}, Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (ContinuousLinearMap.{u4, u4, u3, u1} R R _inst_19 _inst_19 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_19)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_21 _inst_22) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u3 u1, u3, u1} (ContinuousLinearMap.{u4, u4, u3, u1} R R _inst_19 _inst_19 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_20))) _inst_21 _inst_23) M₁ S _inst_4 _inst_26 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u4, u4, u3, u2} (ContinuousLinearMap.{u4, u4, u3, u2} R R _inst_19 _inst_19 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_19)) M₁ _inst_4 _inst_5 S _inst_26 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_20))) _inst_21 _inst_23) R R _inst_19 _inst_19 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_19)) M₁ _inst_4 _inst_5 S _inst_26 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_20))) _inst_21 _inst_23 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, u2} R R _inst_19 _inst_19 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_19)) M₁ _inst_4 _inst_5 S _inst_26 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_20))) _inst_21 _inst_23))) c x) f)
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_right_apply ContinuousLinearMap.smulRight_applyₓ'. -/
@[simp]
theorem smulRight_apply {c : M₁ →L[R] S} {f : M₂} {x : M₁} :
@@ -1996,10 +1711,7 @@ end
variable [Module R₁ M₂] [TopologicalSpace R₁] [ContinuousSMul R₁ M₂]
/- warning: continuous_linear_map.smul_right_one_one -> ContinuousLinearMap.smulRight_one_one is a dubious translation:
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) M₂ _inst_8 _inst_9 (Semiring.toModule.{u2} R₁ _inst_1) _inst_19) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) M₂ _inst_8 _inst_9 (Semiring.toModule.{u2} R₁ _inst_1) _inst_19 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u2, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) M₂ _inst_8 _inst_9 (Semiring.toModule.{u2} R₁ _inst_1) _inst_19))) c (OfNat.ofNat.{u2} R₁ 1 (One.toOfNat1.{u2} R₁ (Semiring.toOne.{u2} R₁ _inst_1))))) c
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_right_one_one ContinuousLinearMap.smulRight_one_oneₓ'. -/
@[simp]
theorem smulRight_one_one (c : R₁ →L[R₁] M₂) : smulRight (1 : R₁ →L[R₁] R₁) (c 1) = c := by
@@ -2007,10 +1719,7 @@ theorem smulRight_one_one (c : R₁ →L[R₁] M₂) : smulRight (1 : R₁ →L[
#align continuous_linear_map.smul_right_one_one ContinuousLinearMap.smulRight_one_one
/- warning: continuous_linear_map.smul_right_one_eq_iff -> ContinuousLinearMap.smulRight_one_eq_iff is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_right_one_eq_iff ContinuousLinearMap.smulRight_one_eq_iffₓ'. -/
@[simp]
theorem smulRight_one_eq_iff {f f' : M₂} :
@@ -2019,10 +1728,7 @@ theorem smulRight_one_eq_iff {f f' : M₂} :
#align continuous_linear_map.smul_right_one_eq_iff ContinuousLinearMap.smulRight_one_eq_iff
/- warning: continuous_linear_map.smul_right_comp -> ContinuousLinearMap.smulRight_comp is a dubious translation:
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_inst_9 _inst_19)))) _inst_20 _inst_8] [_inst_22 : ContinuousMul.{u1} R₁ _inst_20 (Distrib.toHasMul.{u1} R₁ (NonUnitalNonAssocSemiring.toDistrib.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))))] {x : M₂} {c : R₁}, Eq.{max (succ u1) (succ u2)} (ContinuousLinearMap.{u1, u1, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) M₂ _inst_8 _inst_9 (Semiring.toModule.{u1} R₁ _inst_1) _inst_19) (ContinuousLinearMap.comp.{u1, u1, u1, u1, u1, u2} R₁ R₁ R₁ _inst_1 _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 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_inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1)) 1 (One.one.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1)) (ContinuousLinearMap.one.{u1, u1} R₁ _inst_1 R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1))))) x) (ContinuousLinearMap.smulRight.{u1, u1, u1, u1} R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) R₁ R₁ _inst_1 _inst_1 (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1) (IsScalarTower.left.{u1, u1} R₁ R₁ (MonoidWithZero.toMonoid.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)) (Monoid.toMulAction.{u1} R₁ (MonoidWithZero.toMonoid.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)))) _inst_20 (ContinuousMul.to_continuousSMul.{u1} R₁ _inst_20 (Distrib.toHasMul.{u1} R₁ (NonUnitalNonAssocSemiring.toDistrib.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)))) _inst_22) (OfNat.ofNat.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1)) 1 (OfNat.mk.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1))))) c)) (ContinuousLinearMap.smulRight.{u1, u2, u1, u1} R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) M₂ _inst_8 _inst_9 R₁ R₁ _inst_1 _inst_1 (Semiring.toModule.{u1} R₁ _inst_1) _inst_19 (Semiring.toModule.{u1} R₁ _inst_1) _inst_19 (IsScalarTower.left.{u1, u2} R₁ M₂ (MonoidWithZero.toMonoid.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R₁ M₂ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (Module.toMulActionWithZero.{u1, u2} R₁ M₂ _inst_1 _inst_9 _inst_19))) _inst_20 _inst_21 (OfNat.ofNat.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1)) 1 (OfNat.mk.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1)) 1 (One.one.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1)) (ContinuousLinearMap.one.{u1, u1} R₁ _inst_1 R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1))))) (SMul.smul.{u1, u2} R₁ M₂ (SMulZeroClass.toHasSmul.{u1, u2} R₁ M₂ (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (SMulWithZero.toSmulZeroClass.{u1, u2} R₁ M₂ (MulZeroClass.toHasZero.{u1} R₁ (MulZeroOneClass.toMulZeroClass.{u1} R₁ (MonoidWithZero.toMulZeroOneClass.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)))) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (MulActionWithZero.toSMulWithZero.{u1, u2} R₁ M₂ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (Module.toMulActionWithZero.{u1, u2} R₁ M₂ _inst_1 _inst_9 _inst_19)))) c x))
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_right_comp ContinuousLinearMap.smulRight_compₓ'. -/
theorem smulRight_comp [ContinuousMul R₁] {x : M₂} {c : R₁} :
(smulRight (1 : R₁ →L[R₁] R₁) x).comp (smulRight (1 : R₁ →L[R₁] R₁) c) =
@@ -2049,10 +1755,7 @@ def pi (f : ∀ i, M →L[R] φ i) : M →L[R] ∀ i, φ i :=
-/
/- warning: continuous_linear_map.coe_pi' -> ContinuousLinearMap.coe_pi' is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_pi' ContinuousLinearMap.coe_pi'ₓ'. -/
@[simp]
theorem coe_pi' (f : ∀ i, M →L[R] φ i) : ⇑(pi f) = fun c i => f i c :=
@@ -2060,10 +1763,7 @@ theorem coe_pi' (f : ∀ i, M →L[R] φ i) : ⇑(pi f) = fun c i => f i c :=
#align continuous_linear_map.coe_pi' ContinuousLinearMap.coe_pi'
/- warning: continuous_linear_map.coe_pi -> ContinuousLinearMap.coe_pi is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_pi ContinuousLinearMap.coe_piₓ'. -/
@[simp]
theorem coe_pi (f : ∀ i, M →L[R] φ i) : (pi f : M →ₗ[R] ∀ i, φ i) = LinearMap.pi fun i => f i :=
@@ -2071,20 +1771,14 @@ theorem coe_pi (f : ∀ i, M →L[R] φ i) : (pi f : M →ₗ[R] ∀ i, φ i) =
#align continuous_linear_map.coe_pi ContinuousLinearMap.coe_pi
/- warning: continuous_linear_map.pi_apply -> ContinuousLinearMap.pi_apply is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.pi_apply ContinuousLinearMap.pi_applyₓ'. -/
theorem pi_apply (f : ∀ i, M →L[R] φ i) (c : M) (i : ι) : pi f c i = f i c :=
rfl
#align continuous_linear_map.pi_apply ContinuousLinearMap.pi_apply
/- warning: continuous_linear_map.pi_eq_zero -> ContinuousLinearMap.pi_eq_zero is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.pi_eq_zero ContinuousLinearMap.pi_eq_zeroₓ'. -/
theorem pi_eq_zero (f : ∀ i, M →L[R] φ i) : pi f = 0 ↔ ∀ i, f i = 0 :=
by
@@ -2093,20 +1787,14 @@ theorem pi_eq_zero (f : ∀ i, M →L[R] φ i) : pi f = 0 ↔ ∀ i, f i = 0 :=
#align continuous_linear_map.pi_eq_zero ContinuousLinearMap.pi_eq_zero
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.pi_zero ContinuousLinearMap.pi_zeroₓ'. -/
theorem pi_zero : pi (fun i => 0 : ∀ i, M →L[R] φ i) = 0 :=
ext fun _ => rfl
#align continuous_linear_map.pi_zero ContinuousLinearMap.pi_zero
/- warning: continuous_linear_map.pi_comp -> ContinuousLinearMap.pi_comp is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.pi_comp ContinuousLinearMap.pi_compₓ'. -/
theorem pi_comp (f : ∀ i, M →L[R] φ i) (g : M₂ →L[R] M) :
(pi f).comp g = pi fun i => (f i).comp g :=
@@ -2121,10 +1809,7 @@ def proj (i : ι) : (∀ i, φ i) →L[R] φ i :=
-/
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.proj_apply ContinuousLinearMap.proj_applyₓ'. -/
@[simp]
theorem proj_apply (i : ι) (b : ∀ i, φ i) : (proj i : (∀ i, φ i) →L[R] φ i) b = b i :=
@@ -2132,20 +1817,14 @@ theorem proj_apply (i : ι) (b : ∀ i, φ i) : (proj i : (∀ i, φ i) →L[R]
#align continuous_linear_map.proj_apply ContinuousLinearMap.proj_apply
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.proj_pi ContinuousLinearMap.proj_piₓ'. -/
theorem proj_pi (f : ∀ i, M₂ →L[R] φ i) (i : ι) : (proj i).comp (pi f) = f i :=
ext fun c => rfl
#align continuous_linear_map.proj_pi ContinuousLinearMap.proj_pi
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.infi_ker_proj ContinuousLinearMap.iInf_ker_projₓ'. -/
theorem iInf_ker_proj : (⨅ i, ker (proj i : (∀ i, φ i) →L[R] φ i) : Submodule R (∀ i, φ i)) = ⊥ :=
LinearMap.iInf_ker_proj
@@ -2154,10 +1833,7 @@ theorem iInf_ker_proj : (⨅ i, ker (proj i : (∀ i, φ i) →L[R] φ i) : Subm
variable (R φ)
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_inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i))) (ContinuousLinearMap.proj.{u1, u2, u3} R _inst_1 ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a) (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i) i))))) (Pi.module.{u2, u3, u1} (Set.Elem.{u2} ι I) (fun (i : Set.Elem.{u2} ι I) => φ (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) i)) R _inst_1 (fun (i : Set.Elem.{u2} ι I) => _inst_9 (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) i)) (fun (i : Set.Elem.{u2} ι I) => _inst_10 (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) i))))
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.infi_ker_proj_equiv ContinuousLinearMap.iInfKerProjEquivₓ'. -/
/-- If `I` and `J` are complementary index sets, the product of the kernels of the `J`th projections
of `φ` is linearly equivalent to the product over `I`. -/
@@ -2194,30 +1870,21 @@ variable {R : Type _} [Ring R] {R₂ : Type _} [Ring R₂] {R₃ : Type _} [Ring
section
/- warning: continuous_linear_map.map_neg -> ContinuousLinearMap.map_neg is a dubious translation:
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(AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_5))))) x)) (Neg.neg.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (NegZeroClass.toNeg.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) _inst_7))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) f x))
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_neg ContinuousLinearMap.map_negₓ'. -/
protected theorem map_neg (f : M →SL[σ₁₂] M₂) (x : M) : f (-x) = -f x :=
map_neg _ _
#align continuous_linear_map.map_neg ContinuousLinearMap.map_neg
/- warning: continuous_linear_map.map_sub -> ContinuousLinearMap.map_sub is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_sub ContinuousLinearMap.map_subₓ'. -/
protected theorem map_sub (f : M →SL[σ₁₂] M₂) (x y : M) : f (x - y) = f x - f y :=
map_sub _ _ _
#align continuous_linear_map.map_sub ContinuousLinearMap.map_sub
/- warning: continuous_linear_map.sub_apply' -> ContinuousLinearMap.sub_apply' is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.sub_apply' ContinuousLinearMap.sub_apply'ₓ'. -/
@[simp]
theorem sub_apply' (f g : M →SL[σ₁₂] M₂) (x : M) : ((f : M →ₛₗ[σ₁₂] M₂) - g) x = f x - g x :=
@@ -2231,10 +1898,7 @@ section
variable [Module R M₂] [Module R M₃] [Module R M₄]
/- warning: continuous_linear_map.range_prod_eq -> ContinuousLinearMap.range_prod_eq is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] {M₃ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₃] [_inst_9 : AddCommGroup.{u4} M₃] [_inst_12 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_15 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_16 : Module.{u1, u4} R M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)] {f : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15} {g : ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16}, (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12))))) (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u3, u1, u1, u2, u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15)) f) (LinearMap.ker.{u1, u1, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u1, u1, u2, u4} (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16)) g)) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12))) -> (Eq.{succ (max u3 u4)} (Submodule.{u1, max u3 u4} R (Prod.{u3, u4} M₂ M₃) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u3, u4} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)) (Prod.module.{u1, u3, u4} R M₂ M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16)) (LinearMap.range.{u1, u1, u2, max u3 u4, max u2 u3 u4} R R M (Prod.{u3, u4} M₂ M₃) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (Prod.addCommMonoid.{u3, u4} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)) _inst_12 (Prod.module.{u1, u3, u4} R M₂ M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, max u3 u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (Prod.{u3, u4} M₂ M₃) (Prod.topologicalSpace.{u3, u4} M₂ M₃ _inst_6 _inst_8) (Prod.addCommMonoid.{u3, u4} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)) _inst_12 (Prod.module.{u1, u3, u4} R M₂ M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16)) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u3 u4, u1, u1, u2, max u3 u4} (ContinuousLinearMap.{u1, u1, u2, max u3 u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (Prod.{u3, u4} M₂ M₃) (Prod.topologicalSpace.{u3, u4} M₂ M₃ _inst_6 _inst_8) (Prod.addCommMonoid.{u3, u4} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)) _inst_12 (Prod.module.{u1, u3, u4} R M₂ M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16)) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (Prod.{u3, u4} M₂ M₃) (Prod.topologicalSpace.{u3, u4} M₂ M₃ _inst_6 _inst_8) (Prod.addCommMonoid.{u3, u4} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)) _inst_12 (Prod.module.{u1, u3, u4} R M₂ M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, max u3 u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (Prod.{u3, u4} M₂ M₃) (Prod.topologicalSpace.{u3, u4} M₂ M₃ _inst_6 _inst_8) (Prod.addCommMonoid.{u3, u4} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)) _inst_12 (Prod.module.{u1, u3, u4} R M₂ M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousLinearMap.prod.{u1, u2, u3, u4} R (Ring.toSemiring.{u1} R _inst_1) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_15 _inst_16 f g)) (Submodule.prod.{u1, u3, u4} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_15 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u3, u1, u1, u2, u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15)) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f) M₃ (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16 (LinearMap.range.{u1, u1, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u1, u1, u2, u4} (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16)) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) g)))
-but is expected to have type
- forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u2}} [_inst_6 : TopologicalSpace.{u2} M₂] [_inst_7 : AddCommGroup.{u2} M₂] {M₃ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₃] [_inst_9 : AddCommGroup.{u1} M₃] [_inst_12 : Module.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_15 : Module.{u4, u2} R M₂ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7)] [_inst_16 : Module.{u4, u1} R M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)] {f : ContinuousLinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15} {g : ContinuousLinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16}, (Eq.{succ u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (Sup.sup.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (SemilatticeSup.toSup.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (Lattice.toSemilatticeSup.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (ConditionallyCompleteLattice.toLattice.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (Submodule.completeLattice.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12))))) (LinearMap.ker.{u4, u4, u3, u2, max u3 u2} R R M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (ContinuousLinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u2, u4, u4, u3, u2} (ContinuousLinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15) R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15)) f) (LinearMap.ker.{u4, u4, u3, u1, max u3 u1} R R M M₃ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (ContinuousLinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u1, u4, u4, u3, u1} (ContinuousLinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16)) g)) (Top.top.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (Submodule.instTopSubmodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12))) -> (Eq.{max (succ u2) (succ u1)} (Submodule.{u4, max u2 u1} R (Prod.{u2, u1} M₂ M₃) (Ring.toSemiring.{u4} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)) (Prod.module.{u4, u2, u1} R M₂ M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_15 _inst_16)) (LinearMap.range.{u4, u4, u3, max u2 u1, max (max u3 u2) u1} R R M (Prod.{u2, u1} M₂ M₃) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (Prod.instAddCommMonoidSum.{u2, u1} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)) _inst_12 (Prod.module.{u4, u2, u1} R M₂ M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_15 _inst_16) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (ContinuousLinearMap.{u4, u4, u3, max u1 u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (Prod.{u2, u1} M₂ M₃) (instTopologicalSpaceProd.{u2, u1} M₂ M₃ _inst_6 _inst_8) (Prod.instAddCommMonoidSum.{u2, u1} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)) _inst_12 (Prod.module.{u4, u2, u1} R M₂ M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_15 _inst_16)) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max (max u3 u2) u1, u4, u4, u3, max u2 u1} (ContinuousLinearMap.{u4, u4, u3, max u1 u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (Prod.{u2, u1} M₂ M₃) (instTopologicalSpaceProd.{u2, u1} M₂ M₃ _inst_6 _inst_8) (Prod.instAddCommMonoidSum.{u2, u1} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)) _inst_12 (Prod.module.{u4, u2, u1} R M₂ M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_15 _inst_16)) R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (Prod.{u2, u1} M₂ M₃) (instTopologicalSpaceProd.{u2, u1} M₂ M₃ _inst_6 _inst_8) (Prod.instAddCommMonoidSum.{u2, u1} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)) _inst_12 (Prod.module.{u4, u2, u1} R M₂ M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_15 _inst_16) (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, max u2 u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (Prod.{u2, u1} M₂ M₃) (instTopologicalSpaceProd.{u2, u1} M₂ M₃ _inst_6 _inst_8) (Prod.instAddCommMonoidSum.{u2, u1} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)) _inst_12 (Prod.module.{u4, u2, u1} R M₂ M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_15 _inst_16))) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (ContinuousLinearMap.prod.{u4, u3, u2, u1} R (Ring.toSemiring.{u4} R _inst_1) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_15 _inst_16 f g)) (Submodule.prod.{u4, u2, u1} R M₂ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_15 (LinearMap.range.{u4, u4, u3, u2, max u3 u2} R R M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (ContinuousLinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u2, u4, u4, u3, u2} (ContinuousLinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15) R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15)) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) f) M₃ (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_16 (LinearMap.range.{u4, u4, u3, u1, max u3 u1} R R M M₃ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (ContinuousLinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u1, u4, u4, u3, u1} (ContinuousLinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16)) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) g)))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.range_prod_eq ContinuousLinearMap.range_prod_eqₓ'. -/
theorem range_prod_eq {f : M →L[R] M₂} {g : M →L[R] M₃} (h : ker f ⊔ ker g = ⊤) :
range (f.Prod g) = (range f).Prod (range g) :=
@@ -2242,10 +1906,7 @@ theorem range_prod_eq {f : M →L[R] M₂} {g : M →L[R] M₃} (h : ker f ⊔ k
#align continuous_linear_map.range_prod_eq ContinuousLinearMap.range_prod_eq
/- warning: continuous_linear_map.ker_prod_ker_le_ker_coprod -> ContinuousLinearMap.ker_prod_ker_le_ker_coprod is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] {M₃ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₃] [_inst_9 : AddCommGroup.{u4} M₃] [_inst_12 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_15 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_16 : Module.{u1, u4} R M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)] [_inst_18 : ContinuousAdd.{u4} M₃ _inst_8 (AddZeroClass.toHasAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (SubNegMonoid.toAddMonoid.{u4} M₃ (AddGroup.toSubNegMonoid.{u4} M₃ (AddCommGroup.toAddGroup.{u4} M₃ _inst_9)))))] (f : ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (g : ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16), LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M₂) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15)) (Preorder.toHasLe.{max u2 u3} (Submodule.{u1, max 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_inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15)) (Prod.{u2, u3} M M₂) (Submodule.setLike.{u1, max u2 u3} R (Prod.{u2, u3} M M₂) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15))))) (Submodule.prod.{u1, u2, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12 (LinearMap.ker.{u1, u1, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u1, u1, u2, u4} (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16)) f) M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_15 (LinearMap.ker.{u1, u1, u3, u4, max u3 u4} R R M₂ M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u4, u1, u1, u3, u4} (ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16)) g)) (LinearMap.ker.{u1, u1, max u2 u3, u4, max (max u2 u3) u4} R R (Prod.{u2, u3} M M₂) M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, max u2 u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max (max u2 u3) u4, u1, u1, max u2 u3, u4} (ContinuousLinearMap.{u1, u1, max u2 u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, max u2 u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16)) (ContinuousLinearMap.coprod.{u1, u2, u3, u4} R (Ring.toSemiring.{u1} R _inst_1) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_15 _inst_16 _inst_18 f g))
-but is expected to have type
- forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] {M₃ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₃] [_inst_9 : AddCommGroup.{u4} M₃] [_inst_12 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_15 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] [_inst_16 : Module.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)] [_inst_18 : ContinuousAdd.{u4} M₃ _inst_8 (AddZeroClass.toAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (SubNegMonoid.toAddMonoid.{u4} M₃ (AddGroup.toSubNegMonoid.{u4} M₃ (AddCommGroup.toAddGroup.{u4} M₃ _inst_9)))))] (f : ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (g : ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16), LE.le.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (Preorder.toLE.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (PartialOrder.toPreorder.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ 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(Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)))))) (Submodule.prod.{u3, u2, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12 (LinearMap.ker.{u3, u3, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u3, u3, u2, u4} 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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ker_prod_ker_le_ker_coprod ContinuousLinearMap.ker_prod_ker_le_ker_coprodₓ'. -/
theorem ker_prod_ker_le_ker_coprod [ContinuousAdd M₃] (f : M →L[R] M₃) (g : M₂ →L[R] M₃) :
(LinearMap.ker f).Prod (LinearMap.ker g) ≤ LinearMap.ker (f.coprod g) :=
@@ -2253,10 +1914,7 @@ theorem ker_prod_ker_le_ker_coprod [ContinuousAdd M₃] (f : M →L[R] M₃) (g
#align continuous_linear_map.ker_prod_ker_le_ker_coprod ContinuousLinearMap.ker_prod_ker_le_ker_coprod
/- warning: continuous_linear_map.ker_coprod_of_disjoint_range -> ContinuousLinearMap.ker_coprod_of_disjoint_range is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] {M₃ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₃] [_inst_9 : AddCommGroup.{u4} M₃] [_inst_12 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_15 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_16 : Module.{u1, u4} R M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)] [_inst_18 : ContinuousAdd.{u4} M₃ _inst_8 (AddZeroClass.toHasAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (SubNegMonoid.toAddMonoid.{u4} M₃ (AddGroup.toSubNegMonoid.{u4} M₃ (AddCommGroup.toAddGroup.{u4} M₃ _inst_9)))))] (f : ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R 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-but is expected to have type
- forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] {M₃ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₃] [_inst_9 : AddCommGroup.{u4} M₃] [_inst_12 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_15 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] [_inst_16 : Module.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)] [_inst_18 : ContinuousAdd.{u4} M₃ _inst_8 (AddZeroClass.toAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (SubNegMonoid.toAddMonoid.{u4} M₃ (AddGroup.toSubNegMonoid.{u4} M₃ (AddCommGroup.toAddGroup.{u4} M₃ _inst_9)))))] (f : ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R 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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ker_coprod_of_disjoint_range ContinuousLinearMap.ker_coprod_of_disjoint_rangeₓ'. -/
theorem ker_coprod_of_disjoint_range [ContinuousAdd M₃] (f : M →L[R] M₃) (g : M₂ →L[R] M₃)
(hd : Disjoint (range f) (range g)) :
@@ -2274,10 +1932,7 @@ instance : Neg (M →SL[σ₁₂] M₂) :=
⟨fun f => ⟨-f, f.2.neg⟩⟩
/- warning: continuous_linear_map.neg_apply -> ContinuousLinearMap.neg_apply is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.neg_apply ContinuousLinearMap.neg_applyₓ'. -/
@[simp]
theorem neg_apply (f : M →SL[σ₁₂] M₂) (x : M) : (-f) x = -f x :=
@@ -2285,10 +1940,7 @@ theorem neg_apply (f : M →SL[σ₁₂] M₂) (x : M) : (-f) x = -f x :=
#align continuous_linear_map.neg_apply ContinuousLinearMap.neg_apply
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_neg ContinuousLinearMap.coe_negₓ'. -/
@[simp, norm_cast]
theorem coe_neg (f : M →SL[σ₁₂] M₂) : (↑(-f) : M →ₛₗ[σ₁₂] M₂) = -f :=
@@ -2296,10 +1948,7 @@ theorem coe_neg (f : M →SL[σ₁₂] M₂) : (↑(-f) : M →ₛₗ[σ₁₂]
#align continuous_linear_map.coe_neg ContinuousLinearMap.coe_neg
/- warning: continuous_linear_map.coe_neg' -> ContinuousLinearMap.coe_neg' is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_neg' ContinuousLinearMap.coe_neg'ₓ'. -/
@[norm_cast]
theorem coe_neg' (f : M →SL[σ₁₂] M₂) : ⇑(-f) = -f :=
@@ -2333,20 +1982,14 @@ instance : AddCommGroup (M →SL[σ₁₂] M₂) := by
apply_rules [zero_add, add_assoc, add_zero, add_left_neg, add_comm, sub_eq_add_neg]
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.sub_apply ContinuousLinearMap.sub_applyₓ'. -/
theorem sub_apply (f g : M →SL[σ₁₂] M₂) (x : M) : (f - g) x = f x - g x :=
rfl
#align continuous_linear_map.sub_apply ContinuousLinearMap.sub_apply
/- warning: continuous_linear_map.coe_sub -> ContinuousLinearMap.coe_sub is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_sub ContinuousLinearMap.coe_subₓ'. -/
@[simp, norm_cast]
theorem coe_sub (f g : M →SL[σ₁₂] M₂) : (↑(f - g) : M →ₛₗ[σ₁₂] M₂) = f - g :=
@@ -2354,10 +1997,7 @@ theorem coe_sub (f g : M →SL[σ₁₂] M₂) : (↑(f - g) : M →ₛₗ[σ₁
#align continuous_linear_map.coe_sub ContinuousLinearMap.coe_sub
/- warning: continuous_linear_map.coe_sub' -> ContinuousLinearMap.coe_sub' is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_sub' ContinuousLinearMap.coe_sub'ₓ'. -/
@[simp, norm_cast]
theorem coe_sub' (f g : M →SL[σ₁₂] M₂) : ⇑(f - g) = f - g :=
@@ -2367,10 +2007,7 @@ theorem coe_sub' (f g : M →SL[σ₁₂] M₂) : ⇑(f - g) = f - g :=
end
/- warning: continuous_linear_map.comp_neg -> ContinuousLinearMap.comp_neg is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_neg ContinuousLinearMap.comp_negₓ'. -/
@[simp]
theorem comp_neg [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₂] [TopologicalAddGroup M₃]
@@ -2381,10 +2018,7 @@ theorem comp_neg [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddG
#align continuous_linear_map.comp_neg ContinuousLinearMap.comp_neg
/- warning: continuous_linear_map.neg_comp -> ContinuousLinearMap.neg_comp is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.neg_comp ContinuousLinearMap.neg_compₓ'. -/
@[simp]
theorem neg_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₃] (g : M₂ →SL[σ₂₃] M₃)
@@ -2395,10 +2029,7 @@ theorem neg_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddG
#align continuous_linear_map.neg_comp ContinuousLinearMap.neg_comp
/- warning: continuous_linear_map.comp_sub -> ContinuousLinearMap.comp_sub is a dubious translation:
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(Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u3} R₃ (Ring.toNonAssocRing.{u3} R₃ _inst_3))} {σ₁₃ : RingHom.{u1, u3} R R₃ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₃ (Ring.toNonAssocRing.{u3} R₃ _inst_3))} [_inst_15 : RingHomCompTriple.{u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃] [_inst_16 : TopologicalAddGroup.{u5} M₂ _inst_6 (AddCommGroup.toAddGroup.{u5} M₂ _inst_7)] [_inst_17 : TopologicalAddGroup.{u6} M₃ _inst_8 (AddCommGroup.toAddGroup.{u6} M₃ _inst_9)] (g : ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_13 _inst_14) (f₁ : ContinuousLinearMap.{u1, u2, u4, u5} R R₂ (Ring.toSemiring.{u1} R _inst_1) 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_inst_2)) (Semiring.toNonAssocSemiring.{u4} R₃ (Ring.toSemiring.{u4} R₃ _inst_3))} {σ₁₃ : RingHom.{u6, u4} R R₃ (Semiring.toNonAssocSemiring.{u6} R (Ring.toSemiring.{u6} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} R₃ (Ring.toSemiring.{u4} R₃ _inst_3))} [_inst_15 : RingHomCompTriple.{u6, u5, u4} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃] [_inst_16 : TopologicalAddGroup.{u3} M₂ _inst_6 (AddCommGroup.toAddGroup.{u3} M₂ _inst_7)] [_inst_17 : TopologicalAddGroup.{u2} M₃ _inst_8 (AddCommGroup.toAddGroup.{u2} M₃ _inst_9)] (g : ContinuousLinearMap.{u5, u4, u3, u2} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_13 _inst_14) (f₁ : ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_sub ContinuousLinearMap.comp_subₓ'. -/
@[simp]
theorem comp_sub [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₂] [TopologicalAddGroup M₃]
@@ -2409,10 +2040,7 @@ theorem comp_sub [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddG
#align continuous_linear_map.comp_sub ContinuousLinearMap.comp_sub
/- warning: continuous_linear_map.sub_comp -> ContinuousLinearMap.sub_comp is a dubious translation:
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_inst_2)) (Semiring.toNonAssocSemiring.{u4} R₃ (Ring.toSemiring.{u4} R₃ _inst_3))} {σ₁₃ : RingHom.{u6, u4} R R₃ (Semiring.toNonAssocSemiring.{u6} R (Ring.toSemiring.{u6} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} R₃ (Ring.toSemiring.{u4} R₃ _inst_3))} [_inst_15 : RingHomCompTriple.{u6, u5, u4} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃] [_inst_16 : TopologicalAddGroup.{u3} M₃ _inst_8 (AddCommGroup.toAddGroup.{u3} M₃ _inst_9)] (g₁ : ContinuousLinearMap.{u5, u4, u2, u3} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_13 _inst_14) (g₂ : ContinuousLinearMap.{u5, u4, u2, u3} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ 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_inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g₂ f))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.sub_comp ContinuousLinearMap.sub_compₓ'. -/
@[simp]
theorem sub_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₃] (g₁ g₂ : M₂ →SL[σ₂₃] M₃)
@@ -2429,10 +2057,7 @@ instance [TopologicalAddGroup M] : Ring (M →L[R] M) :=
one := 1 }
/- warning: continuous_linear_map.smul_right_one_pow -> ContinuousLinearMap.smulRight_one_pow is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_right_one_pow ContinuousLinearMap.smulRight_one_powₓ'. -/
theorem smulRight_one_pow [TopologicalSpace R] [TopologicalRing R] (c : R) (n : ℕ) :
smulRight (1 : R →L[R] R) c ^ n = smulRight (1 : R →L[R] R) (c ^ n) :=
@@ -2448,10 +2073,7 @@ section
variable {σ₂₁ : R₂ →+* R} [RingHomInvPair σ₁₂ σ₂₁]
/- warning: continuous_linear_map.proj_ker_of_right_inverse -> ContinuousLinearMap.projKerOfRightInverse is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u1} R₂ R (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))} [_inst_15 : RingHomInvPair.{u1, u2} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : 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- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R₂ (Ring.toSemiring.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u1} R₂ R (Semiring.toNonAssocSemiring.{u2} R₂ (Ring.toSemiring.{u2} R₂ _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))} [_inst_15 : RingHomInvPair.{u1, u2} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : TopologicalAddGroup.{u3} M _inst_4 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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.proj_ker_of_right_inverse ContinuousLinearMap.projKerOfRightInverseₓ'. -/
/-- Given a right inverse `f₂ : M₂ →L[R] M` to `f₁ : M →L[R] M₂`,
`proj_ker_of_right_inverse f₁ f₂ h` is the projection `M →L[R] f₁.ker` along `f₂.range`. -/
@@ -2461,10 +2083,7 @@ def projKerOfRightInverse [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂
#align continuous_linear_map.proj_ker_of_right_inverse ContinuousLinearMap.projKerOfRightInverse
/- warning: continuous_linear_map.coe_proj_ker_of_right_inverse_apply -> ContinuousLinearMap.coe_projKerOfRightInverse_apply is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u1} R₂ R (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))} [_inst_15 : RingHomInvPair.{u1, u2} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : 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R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 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_inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) 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_inst_12 _inst_13)) f₁))) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) 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R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_12 (Submodule.module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} 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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_proj_ker_of_right_inverse_apply ContinuousLinearMap.coe_projKerOfRightInverse_applyₓ'. -/
@[simp]
theorem coe_projKerOfRightInverse_apply [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂)
@@ -2474,10 +2093,7 @@ theorem coe_projKerOfRightInverse_apply [TopologicalAddGroup M] (f₁ : M →SL[
#align continuous_linear_map.coe_proj_ker_of_right_inverse_apply ContinuousLinearMap.coe_projKerOfRightInverse_apply
/- warning: continuous_linear_map.proj_ker_of_right_inverse_apply_idem -> ContinuousLinearMap.projKerOfRightInverse_apply_idem is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u1} R₂ R (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))} [_inst_15 : RingHomInvPair.{u1, u2} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : 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_inst_12 _inst_13)) f₁))) (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) 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(ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) M (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) _inst_4 (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) 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_inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} 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_inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (Submodule.addCommMonoid.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_12 (Submodule.module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} 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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.proj_ker_of_right_inverse_apply_idem ContinuousLinearMap.projKerOfRightInverse_apply_idemₓ'. -/
@[simp]
theorem projKerOfRightInverse_apply_idem [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂)
@@ -2487,10 +2103,7 @@ theorem projKerOfRightInverse_apply_idem [TopologicalAddGroup M] (f₁ : M →SL
#align continuous_linear_map.proj_ker_of_right_inverse_apply_idem ContinuousLinearMap.projKerOfRightInverse_apply_idem
/- warning: continuous_linear_map.proj_ker_of_right_inverse_comp_inv -> ContinuousLinearMap.projKerOfRightInverse_comp_inv is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u1} R₂ R (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))} [_inst_15 : RingHomInvPair.{u1, u2} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : 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(AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) _inst_4 (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) 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_inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (Submodule.addCommMonoid.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_12 (Submodule.module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ 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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.proj_ker_of_right_inverse_comp_inv ContinuousLinearMap.projKerOfRightInverse_comp_invₓ'. -/
@[simp]
theorem projKerOfRightInverse_comp_inv [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂)
@@ -2508,10 +2121,7 @@ section DivisionMonoid
variable {R M : Type _}
/- warning: continuous_linear_map.is_open_map_of_ne_zero -> ContinuousLinearMap.isOpenMap_of_ne_zero is a dubious translation:
-lean 3 declaration is
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- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} R] [_inst_2 : DivisionRing.{u2} R] [_inst_3 : ContinuousSub.{u2} R _inst_1 (Ring.toSub.{u2} R (DivisionRing.toRing.{u2} R _inst_2))] [_inst_4 : AddCommGroup.{u1} M] [_inst_5 : TopologicalSpace.{u1} M] [_inst_6 : ContinuousAdd.{u1} M _inst_5 (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_4)))))] [_inst_7 : Module.{u2, u1} R M (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4)] [_inst_8 : ContinuousSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (Module.toMulActionWithZero.{u2, u1} R M (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_7)))) _inst_1 _inst_5] (f : ContinuousLinearMap.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))), (Ne.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2))) (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))))) f))
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.is_open_map_of_ne_zero ContinuousLinearMap.isOpenMap_of_ne_zeroₓ'. -/
/-- A nonzero continuous linear functional is open. -/
protected theorem isOpenMap_of_ne_zero [TopologicalSpace R] [DivisionRing R] [ContinuousSub R]
@@ -2540,10 +2150,7 @@ variable {R R₂ R₃ S S₃ : Type _} [Semiring R] [Semiring R₂] [Semiring R
include σ₁₃
/- warning: continuous_linear_map.smul_comp -> ContinuousLinearMap.smul_comp is a dubious translation:
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- forall {R : Type.{u1}} {R₂ : Type.{u2}} {R₃ : Type.{u3}} {S₃ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : Semiring.{u3} R₃] [_inst_5 : Monoid.{u4} S₃] {M : Type.{u5}} [_inst_6 : TopologicalSpace.{u5} M] [_inst_7 : AddCommMonoid.{u5} M] [_inst_8 : Module.{u1, u5} R M _inst_1 _inst_7] {M₂ : Type.{u6}} [_inst_9 : TopologicalSpace.{u6} M₂] [_inst_10 : AddCommMonoid.{u6} M₂] [_inst_11 : Module.{u2, u6} R₂ M₂ _inst_2 _inst_10] {M₃ : Type.{u7}} [_inst_12 : TopologicalSpace.{u7} M₃] [_inst_13 : AddCommMonoid.{u7} M₃] [_inst_14 : Module.{u3, u7} R₃ M₃ _inst_3 _inst_13] [_inst_21 : DistribMulAction.{u4, u7} S₃ M₃ _inst_5 (AddCommMonoid.toAddMonoid.{u7} M₃ _inst_13)] [_inst_22 : SMulCommClass.{u3, u4, u7} R₃ S₃ M₃ (SMulZeroClass.toHasSmul.{u3, u7} R₃ M₃ (AddZeroClass.toHasZero.{u7} M₃ (AddMonoid.toAddZeroClass.{u7} M₃ (AddCommMonoid.toAddMonoid.{u7} M₃ _inst_13))) (SMulWithZero.toSmulZeroClass.{u3, u7} R₃ M₃ (MulZeroClass.toHasZero.{u3} R₃ (MulZeroOneClass.toMulZeroClass.{u3} R₃ (MonoidWithZero.toMulZeroOneClass.{u3} R₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3)))) (AddZeroClass.toHasZero.{u7} M₃ (AddMonoid.toAddZeroClass.{u7} M₃ (AddCommMonoid.toAddMonoid.{u7} M₃ _inst_13))) (MulActionWithZero.toSMulWithZero.{u3, u7} R₃ M₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3) (AddZeroClass.toHasZero.{u7} M₃ (AddMonoid.toAddZeroClass.{u7} M₃ (AddCommMonoid.toAddMonoid.{u7} M₃ _inst_13))) (Module.toMulActionWithZero.{u3, u7} R₃ M₃ _inst_3 _inst_13 _inst_14)))) (SMulZeroClass.toHasSmul.{u4, u7} S₃ M₃ (AddZeroClass.toHasZero.{u7} M₃ (AddMonoid.toAddZeroClass.{u7} M₃ (AddCommMonoid.toAddMonoid.{u7} M₃ _inst_13))) (DistribSMul.toSmulZeroClass.{u4, u7} S₃ M₃ (AddMonoid.toAddZeroClass.{u7} M₃ (AddCommMonoid.toAddMonoid.{u7} M₃ _inst_13)) (DistribMulAction.toDistribSMul.{u4, u7} S₃ M₃ _inst_5 (AddCommMonoid.toAddMonoid.{u7} M₃ _inst_13) _inst_21)))] [_inst_23 : ContinuousConstSMul.{u4, u7} S₃ M₃ _inst_12 (SMulZeroClass.toHasSmul.{u4, u7} S₃ M₃ (AddZeroClass.toHasZero.{u7} M₃ (AddMonoid.toAddZeroClass.{u7} M₃ (AddCommMonoid.toAddMonoid.{u7} M₃ _inst_13))) (DistribSMul.toSmulZeroClass.{u4, u7} S₃ M₃ (AddMonoid.toAddZeroClass.{u7} M₃ (AddCommMonoid.toAddMonoid.{u7} M₃ _inst_13)) (DistribMulAction.toDistribSMul.{u4, u7} S₃ M₃ _inst_5 (AddCommMonoid.toAddMonoid.{u7} M₃ _inst_13) _inst_21)))] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₃ : RingHom.{u2, u3} R₂ R₃ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {σ₁₃ : RingHom.{u1, u3} R R₃ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} [_inst_27 : RingHomCompTriple.{u1, u2, u3} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] (c : S₃) (h : ContinuousLinearMap.{u2, u3, u6, u7} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14) (f : ContinuousLinearMap.{u1, u2, u5, u6} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11), Eq.{max (succ u5) (succ u7)} (ContinuousLinearMap.{u1, u3, u5, u7} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (ContinuousLinearMap.comp.{u1, u2, u3, u5, u6, u7} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_8 _inst_11 _inst_14 _inst_27 (SMul.smul.{u4, max u6 u7} S₃ (ContinuousLinearMap.{u2, u3, u6, u7} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14) (MulAction.toHasSmul.{u4, max u6 u7} S₃ (ContinuousLinearMap.{u2, u3, u6, u7} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14) _inst_5 (ContinuousLinearMap.mulAction.{u2, u3, u6, u7, u4} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14 S₃ _inst_5 _inst_21 _inst_22 _inst_23)) c h) f) (SMul.smul.{u4, max u5 u7} S₃ (ContinuousLinearMap.{u1, u3, u5, u7} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (MulAction.toHasSmul.{u4, max u5 u7} S₃ (ContinuousLinearMap.{u1, u3, u5, u7} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) _inst_5 (ContinuousLinearMap.mulAction.{u1, u3, u5, u7, u4} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14 S₃ _inst_5 _inst_21 _inst_22 _inst_23)) c (ContinuousLinearMap.comp.{u1, u2, u3, u5, u6, u7} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_8 _inst_11 _inst_14 _inst_27 h f))
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- forall {R : Type.{u3}} {R₂ : Type.{u7}} {R₃ : Type.{u6}} {S₃ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : Semiring.{u7} R₂] [_inst_3 : Semiring.{u6} R₃] [_inst_5 : Monoid.{u1} S₃] {M : Type.{u2}} [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : AddCommMonoid.{u2} M] [_inst_8 : Module.{u3, u2} R M _inst_1 _inst_7] {M₂ : Type.{u5}} [_inst_9 : TopologicalSpace.{u5} M₂] [_inst_10 : AddCommMonoid.{u5} M₂] [_inst_11 : Module.{u7, u5} R₂ M₂ _inst_2 _inst_10] {M₃ : Type.{u4}} [_inst_12 : TopologicalSpace.{u4} M₃] [_inst_13 : AddCommMonoid.{u4} M₃] [_inst_14 : Module.{u6, u4} R₃ M₃ _inst_3 _inst_13] [_inst_21 : DistribMulAction.{u1, u4} S₃ M₃ _inst_5 (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_13)] [_inst_22 : SMulCommClass.{u6, u1, u4} R₃ S₃ M₃ (SMulZeroClass.toSMul.{u6, u4} R₃ M₃ (AddMonoid.toZero.{u4} M₃ (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_13)) (SMulWithZero.toSMulZeroClass.{u6, u4} R₃ M₃ (MonoidWithZero.toZero.{u6} R₃ (Semiring.toMonoidWithZero.{u6} R₃ _inst_3)) (AddMonoid.toZero.{u4} M₃ (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_13)) (MulActionWithZero.toSMulWithZero.{u6, u4} R₃ M₃ (Semiring.toMonoidWithZero.{u6} R₃ _inst_3) (AddMonoid.toZero.{u4} M₃ (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_13)) (Module.toMulActionWithZero.{u6, u4} R₃ M₃ _inst_3 _inst_13 _inst_14)))) (SMulZeroClass.toSMul.{u1, u4} S₃ M₃ (AddMonoid.toZero.{u4} M₃ (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_13)) (DistribSMul.toSMulZeroClass.{u1, u4} S₃ M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_13)) (DistribMulAction.toDistribSMul.{u1, u4} S₃ M₃ _inst_5 (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_13) _inst_21)))] [_inst_23 : ContinuousConstSMul.{u1, u4} S₃ M₃ _inst_12 (SMulZeroClass.toSMul.{u1, u4} S₃ M₃ (AddMonoid.toZero.{u4} M₃ (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_13)) (DistribSMul.toSMulZeroClass.{u1, u4} S₃ M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_13)) (DistribMulAction.toDistribSMul.{u1, u4} S₃ M₃ _inst_5 (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_13) _inst_21)))] {σ₁₂ : RingHom.{u3, u7} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u7} R₂ _inst_2)} {σ₂₃ : RingHom.{u7, u6} R₂ R₃ (Semiring.toNonAssocSemiring.{u7} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u6} R₃ _inst_3)} {σ₁₃ : RingHom.{u3, u6} R R₃ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u6} R₃ _inst_3)} [_inst_27 : RingHomCompTriple.{u3, u7, u6} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] (c : S₃) (h : ContinuousLinearMap.{u7, u6, u5, u4} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14) (f : ContinuousLinearMap.{u3, u7, u2, u5} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11), Eq.{max (succ u2) (succ u4)} (ContinuousLinearMap.{u3, u6, u2, u4} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (ContinuousLinearMap.comp.{u3, u7, u6, u2, u5, u4} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_8 _inst_11 _inst_14 _inst_27 (HSMul.hSMul.{u1, max u4 u5, max u4 u5} S₃ (ContinuousLinearMap.{u7, u6, u5, u4} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14) (ContinuousLinearMap.{u7, u6, u5, u4} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14) (instHSMul.{u1, max u4 u5} S₃ (ContinuousLinearMap.{u7, u6, u5, u4} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14) (MulAction.toSMul.{u1, max u4 u5} S₃ (ContinuousLinearMap.{u7, u6, u5, u4} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14) _inst_5 (ContinuousLinearMap.mulAction.{u7, u6, u5, u4, u1} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14 S₃ _inst_5 _inst_21 _inst_22 _inst_23))) c h) f) (HSMul.hSMul.{u1, max u4 u2, max u4 u2} S₃ (ContinuousLinearMap.{u3, u6, u2, u4} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (ContinuousLinearMap.{u3, u6, u2, u4} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (instHSMul.{u1, max u4 u2} S₃ (ContinuousLinearMap.{u3, u6, u2, u4} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (MulAction.toSMul.{u1, max u4 u2} S₃ (ContinuousLinearMap.{u3, u6, u2, u4} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) _inst_5 (ContinuousLinearMap.mulAction.{u3, u6, u2, u4, u1} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14 S₃ _inst_5 _inst_21 _inst_22 _inst_23))) c (ContinuousLinearMap.comp.{u3, u7, u6, u2, u5, u4} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_8 _inst_11 _inst_14 _inst_27 h f))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_comp ContinuousLinearMap.smul_compₓ'. -/
@[simp]
theorem smul_comp (c : S₃) (h : M₂ →SL[σ₂₃] M₃) (f : M →SL[σ₁₂] M₂) :
@@ -2558,10 +2165,7 @@ variable [DistribMulAction S₃ M₂] [ContinuousConstSMul S₃ M₂] [SMulCommC
variable [DistribMulAction S N₂] [ContinuousConstSMul S N₂] [SMulCommClass R S N₂]
/- warning: continuous_linear_map.comp_smul -> ContinuousLinearMap.comp_smul is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_4 : Monoid.{u2} S] {M : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : AddCommMonoid.{u3} M] [_inst_8 : Module.{u1, u3} R M _inst_1 _inst_7] {N₂ : Type.{u4}} [_inst_15 : TopologicalSpace.{u4} N₂] [_inst_16 : AddCommMonoid.{u4} N₂] [_inst_17 : Module.{u1, u4} R N₂ _inst_1 _inst_16] {N₃ : Type.{u5}} [_inst_18 : TopologicalSpace.{u5} N₃] [_inst_19 : AddCommMonoid.{u5} N₃] [_inst_20 : Module.{u1, u5} R N₃ _inst_1 _inst_19] [_inst_24 : DistribMulAction.{u2, u5} S N₃ _inst_4 (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)] [_inst_25 : SMulCommClass.{u1, u2, u5} R S N₃ (SMulZeroClass.toHasSmul.{u1, u5} R N₃ (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (SMulWithZero.toSmulZeroClass.{u1, u5} R N₃ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (MulActionWithZero.toSMulWithZero.{u1, u5} R N₃ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (Module.toMulActionWithZero.{u1, u5} R N₃ _inst_1 _inst_19 _inst_20)))) (SMulZeroClass.toHasSmul.{u2, u5} S N₃ (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (DistribSMul.toSmulZeroClass.{u2, u5} S N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (DistribMulAction.toDistribSMul.{u2, u5} S N₃ _inst_4 (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19) _inst_24)))] [_inst_26 : ContinuousConstSMul.{u2, u5} S N₃ _inst_18 (SMulZeroClass.toHasSmul.{u2, u5} S N₃ (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (DistribSMul.toSmulZeroClass.{u2, u5} S N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (DistribMulAction.toDistribSMul.{u2, u5} S N₃ _inst_4 (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19) _inst_24)))] [_inst_31 : DistribMulAction.{u2, u4} S N₂ _inst_4 (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)] [_inst_32 : ContinuousConstSMul.{u2, u4} S N₂ _inst_15 (SMulZeroClass.toHasSmul.{u2, u4} S N₂ (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (DistribSMul.toSmulZeroClass.{u2, u4} S N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (DistribMulAction.toDistribSMul.{u2, u4} S N₂ _inst_4 (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16) _inst_31)))] [_inst_33 : SMulCommClass.{u1, u2, u4} R S N₂ (SMulZeroClass.toHasSmul.{u1, u4} R N₂ (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (SMulWithZero.toSmulZeroClass.{u1, u4} R N₂ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (MulActionWithZero.toSMulWithZero.{u1, u4} R N₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (Module.toMulActionWithZero.{u1, u4} R N₂ _inst_1 _inst_16 _inst_17)))) (SMulZeroClass.toHasSmul.{u2, u4} S N₂ (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (DistribSMul.toSmulZeroClass.{u2, u4} S N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (DistribMulAction.toDistribSMul.{u2, u4} S N₂ _inst_4 (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16) _inst_31)))] [_inst_34 : LinearMap.CompatibleSMul.{u4, u5, u2, u1} N₂ N₃ _inst_16 _inst_19 S R _inst_1 (SMulZeroClass.toHasSmul.{u2, u4} S N₂ (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (DistribSMul.toSmulZeroClass.{u2, u4} S N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (DistribMulAction.toDistribSMul.{u2, u4} S N₂ _inst_4 (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16) _inst_31))) _inst_17 (SMulZeroClass.toHasSmul.{u2, u5} S N₃ (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (DistribSMul.toSmulZeroClass.{u2, u5} S N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (DistribMulAction.toDistribSMul.{u2, u5} S N₃ _inst_4 (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19) _inst_24))) _inst_20] (hₗ : ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) N₂ _inst_15 _inst_16 N₃ _inst_18 _inst_19 _inst_17 _inst_20) (c : S) (fₗ : ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17), Eq.{max (succ u3) (succ u5)} (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) (ContinuousLinearMap.comp.{u1, u1, u1, u3, u4, u5} R R R _inst_1 _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 N₃ _inst_18 _inst_19 _inst_8 _inst_17 _inst_20 (RingHomCompTriple.right_ids.{u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) hₗ (SMul.smul.{u2, max u3 u4} S (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (MulAction.toHasSmul.{u2, max u3 u4} S (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) _inst_4 (ContinuousLinearMap.mulAction.{u1, u1, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17 S _inst_4 _inst_31 _inst_33 _inst_32)) c fₗ)) (SMul.smul.{u2, max u3 u5} S (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) (MulAction.toHasSmul.{u2, max u3 u5} S (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) _inst_4 (ContinuousLinearMap.mulAction.{u1, u1, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20 S _inst_4 _inst_24 _inst_25 _inst_26)) c (ContinuousLinearMap.comp.{u1, u1, u1, u3, u4, u5} R R R _inst_1 _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 N₃ _inst_18 _inst_19 _inst_8 _inst_17 _inst_20 (RingHomCompTriple.right_ids.{u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) hₗ fₗ))
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- forall {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : Semiring.{u2} R] [_inst_4 : Monoid.{u3} S] {M : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M] [_inst_7 : AddCommMonoid.{u1} M] [_inst_8 : Module.{u2, u1} R M _inst_1 _inst_7] {N₂ : Type.{u5}} [_inst_15 : TopologicalSpace.{u5} N₂] [_inst_16 : AddCommMonoid.{u5} N₂] [_inst_17 : Module.{u2, u5} R N₂ _inst_1 _inst_16] {N₃ : Type.{u4}} [_inst_18 : TopologicalSpace.{u4} N₃] [_inst_19 : AddCommMonoid.{u4} N₃] [_inst_20 : Module.{u2, u4} R N₃ _inst_1 _inst_19] [_inst_24 : DistribMulAction.{u3, u4} S N₃ _inst_4 (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)] [_inst_25 : SMulCommClass.{u2, u3, u4} R S N₃ (SMulZeroClass.toSMul.{u2, u4} R N₃ (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (SMulWithZero.toSMulZeroClass.{u2, u4} R N₃ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (MulActionWithZero.toSMulWithZero.{u2, u4} R N₃ (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (Module.toMulActionWithZero.{u2, u4} R N₃ _inst_1 _inst_19 _inst_20)))) (SMulZeroClass.toSMul.{u3, u4} S N₃ (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (DistribSMul.toSMulZeroClass.{u3, u4} S N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (DistribMulAction.toDistribSMul.{u3, u4} S N₃ _inst_4 (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19) _inst_24)))] [_inst_26 : ContinuousConstSMul.{u3, u4} S N₃ _inst_18 (SMulZeroClass.toSMul.{u3, u4} S N₃ (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (DistribSMul.toSMulZeroClass.{u3, u4} S N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (DistribMulAction.toDistribSMul.{u3, u4} S N₃ _inst_4 (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19) _inst_24)))] [_inst_31 : DistribMulAction.{u3, u5} S N₂ _inst_4 (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16)] [_inst_32 : ContinuousConstSMul.{u3, u5} S N₂ _inst_15 (SMulZeroClass.toSMul.{u3, u5} S N₂ (AddMonoid.toZero.{u5} N₂ (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16)) (DistribSMul.toSMulZeroClass.{u3, u5} S N₂ (AddMonoid.toAddZeroClass.{u5} N₂ (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16)) (DistribMulAction.toDistribSMul.{u3, u5} S N₂ _inst_4 (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16) _inst_31)))] [_inst_33 : SMulCommClass.{u2, u3, u5} R S N₂ (SMulZeroClass.toSMul.{u2, u5} R N₂ (AddMonoid.toZero.{u5} N₂ (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16)) (SMulWithZero.toSMulZeroClass.{u2, u5} R N₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u5} N₂ (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16)) (MulActionWithZero.toSMulWithZero.{u2, u5} R N₂ (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u5} N₂ (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16)) (Module.toMulActionWithZero.{u2, u5} R N₂ _inst_1 _inst_16 _inst_17)))) (SMulZeroClass.toSMul.{u3, u5} S N₂ (AddMonoid.toZero.{u5} N₂ (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16)) (DistribSMul.toSMulZeroClass.{u3, u5} S N₂ (AddMonoid.toAddZeroClass.{u5} N₂ (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16)) (DistribMulAction.toDistribSMul.{u3, u5} S N₂ _inst_4 (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16) _inst_31)))] [_inst_34 : LinearMap.CompatibleSMul.{u5, u4, u3, u2} N₂ N₃ _inst_16 _inst_19 S R _inst_1 (SMulZeroClass.toSMul.{u3, u5} S N₂ (AddMonoid.toZero.{u5} N₂ (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16)) (DistribSMul.toSMulZeroClass.{u3, u5} S N₂ (AddMonoid.toAddZeroClass.{u5} N₂ (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16)) (DistribMulAction.toDistribSMul.{u3, u5} S N₂ _inst_4 (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16) _inst_31))) _inst_17 (SMulZeroClass.toSMul.{u3, u4} S N₃ (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (DistribSMul.toSMulZeroClass.{u3, u4} S N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (DistribMulAction.toDistribSMul.{u3, u4} S N₃ _inst_4 (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19) _inst_24))) _inst_20] (hₗ : ContinuousLinearMap.{u2, u2, u5, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) N₂ _inst_15 _inst_16 N₃ _inst_18 _inst_19 _inst_17 _inst_20) (c : S) (fₗ : ContinuousLinearMap.{u2, u2, u1, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17), Eq.{max (succ u1) (succ u4)} (ContinuousLinearMap.{u2, u2, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) (ContinuousLinearMap.comp.{u2, u2, u2, u1, u5, u4} R R R _inst_1 _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 N₃ _inst_18 _inst_19 _inst_8 _inst_17 _inst_20 (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) hₗ (HSMul.hSMul.{u3, max u5 u1, max u5 u1} S (ContinuousLinearMap.{u2, u2, u1, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u2, u2, u1, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (instHSMul.{u3, max u5 u1} S (ContinuousLinearMap.{u2, u2, u1, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (MulAction.toSMul.{u3, max u5 u1} S (ContinuousLinearMap.{u2, u2, u1, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) _inst_4 (ContinuousLinearMap.mulAction.{u2, u2, u1, u5, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17 S _inst_4 _inst_31 _inst_33 _inst_32))) c fₗ)) (HSMul.hSMul.{u3, max u4 u1, max u4 u1} S (ContinuousLinearMap.{u2, u2, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) (ContinuousLinearMap.{u2, u2, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) (instHSMul.{u3, max u4 u1} S (ContinuousLinearMap.{u2, u2, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) (MulAction.toSMul.{u3, max u4 u1} S (ContinuousLinearMap.{u2, u2, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) _inst_4 (ContinuousLinearMap.mulAction.{u2, u2, u1, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20 S _inst_4 _inst_24 _inst_25 _inst_26))) c (ContinuousLinearMap.comp.{u2, u2, u2, u1, u5, u4} R R R _inst_1 _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 N₃ _inst_18 _inst_19 _inst_8 _inst_17 _inst_20 (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) hₗ fₗ))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_smul ContinuousLinearMap.comp_smulₓ'. -/
@[simp]
theorem comp_smul [LinearMap.CompatibleSMul N₂ N₃ S R] (hₗ : N₂ →L[R] N₃) (c : S)
@@ -2574,10 +2178,7 @@ theorem comp_smul [LinearMap.CompatibleSMul N₂ N₃ S R] (hₗ : N₂ →L[R]
include σ₁₃
/- warning: continuous_linear_map.comp_smulₛₗ -> ContinuousLinearMap.comp_smulₛₗ is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {R₂ : Type.{u2}} {R₃ : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : Semiring.{u3} R₃] {M : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M] [_inst_7 : AddCommMonoid.{u4} M] [_inst_8 : Module.{u1, u4} R M _inst_1 _inst_7] {M₂ : Type.{u5}} [_inst_9 : TopologicalSpace.{u5} M₂] [_inst_10 : AddCommMonoid.{u5} M₂] [_inst_11 : Module.{u2, u5} R₂ M₂ _inst_2 _inst_10] {M₃ : Type.{u6}} [_inst_12 : TopologicalSpace.{u6} M₃] [_inst_13 : AddCommMonoid.{u6} M₃] [_inst_14 : Module.{u3, u6} R₃ M₃ _inst_3 _inst_13] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₃ : RingHom.{u2, u3} R₂ R₃ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {σ₁₃ : RingHom.{u1, u3} R R₃ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} [_inst_27 : RingHomCompTriple.{u1, u2, u3} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] [_inst_34 : SMulCommClass.{u2, u2, u5} R₂ R₂ M₂ (SMulZeroClass.toHasSmul.{u2, u5} R₂ M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (SMulWithZero.toSmulZeroClass.{u2, u5} R₂ M₂ (MulZeroClass.toHasZero.{u2} R₂ (MulZeroOneClass.toMulZeroClass.{u2} R₂ (MonoidWithZero.toMulZeroOneClass.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (MulActionWithZero.toSMulWithZero.{u2, u5} R₂ M₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (Module.toMulActionWithZero.{u2, u5} R₂ M₂ _inst_2 _inst_10 _inst_11)))) (SMulZeroClass.toHasSmul.{u2, u5} R₂ M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (SMulWithZero.toSmulZeroClass.{u2, u5} R₂ M₂ (MulZeroClass.toHasZero.{u2} R₂ (MulZeroOneClass.toMulZeroClass.{u2} R₂ (MonoidWithZero.toMulZeroOneClass.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (MulActionWithZero.toSMulWithZero.{u2, u5} R₂ M₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (Module.toMulActionWithZero.{u2, u5} R₂ M₂ _inst_2 _inst_10 _inst_11))))] [_inst_35 : SMulCommClass.{u3, u3, u6} R₃ R₃ M₃ (SMulZeroClass.toHasSmul.{u3, u6} R₃ M₃ (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (SMulWithZero.toSmulZeroClass.{u3, u6} R₃ M₃ (MulZeroClass.toHasZero.{u3} R₃ (MulZeroOneClass.toMulZeroClass.{u3} R₃ (MonoidWithZero.toMulZeroOneClass.{u3} R₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3)))) (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (MulActionWithZero.toSMulWithZero.{u3, u6} R₃ M₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3) (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (Module.toMulActionWithZero.{u3, u6} R₃ M₃ _inst_3 _inst_13 _inst_14)))) (SMulZeroClass.toHasSmul.{u3, u6} R₃ M₃ (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (SMulWithZero.toSmulZeroClass.{u3, u6} R₃ M₃ (MulZeroClass.toHasZero.{u3} R₃ (MulZeroOneClass.toMulZeroClass.{u3} R₃ (MonoidWithZero.toMulZeroOneClass.{u3} R₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3)))) (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (MulActionWithZero.toSMulWithZero.{u3, u6} R₃ M₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3) (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (Module.toMulActionWithZero.{u3, u6} R₃ M₃ _inst_3 _inst_13 _inst_14))))] [_inst_36 : ContinuousConstSMul.{u2, u5} R₂ M₂ _inst_9 (SMulZeroClass.toHasSmul.{u2, u5} R₂ M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (SMulWithZero.toSmulZeroClass.{u2, u5} R₂ M₂ (MulZeroClass.toHasZero.{u2} R₂ (MulZeroOneClass.toMulZeroClass.{u2} R₂ (MonoidWithZero.toMulZeroOneClass.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (MulActionWithZero.toSMulWithZero.{u2, u5} R₂ M₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (Module.toMulActionWithZero.{u2, u5} R₂ M₂ _inst_2 _inst_10 _inst_11))))] [_inst_37 : ContinuousConstSMul.{u3, u6} R₃ M₃ _inst_12 (SMulZeroClass.toHasSmul.{u3, u6} R₃ M₃ (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (SMulWithZero.toSmulZeroClass.{u3, u6} R₃ M₃ (MulZeroClass.toHasZero.{u3} R₃ (MulZeroOneClass.toMulZeroClass.{u3} R₃ (MonoidWithZero.toMulZeroOneClass.{u3} R₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3)))) (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (MulActionWithZero.toSMulWithZero.{u3, u6} R₃ M₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3) (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (Module.toMulActionWithZero.{u3, u6} R₃ M₃ _inst_3 _inst_13 _inst_14))))] (h : ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14) (c : R₂) (f : ContinuousLinearMap.{u1, u2, u4, u5} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11), Eq.{max (succ u4) (succ u6)} (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_8 _inst_11 _inst_14 _inst_27 h (SMul.smul.{u2, max u4 u5} R₂ (ContinuousLinearMap.{u1, u2, u4, u5} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11) (MulAction.toHasSmul.{u2, max u4 u5} R₂ (ContinuousLinearMap.{u1, u2, u4, u5} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11) (MonoidWithZero.toMonoid.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)) (ContinuousLinearMap.mulAction.{u1, u2, u4, u5, u2} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11 R₂ (MonoidWithZero.toMonoid.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)) (Module.toDistribMulAction.{u2, u5} R₂ M₂ _inst_2 _inst_10 _inst_11) _inst_34 _inst_36)) c f)) (SMul.smul.{u3, max u4 u6} R₃ (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (MulAction.toHasSmul.{u3, max u4 u6} R₃ (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (MonoidWithZero.toMonoid.{u3} R₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3)) (ContinuousLinearMap.mulAction.{u1, u3, u4, u6, u3} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14 R₃ (MonoidWithZero.toMonoid.{u3} R₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3)) (Module.toDistribMulAction.{u3, u6} R₃ M₃ _inst_3 _inst_13 _inst_14) _inst_35 _inst_37)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} R₂ R₃ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)) (fun (_x : RingHom.{u2, u3} R₂ R₃ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)) => R₂ -> R₃) (RingHom.hasCoeToFun.{u2, u3} R₂ R₃ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)) σ₂₃ c) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_8 _inst_11 _inst_14 _inst_27 h f))
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σ₁₂ σ₂₃ σ₁₃] [_inst_34 : SMulCommClass.{u6, u6, u5} R₂ R₂ M₂ (SMulZeroClass.toSMul.{u6, u5} R₂ M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (SMulWithZero.toSMulZeroClass.{u6, u5} R₂ M₂ (MonoidWithZero.toZero.{u6} R₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (MulActionWithZero.toSMulWithZero.{u6, u5} R₂ M₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (Module.toMulActionWithZero.{u6, u5} R₂ M₂ _inst_2 _inst_10 _inst_11)))) (SMulZeroClass.toSMul.{u6, u5} R₂ M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (SMulWithZero.toSMulZeroClass.{u6, u5} R₂ M₂ (MonoidWithZero.toZero.{u6} R₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (MulActionWithZero.toSMulWithZero.{u6, u5} R₂ M₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (Module.toMulActionWithZero.{u6, u5} R₂ M₂ _inst_2 _inst_10 _inst_11))))] [_inst_35 : SMulCommClass.{u4, u4, u3} R₃ R₃ M₃ (SMulZeroClass.toSMul.{u4, u3} R₃ M₃ (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (SMulWithZero.toSMulZeroClass.{u4, u3} R₃ M₃ (MonoidWithZero.toZero.{u4} R₃ (Semiring.toMonoidWithZero.{u4} R₃ _inst_3)) (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (MulActionWithZero.toSMulWithZero.{u4, u3} R₃ M₃ (Semiring.toMonoidWithZero.{u4} R₃ _inst_3) (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (Module.toMulActionWithZero.{u4, u3} R₃ M₃ _inst_3 _inst_13 _inst_14)))) (SMulZeroClass.toSMul.{u4, u3} R₃ M₃ (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (SMulWithZero.toSMulZeroClass.{u4, u3} R₃ M₃ (MonoidWithZero.toZero.{u4} R₃ (Semiring.toMonoidWithZero.{u4} R₃ _inst_3)) (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (MulActionWithZero.toSMulWithZero.{u4, u3} R₃ M₃ (Semiring.toMonoidWithZero.{u4} R₃ _inst_3) (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (Module.toMulActionWithZero.{u4, u3} R₃ M₃ _inst_3 _inst_13 _inst_14))))] [_inst_36 : ContinuousConstSMul.{u6, u5} R₂ M₂ _inst_9 (SMulZeroClass.toSMul.{u6, u5} R₂ M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (SMulWithZero.toSMulZeroClass.{u6, u5} R₂ M₂ (MonoidWithZero.toZero.{u6} R₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (MulActionWithZero.toSMulWithZero.{u6, u5} R₂ M₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (Module.toMulActionWithZero.{u6, u5} R₂ M₂ _inst_2 _inst_10 _inst_11))))] [_inst_37 : ContinuousConstSMul.{u4, u3} R₃ M₃ _inst_12 (SMulZeroClass.toSMul.{u4, u3} R₃ M₃ (AddMonoid.toZero.{u3} M₃ 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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_smulₛₗ ContinuousLinearMap.comp_smulₛₗₓ'. -/
@[simp]
theorem comp_smulₛₗ [SMulCommClass R₂ R₂ M₂] [SMulCommClass R₃ R₃ M₃] [ContinuousConstSMul R₂ M₂]
@@ -2611,10 +2212,7 @@ variable {R R₂ R₃ S S₃ : Type _} [Semiring R] [Semiring R₂] [Semiring R
(h : M₂ →SL[σ₂₃] M₃) (f g : M →SL[σ₁₂] M₂) (x y z : M)
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.prod_equiv ContinuousLinearMap.prodEquivₓ'. -/
/-- `continuous_linear_map.prod` as an `equiv`. -/
@[simps apply]
@@ -2627,10 +2225,7 @@ def prodEquiv : (M →L[R] N₂) × (M →L[R] N₃) ≃ (M →L[R] N₂ × N₃
#align continuous_linear_map.prod_equiv ContinuousLinearMap.prodEquiv
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.prod_ext_iff ContinuousLinearMap.prod_ext_iffₓ'. -/
theorem prod_ext_iff {f g : M × N₂ →L[R] N₃} :
f = g ↔ f.comp (inl _ _ _) = g.comp (inl _ _ _) ∧ f.comp (inr _ _ _) = g.comp (inr _ _ _) :=
@@ -2640,10 +2235,7 @@ theorem prod_ext_iff {f g : M × N₂ →L[R] N₃} :
#align continuous_linear_map.prod_ext_iff ContinuousLinearMap.prod_ext_iff
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(instTopologicalSpaceProd.{u2, u3} M N₂ _inst_6 _inst_15) (Prod.instAddCommMonoidSum.{u2, u3} M N₂ _inst_7 _inst_16) N₃ _inst_18 _inst_19 (Prod.module.{u4, u2, u3} R M N₂ _inst_1 _inst_7 _inst_16 _inst_8 _inst_17) _inst_20) f g)
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.prod_ext ContinuousLinearMap.prod_extₓ'. -/
@[ext]
theorem prod_ext {f g : M × N₂ →L[R] N₃} (hl : f.comp (inl _ _ _) = g.comp (inl _ _ _))
@@ -2664,10 +2256,7 @@ instance [Module S₃ᵐᵒᵖ M₃] [IsCentralScalar S₃ M₃] : IsCentralScal
variable (S) [ContinuousAdd N₃]
/- warning: continuous_linear_map.prodₗ -> ContinuousLinearMap.prodₗ is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} (S : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_4 : Semiring.{u2} S] {M : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : AddCommMonoid.{u3} M] [_inst_8 : Module.{u1, u3} R M _inst_1 _inst_7] {N₂ : Type.{u4}} [_inst_15 : TopologicalSpace.{u4} N₂] [_inst_16 : AddCommMonoid.{u4} N₂] [_inst_17 : Module.{u1, u4} R N₂ _inst_1 _inst_16] {N₃ : Type.{u5}} [_inst_18 : TopologicalSpace.{u5} N₃] [_inst_19 : AddCommMonoid.{u5} N₃] [_inst_20 : Module.{u1, u5} R N₃ _inst_1 _inst_19] [_inst_24 : Module.{u2, u4} S N₂ _inst_4 _inst_16] [_inst_25 : ContinuousConstSMul.{u2, u4} S N₂ _inst_15 (SMulZeroClass.toHasSmul.{u2, u4} S N₂ (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (SMulWithZero.toSmulZeroClass.{u2, u4} S N₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)))) (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (MulActionWithZero.toSMulWithZero.{u2, u4} S N₂ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (Module.toMulActionWithZero.{u2, u4} S N₂ _inst_4 _inst_16 _inst_24))))] [_inst_26 : SMulCommClass.{u1, u2, u4} R S N₂ (SMulZeroClass.toHasSmul.{u1, u4} R N₂ (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (SMulWithZero.toSmulZeroClass.{u1, u4} R N₂ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (MulActionWithZero.toSMulWithZero.{u1, u4} R N₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (Module.toMulActionWithZero.{u1, u4} R N₂ _inst_1 _inst_16 _inst_17)))) (SMulZeroClass.toHasSmul.{u2, u4} S N₂ (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (SMulWithZero.toSmulZeroClass.{u2, u4} S N₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)))) (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (MulActionWithZero.toSMulWithZero.{u2, u4} S N₂ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (Module.toMulActionWithZero.{u2, u4} S N₂ _inst_4 _inst_16 _inst_24))))] [_inst_27 : Module.{u2, u5} S N₃ _inst_4 _inst_19] [_inst_28 : SMulCommClass.{u1, u2, u5} R S N₃ (SMulZeroClass.toHasSmul.{u1, u5} R N₃ (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (SMulWithZero.toSmulZeroClass.{u1, u5} R N₃ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (MulActionWithZero.toSMulWithZero.{u1, u5} R N₃ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (Module.toMulActionWithZero.{u1, u5} R N₃ _inst_1 _inst_19 _inst_20)))) (SMulZeroClass.toHasSmul.{u2, u5} S N₃ (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (SMulWithZero.toSmulZeroClass.{u2, u5} S N₃ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)))) (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (MulActionWithZero.toSMulWithZero.{u2, u5} S N₃ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (Module.toMulActionWithZero.{u2, u5} S N₃ _inst_4 _inst_19 _inst_27))))] [_inst_29 : ContinuousConstSMul.{u2, u5} S N₃ _inst_18 (SMulZeroClass.toHasSmul.{u2, u5} S N₃ (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (SMulWithZero.toSmulZeroClass.{u2, u5} S N₃ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)))) (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (MulActionWithZero.toSMulWithZero.{u2, u5} S N₃ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (Module.toMulActionWithZero.{u2, u5} S N₃ _inst_4 _inst_19 _inst_27))))] [_inst_33 : ContinuousAdd.{u4} N₂ _inst_15 (AddZeroClass.toHasAdd.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)))] [_inst_34 : ContinuousAdd.{u5} N₃ _inst_18 (AddZeroClass.toHasAdd.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)))], LinearEquiv.{u2, u2, max (max u3 u4) u3 u5, max u3 u4 u5} S S _inst_4 _inst_4 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_4)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_4)) (RingHomInvPair.ids.{u2} S _inst_4) (RingHomInvPair.ids.{u2} S _inst_4) (Prod.{max u3 u4, max u3 u5} (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20)) (ContinuousLinearMap.{u1, u1, u3, max u4 u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 (Prod.{u4, u5} N₂ N₃) (Prod.topologicalSpace.{u4, u5} N₂ N₃ _inst_15 _inst_18) (Prod.addCommMonoid.{u4, u5} N₂ N₃ _inst_16 _inst_19) _inst_8 (Prod.module.{u1, u4, u5} R N₂ N₃ _inst_1 _inst_16 _inst_19 _inst_17 _inst_20)) (Prod.addCommMonoid.{max u3 u4, max u3 u5} (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17 _inst_33) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20 _inst_34)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, max u4 u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 (Prod.{u4, u5} N₂ N₃) (Prod.topologicalSpace.{u4, u5} N₂ N₃ _inst_15 _inst_18) (Prod.addCommMonoid.{u4, u5} N₂ N₃ _inst_16 _inst_19) _inst_8 (Prod.module.{u1, u4, u5} R N₂ N₃ _inst_1 _inst_16 _inst_19 _inst_17 _inst_20) (ContinuousLinearMap.prodₗ._proof_1.{u5, u4} N₂ _inst_15 _inst_16 N₃ _inst_18 _inst_19 _inst_33 _inst_34)) (Prod.module.{u2, max u3 u4, max u3 u5} S (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) _inst_4 (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17 _inst_33) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20 _inst_34) (ContinuousLinearMap.module.{u1, u1, u2, u3, u4} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 N₂ _inst_15 _inst_16 _inst_17 _inst_24 _inst_26 _inst_25 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_33) (ContinuousLinearMap.module.{u1, u1, u2, u3, u5} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 N₃ _inst_18 _inst_19 _inst_20 _inst_27 _inst_28 _inst_29 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_34)) (ContinuousLinearMap.module.{u1, u1, u2, u3, max u4 u5} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 (Prod.{u4, u5} N₂ N₃) (Prod.topologicalSpace.{u4, u5} N₂ N₃ _inst_15 _inst_18) (Prod.addCommMonoid.{u4, u5} N₂ N₃ _inst_16 _inst_19) (Prod.module.{u1, u4, u5} R N₂ N₃ _inst_1 _inst_16 _inst_19 _inst_17 _inst_20) (Prod.module.{u2, u4, u5} S N₂ N₃ _inst_4 _inst_16 _inst_19 _inst_24 _inst_27) (ContinuousLinearMap.prodₗ._proof_2.{u1, u5, u2, u4} R S _inst_1 _inst_4 N₂ _inst_16 _inst_17 N₃ _inst_19 _inst_20 _inst_24 _inst_26 _inst_27 _inst_28) (ContinuousLinearMap.prodₗ._proof_3.{u5, u2, u4} S _inst_4 N₂ _inst_15 _inst_16 N₃ _inst_18 _inst_19 _inst_24 _inst_25 _inst_27 _inst_29) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (ContinuousLinearMap.prodₗ._proof_4.{u5, u4} N₂ _inst_15 _inst_16 N₃ _inst_18 _inst_19 _inst_33 _inst_34))
-but is expected to have type
- forall {R : Type.{u1}} (S : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_4 : Semiring.{u2} S] {M : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : AddCommMonoid.{u3} M] [_inst_8 : Module.{u1, u3} R M _inst_1 _inst_7] {N₂ : Type.{u4}} [_inst_15 : TopologicalSpace.{u4} N₂] [_inst_16 : AddCommMonoid.{u4} N₂] [_inst_17 : Module.{u1, u4} R N₂ _inst_1 _inst_16] {N₃ : Type.{u5}} [_inst_18 : TopologicalSpace.{u5} N₃] [_inst_19 : AddCommMonoid.{u5} N₃] [_inst_20 : Module.{u1, u5} R N₃ _inst_1 _inst_19] [_inst_24 : Module.{u2, u4} S N₂ _inst_4 _inst_16] [_inst_25 : ContinuousConstSMul.{u2, u4} S N₂ _inst_15 (SMulZeroClass.toSMul.{u2, u4} S N₂ (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (SMulWithZero.toSMulZeroClass.{u2, u4} S N₂ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (MulActionWithZero.toSMulWithZero.{u2, u4} S N₂ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (Module.toMulActionWithZero.{u2, u4} S N₂ _inst_4 _inst_16 _inst_24))))] [_inst_26 : SMulCommClass.{u1, u2, u4} R S N₂ (SMulZeroClass.toSMul.{u1, u4} R N₂ (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (SMulWithZero.toSMulZeroClass.{u1, u4} R N₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (MulActionWithZero.toSMulWithZero.{u1, u4} R N₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (Module.toMulActionWithZero.{u1, u4} R N₂ _inst_1 _inst_16 _inst_17)))) (SMulZeroClass.toSMul.{u2, u4} S N₂ (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (SMulWithZero.toSMulZeroClass.{u2, u4} S N₂ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (MulActionWithZero.toSMulWithZero.{u2, u4} S N₂ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (Module.toMulActionWithZero.{u2, u4} S N₂ _inst_4 _inst_16 _inst_24))))] [_inst_27 : Module.{u2, u5} S N₃ _inst_4 _inst_19] [_inst_28 : SMulCommClass.{u1, u2, u5} R S N₃ (SMulZeroClass.toSMul.{u1, u5} R N₃ (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (SMulWithZero.toSMulZeroClass.{u1, u5} R N₃ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (MulActionWithZero.toSMulWithZero.{u1, u5} R N₃ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (Module.toMulActionWithZero.{u1, u5} R N₃ _inst_1 _inst_19 _inst_20)))) (SMulZeroClass.toSMul.{u2, u5} S N₃ (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (SMulWithZero.toSMulZeroClass.{u2, u5} S N₃ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (MulActionWithZero.toSMulWithZero.{u2, u5} S N₃ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (Module.toMulActionWithZero.{u2, u5} S N₃ _inst_4 _inst_19 _inst_27))))] [_inst_29 : ContinuousConstSMul.{u2, u5} S N₃ _inst_18 (SMulZeroClass.toSMul.{u2, u5} S N₃ (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (SMulWithZero.toSMulZeroClass.{u2, u5} S N₃ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (MulActionWithZero.toSMulWithZero.{u2, u5} S N₃ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (Module.toMulActionWithZero.{u2, u5} S N₃ _inst_4 _inst_19 _inst_27))))] [_inst_33 : ContinuousAdd.{u4} N₂ _inst_15 (AddZeroClass.toAdd.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)))] [_inst_34 : ContinuousAdd.{u5} N₃ _inst_18 (AddZeroClass.toAdd.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)))], LinearEquiv.{u2, u2, max (max u5 u3) u4 u3, max (max u5 u4) u3} S S _inst_4 _inst_4 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_4)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_4)) (RingHomInvPair.ids.{u2} S _inst_4) (RingHomInvPair.ids.{u2} S _inst_4) (Prod.{max u4 u3, max u5 u3} (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20)) (ContinuousLinearMap.{u1, u1, u3, max u5 u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 (Prod.{u4, u5} N₂ N₃) (instTopologicalSpaceProd.{u4, u5} N₂ N₃ _inst_15 _inst_18) (Prod.instAddCommMonoidSum.{u4, u5} N₂ N₃ _inst_16 _inst_19) _inst_8 (Prod.module.{u1, u4, u5} R N₂ N₃ _inst_1 _inst_16 _inst_19 _inst_17 _inst_20)) (Prod.instAddCommMonoidSum.{max u3 u4, max u3 u5} (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17 _inst_33) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20 _inst_34)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, max u4 u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 (Prod.{u4, u5} N₂ N₃) (instTopologicalSpaceProd.{u4, u5} N₂ N₃ _inst_15 _inst_18) (Prod.instAddCommMonoidSum.{u4, u5} N₂ N₃ _inst_16 _inst_19) _inst_8 (Prod.module.{u1, u4, u5} R N₂ N₃ _inst_1 _inst_16 _inst_19 _inst_17 _inst_20) (Prod.continuousAdd.{u4, u5} N₂ N₃ _inst_15 (AddSemigroup.toAdd.{u4} N₂ (AddMonoid.toAddSemigroup.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) _inst_33 _inst_18 (AddSemigroup.toAdd.{u5} N₃ (AddMonoid.toAddSemigroup.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) _inst_34)) (Prod.module.{u2, max u3 u4, max u3 u5} S (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) _inst_4 (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17 _inst_33) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20 _inst_34) (ContinuousLinearMap.module.{u1, u1, u2, u3, u4} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 N₂ _inst_15 _inst_16 _inst_17 _inst_24 _inst_26 _inst_25 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_33) (ContinuousLinearMap.module.{u1, u1, u2, u3, u5} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 N₃ _inst_18 _inst_19 _inst_20 _inst_27 _inst_28 _inst_29 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_34)) (ContinuousLinearMap.module.{u1, u1, u2, u3, max u4 u5} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 (Prod.{u4, u5} N₂ N₃) (instTopologicalSpaceProd.{u4, u5} N₂ N₃ _inst_15 _inst_18) (Prod.instAddCommMonoidSum.{u4, u5} N₂ N₃ _inst_16 _inst_19) (Prod.module.{u1, u4, u5} R N₂ N₃ _inst_1 _inst_16 _inst_19 _inst_17 _inst_20) (Prod.module.{u2, u4, u5} S N₂ N₃ _inst_4 _inst_16 _inst_19 _inst_24 _inst_27) (Prod.smulCommClass.{u1, u2, u4, u5} R S N₂ N₃ (MulAction.toSMul.{u1, u4} R N₂ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (DistribMulAction.toMulAction.{u1, u4} R N₂ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16) (Module.toDistribMulAction.{u1, u4} R N₂ _inst_1 _inst_16 _inst_17))) (MulAction.toSMul.{u1, u5} R N₃ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (DistribMulAction.toMulAction.{u1, u5} R N₃ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19) (Module.toDistribMulAction.{u1, u5} R N₃ _inst_1 _inst_19 _inst_20))) (MulAction.toSMul.{u2, u4} S N₂ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (DistribMulAction.toMulAction.{u2, u4} S N₂ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16) (Module.toDistribMulAction.{u2, u4} S N₂ _inst_4 _inst_16 _inst_24))) (MulAction.toSMul.{u2, u5} S N₃ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (DistribMulAction.toMulAction.{u2, u5} S N₃ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19) (Module.toDistribMulAction.{u2, u5} S N₃ _inst_4 _inst_19 _inst_27))) _inst_26 _inst_28) (Prod.continuousConstSMul.{u2, u4, u5} S N₂ N₃ _inst_15 (MulAction.toSMul.{u2, u4} S N₂ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (DistribMulAction.toMulAction.{u2, u4} S N₂ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16) (Module.toDistribMulAction.{u2, u4} S N₂ _inst_4 _inst_16 _inst_24))) _inst_25 _inst_18 (MulAction.toSMul.{u2, u5} S N₃ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (DistribMulAction.toMulAction.{u2, u5} S N₃ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19) (Module.toDistribMulAction.{u2, u5} S N₃ _inst_4 _inst_19 _inst_27))) _inst_29) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Prod.continuousAdd.{u4, u5} N₂ N₃ _inst_15 (AddSemigroup.toAdd.{u4} N₂ (AddMonoid.toAddSemigroup.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) _inst_33 _inst_18 (AddSemigroup.toAdd.{u5} N₃ (AddMonoid.toAddSemigroup.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) _inst_34))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.prodₗ ContinuousLinearMap.prodₗₓ'. -/
/-- `continuous_linear_map.prod` as a `linear_equiv`. -/
@[simps apply]
@@ -2678,10 +2267,7 @@ def prodₗ : ((M →L[R] N₂) × (M →L[R] N₃)) ≃ₗ[S] M →L[R] N₂ ×
#align continuous_linear_map.prodₗ ContinuousLinearMap.prodₗ
/- warning: continuous_linear_map.coe_lm -> ContinuousLinearMap.coeLM is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} (S : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_4 : Semiring.{u2} S] {M : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : AddCommMonoid.{u3} M] [_inst_8 : Module.{u1, u3} R M _inst_1 _inst_7] {N₃ : Type.{u4}} [_inst_18 : TopologicalSpace.{u4} N₃] [_inst_19 : AddCommMonoid.{u4} N₃] [_inst_20 : Module.{u1, u4} R N₃ _inst_1 _inst_19] [_inst_27 : Module.{u2, u4} S N₃ _inst_4 _inst_19] [_inst_28 : SMulCommClass.{u1, u2, u4} R S N₃ (SMulZeroClass.toHasSmul.{u1, u4} R N₃ (AddZeroClass.toHasZero.{u4} N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19))) (SMulWithZero.toSmulZeroClass.{u1, u4} R N₃ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u4} N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19))) (MulActionWithZero.toSMulWithZero.{u1, u4} R N₃ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u4} N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19))) (Module.toMulActionWithZero.{u1, u4} R N₃ _inst_1 _inst_19 _inst_20)))) (SMulZeroClass.toHasSmul.{u2, u4} S N₃ (AddZeroClass.toHasZero.{u4} N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19))) (SMulWithZero.toSmulZeroClass.{u2, u4} S N₃ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)))) (AddZeroClass.toHasZero.{u4} N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19))) (MulActionWithZero.toSMulWithZero.{u2, u4} S N₃ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddZeroClass.toHasZero.{u4} N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19))) (Module.toMulActionWithZero.{u2, u4} S N₃ _inst_4 _inst_19 _inst_27))))] [_inst_29 : ContinuousConstSMul.{u2, u4} S N₃ _inst_18 (SMulZeroClass.toHasSmul.{u2, u4} S N₃ (AddZeroClass.toHasZero.{u4} N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19))) (SMulWithZero.toSmulZeroClass.{u2, u4} S N₃ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)))) (AddZeroClass.toHasZero.{u4} N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19))) (MulActionWithZero.toSMulWithZero.{u2, u4} S N₃ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddZeroClass.toHasZero.{u4} N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19))) (Module.toMulActionWithZero.{u2, u4} S N₃ _inst_4 _inst_19 _inst_27))))] [_inst_34 : ContinuousAdd.{u4} N₃ _inst_18 (AddZeroClass.toHasAdd.{u4} N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)))], LinearMap.{u2, u2, max u3 u4, max u3 u4} S S _inst_4 _inst_4 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_4)) (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) (LinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N₃ _inst_7 _inst_19 _inst_8 _inst_20) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20 _inst_34) (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R M N₃ _inst_1 _inst_1 _inst_7 _inst_19 _inst_8 _inst_20 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (ContinuousLinearMap.module.{u1, u1, u2, u3, u4} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 N₃ _inst_18 _inst_19 _inst_20 _inst_27 _inst_28 _inst_29 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_34) (LinearMap.module.{u1, u1, u2, u3, u4} R R S M N₃ _inst_1 _inst_1 _inst_7 _inst_19 _inst_8 _inst_20 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_4 _inst_27 _inst_28)
-but is expected to have type
- forall {R : Type.{u1}} (S : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_4 : Semiring.{u2} S] {M : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : AddCommMonoid.{u3} M] [_inst_8 : Module.{u1, u3} R M _inst_1 _inst_7] {N₃ : Type.{u4}} [_inst_18 : TopologicalSpace.{u4} N₃] [_inst_19 : AddCommMonoid.{u4} N₃] [_inst_20 : Module.{u1, u4} R N₃ _inst_1 _inst_19] [_inst_27 : Module.{u2, u4} S N₃ _inst_4 _inst_19] [_inst_28 : SMulCommClass.{u1, u2, u4} R S N₃ (SMulZeroClass.toSMul.{u1, u4} R N₃ (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (SMulWithZero.toSMulZeroClass.{u1, u4} R N₃ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (MulActionWithZero.toSMulWithZero.{u1, u4} R N₃ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (Module.toMulActionWithZero.{u1, u4} R N₃ _inst_1 _inst_19 _inst_20)))) (SMulZeroClass.toSMul.{u2, u4} S N₃ (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (SMulWithZero.toSMulZeroClass.{u2, u4} S N₃ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (MulActionWithZero.toSMulWithZero.{u2, u4} S N₃ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (Module.toMulActionWithZero.{u2, u4} S N₃ _inst_4 _inst_19 _inst_27))))] [_inst_29 : ContinuousConstSMul.{u2, u4} S N₃ _inst_18 (SMulZeroClass.toSMul.{u2, u4} S N₃ (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (SMulWithZero.toSMulZeroClass.{u2, u4} S N₃ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (MulActionWithZero.toSMulWithZero.{u2, u4} S N₃ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (Module.toMulActionWithZero.{u2, u4} S N₃ _inst_4 _inst_19 _inst_27))))] [_inst_34 : ContinuousAdd.{u4} N₃ _inst_18 (AddZeroClass.toAdd.{u4} N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)))], LinearMap.{u2, u2, max u4 u3, max u4 u3} S S _inst_4 _inst_4 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_4)) (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) (LinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N₃ _inst_7 _inst_19 _inst_8 _inst_20) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20 _inst_34) (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R M N₃ _inst_1 _inst_1 _inst_7 _inst_19 _inst_8 _inst_20 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (ContinuousLinearMap.module.{u1, u1, u2, u3, u4} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 N₃ _inst_18 _inst_19 _inst_20 _inst_27 _inst_28 _inst_29 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_34) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u2, u3, u4} R R S M N₃ _inst_1 _inst_1 _inst_7 _inst_19 _inst_8 _inst_20 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_4 _inst_27 _inst_28)
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_lm ContinuousLinearMap.coeLMₓ'. -/
/-- The coercion from `M →L[R] M₂` to `M →ₗ[R] M₂`, as a linear map. -/
@[simps]
@@ -2695,10 +2281,7 @@ def coeLM : (M →L[R] N₃) →ₗ[S] M →ₗ[R] N₃
variable {S} (σ₁₃)
/- warning: continuous_linear_map.coe_lmₛₗ -> ContinuousLinearMap.coeLMₛₗ is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {R₃ : Type.{u2}} {S₃ : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_3 : Semiring.{u2} R₃] [_inst_5 : Semiring.{u3} S₃] {M : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M] [_inst_7 : AddCommMonoid.{u4} M] [_inst_8 : Module.{u1, u4} R M _inst_1 _inst_7] {M₃ : Type.{u5}} [_inst_12 : TopologicalSpace.{u5} M₃] [_inst_13 : AddCommMonoid.{u5} M₃] [_inst_14 : Module.{u2, u5} R₃ M₃ _inst_3 _inst_13] [_inst_21 : Module.{u3, u5} S₃ M₃ _inst_5 _inst_13] [_inst_22 : SMulCommClass.{u2, u3, u5} R₃ S₃ M₃ (SMulZeroClass.toHasSmul.{u2, u5} R₃ M₃ (AddZeroClass.toHasZero.{u5} M₃ (AddMonoid.toAddZeroClass.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13))) (SMulWithZero.toSmulZeroClass.{u2, u5} R₃ M₃ (MulZeroClass.toHasZero.{u2} R₃ (MulZeroOneClass.toMulZeroClass.{u2} R₃ (MonoidWithZero.toMulZeroOneClass.{u2} R₃ (Semiring.toMonoidWithZero.{u2} R₃ _inst_3)))) (AddZeroClass.toHasZero.{u5} M₃ (AddMonoid.toAddZeroClass.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13))) (MulActionWithZero.toSMulWithZero.{u2, u5} R₃ M₃ (Semiring.toMonoidWithZero.{u2} R₃ _inst_3) (AddZeroClass.toHasZero.{u5} M₃ (AddMonoid.toAddZeroClass.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13))) (Module.toMulActionWithZero.{u2, u5} R₃ M₃ _inst_3 _inst_13 _inst_14)))) (SMulZeroClass.toHasSmul.{u3, u5} S₃ M₃ (AddZeroClass.toHasZero.{u5} M₃ (AddMonoid.toAddZeroClass.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13))) (SMulWithZero.toSmulZeroClass.{u3, u5} S₃ M₃ (MulZeroClass.toHasZero.{u3} S₃ (MulZeroOneClass.toMulZeroClass.{u3} S₃ (MonoidWithZero.toMulZeroOneClass.{u3} S₃ (Semiring.toMonoidWithZero.{u3} S₃ _inst_5)))) (AddZeroClass.toHasZero.{u5} M₃ (AddMonoid.toAddZeroClass.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13))) (MulActionWithZero.toSMulWithZero.{u3, u5} S₃ M₃ (Semiring.toMonoidWithZero.{u3} S₃ _inst_5) (AddZeroClass.toHasZero.{u5} M₃ (AddMonoid.toAddZeroClass.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13))) (Module.toMulActionWithZero.{u3, u5} S₃ M₃ _inst_5 _inst_13 _inst_21))))] [_inst_23 : ContinuousConstSMul.{u3, u5} S₃ M₃ _inst_12 (SMulZeroClass.toHasSmul.{u3, u5} S₃ M₃ (AddZeroClass.toHasZero.{u5} M₃ (AddMonoid.toAddZeroClass.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13))) (SMulWithZero.toSmulZeroClass.{u3, u5} S₃ M₃ (MulZeroClass.toHasZero.{u3} S₃ (MulZeroOneClass.toMulZeroClass.{u3} S₃ (MonoidWithZero.toMulZeroOneClass.{u3} S₃ (Semiring.toMonoidWithZero.{u3} S₃ _inst_5)))) (AddZeroClass.toHasZero.{u5} M₃ (AddMonoid.toAddZeroClass.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13))) (MulActionWithZero.toSMulWithZero.{u3, u5} S₃ M₃ (Semiring.toMonoidWithZero.{u3} S₃ _inst_5) (AddZeroClass.toHasZero.{u5} M₃ (AddMonoid.toAddZeroClass.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13))) (Module.toMulActionWithZero.{u3, u5} S₃ M₃ _inst_5 _inst_13 _inst_21))))] (σ₁₃ : RingHom.{u1, u2} R R₃ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₃ _inst_3)) [_inst_32 : ContinuousAdd.{u5} M₃ _inst_12 (AddZeroClass.toHasAdd.{u5} M₃ (AddMonoid.toAddZeroClass.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13)))], LinearMap.{u3, u3, max u4 u5, max u4 u5} S₃ S₃ _inst_5 _inst_5 (RingHom.id.{u3} S₃ (Semiring.toNonAssocSemiring.{u3} S₃ _inst_5)) (ContinuousLinearMap.{u1, u2, u4, u5} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (LinearMap.{u1, u2, u4, u5} R R₃ _inst_1 _inst_3 σ₁₃ M M₃ _inst_7 _inst_13 _inst_8 _inst_14) (ContinuousLinearMap.addCommMonoid.{u1, u2, u4, u5} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14 _inst_32) (LinearMap.addCommMonoid.{u1, u2, u4, u5} R R₃ M M₃ _inst_1 _inst_3 _inst_7 _inst_13 _inst_8 _inst_14 σ₁₃) (ContinuousLinearMap.module.{u1, u2, u3, u4, u5} R R₃ S₃ _inst_1 _inst_3 _inst_5 M _inst_6 _inst_7 _inst_8 M₃ _inst_12 _inst_13 _inst_14 _inst_21 _inst_22 _inst_23 σ₁₃ _inst_32) (LinearMap.module.{u1, u2, u3, u4, u5} R R₃ S₃ M M₃ _inst_1 _inst_3 _inst_7 _inst_13 _inst_8 _inst_14 σ₁₃ _inst_5 _inst_21 _inst_22)
-but is expected to have type
- forall {R : Type.{u1}} {R₃ : Type.{u2}} {S₃ : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_3 : Semiring.{u2} R₃] [_inst_5 : Semiring.{u3} S₃] {M : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M] [_inst_7 : AddCommMonoid.{u4} M] [_inst_8 : Module.{u1, u4} R M _inst_1 _inst_7] {M₃ : Type.{u5}} [_inst_12 : TopologicalSpace.{u5} M₃] [_inst_13 : AddCommMonoid.{u5} M₃] [_inst_14 : Module.{u2, u5} R₃ M₃ _inst_3 _inst_13] [_inst_21 : Module.{u3, u5} S₃ M₃ _inst_5 _inst_13] [_inst_22 : SMulCommClass.{u2, u3, u5} R₃ S₃ M₃ (SMulZeroClass.toSMul.{u2, u5} R₃ M₃ (AddMonoid.toZero.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13)) (SMulWithZero.toSMulZeroClass.{u2, u5} R₃ M₃ (MonoidWithZero.toZero.{u2} R₃ (Semiring.toMonoidWithZero.{u2} R₃ _inst_3)) (AddMonoid.toZero.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13)) (MulActionWithZero.toSMulWithZero.{u2, u5} R₃ M₃ (Semiring.toMonoidWithZero.{u2} R₃ _inst_3) (AddMonoid.toZero.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13)) (Module.toMulActionWithZero.{u2, u5} R₃ M₃ _inst_3 _inst_13 _inst_14)))) (SMulZeroClass.toSMul.{u3, u5} S₃ M₃ (AddMonoid.toZero.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13)) (SMulWithZero.toSMulZeroClass.{u3, u5} S₃ M₃ (MonoidWithZero.toZero.{u3} S₃ (Semiring.toMonoidWithZero.{u3} S₃ _inst_5)) (AddMonoid.toZero.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13)) (MulActionWithZero.toSMulWithZero.{u3, u5} S₃ M₃ (Semiring.toMonoidWithZero.{u3} S₃ _inst_5) (AddMonoid.toZero.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13)) (Module.toMulActionWithZero.{u3, u5} S₃ M₃ _inst_5 _inst_13 _inst_21))))] [_inst_23 : ContinuousConstSMul.{u3, u5} S₃ M₃ _inst_12 (SMulZeroClass.toSMul.{u3, u5} S₃ M₃ (AddMonoid.toZero.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13)) (SMulWithZero.toSMulZeroClass.{u3, u5} S₃ M₃ (MonoidWithZero.toZero.{u3} S₃ (Semiring.toMonoidWithZero.{u3} S₃ _inst_5)) (AddMonoid.toZero.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13)) (MulActionWithZero.toSMulWithZero.{u3, u5} S₃ M₃ (Semiring.toMonoidWithZero.{u3} S₃ _inst_5) (AddMonoid.toZero.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13)) (Module.toMulActionWithZero.{u3, u5} S₃ M₃ _inst_5 _inst_13 _inst_21))))] (σ₁₃ : RingHom.{u1, u2} R R₃ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₃ _inst_3)) [_inst_32 : ContinuousAdd.{u5} M₃ _inst_12 (AddZeroClass.toAdd.{u5} M₃ (AddMonoid.toAddZeroClass.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13)))], LinearMap.{u3, u3, max u5 u4, max u5 u4} S₃ S₃ _inst_5 _inst_5 (RingHom.id.{u3} S₃ (Semiring.toNonAssocSemiring.{u3} S₃ _inst_5)) (ContinuousLinearMap.{u1, u2, u4, u5} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (LinearMap.{u1, u2, u4, u5} R R₃ _inst_1 _inst_3 σ₁₃ M M₃ _inst_7 _inst_13 _inst_8 _inst_14) (ContinuousLinearMap.addCommMonoid.{u1, u2, u4, u5} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14 _inst_32) (LinearMap.addCommMonoid.{u1, u2, u4, u5} R R₃ M M₃ _inst_1 _inst_3 _inst_7 _inst_13 _inst_8 _inst_14 σ₁₃) (ContinuousLinearMap.module.{u1, u2, u3, u4, u5} R R₃ S₃ _inst_1 _inst_3 _inst_5 M _inst_6 _inst_7 _inst_8 M₃ _inst_12 _inst_13 _inst_14 _inst_21 _inst_22 _inst_23 σ₁₃ _inst_32) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u2, u3, u4, u5} R R₃ S₃ M M₃ _inst_1 _inst_3 _inst_7 _inst_13 _inst_8 _inst_14 σ₁₃ _inst_5 _inst_21 _inst_22)
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_lmₛₗ ContinuousLinearMap.coeLMₛₗₓ'. -/
/-- The coercion from `M →SL[σ] M₂` to `M →ₛₗ[σ] M₂`, as a linear map. -/
@[simps]
@@ -2722,10 +2305,7 @@ variable {R S T M M₂ : Type _} [Semiring R] [Semiring S] [Semiring T] [Module
[SMulCommClass S T M₂]
/- warning: continuous_linear_map.smul_rightₗ -> ContinuousLinearMap.smulRightₗ is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} {M : Type.{u4}} {M₂ : Type.{u5}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : Semiring.{u3} T] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : AddCommMonoid.{u5} M₂] [_inst_6 : Module.{u1, u5} R M₂ _inst_1 _inst_5] [_inst_7 : Module.{u2, u5} S M₂ _inst_2 _inst_5] [_inst_8 : IsScalarTower.{u1, u2, u5} R S M₂ (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u5} S M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u2, u5} S M₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u5} R M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u1, u5} R M₂ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u1, u5} R M₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u1, u5} R M₂ _inst_1 _inst_5 _inst_6))))] [_inst_9 : TopologicalSpace.{u2} S] [_inst_10 : TopologicalSpace.{u5} M₂] [_inst_11 : ContinuousSMul.{u2, u5} S M₂ (SMulZeroClass.toHasSmul.{u2, u5} S M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u2, u5} S M₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) _inst_9 _inst_10] [_inst_12 : TopologicalSpace.{u4} M] [_inst_13 : AddCommMonoid.{u4} M] [_inst_14 : Module.{u1, u4} R M _inst_1 _inst_13] [_inst_15 : ContinuousAdd.{u5} M₂ _inst_10 (AddZeroClass.toHasAdd.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)))] [_inst_16 : Module.{u3, u5} T M₂ _inst_3 _inst_5] [_inst_17 : ContinuousConstSMul.{u3, u5} T M₂ _inst_10 (SMulZeroClass.toHasSmul.{u3, u5} T M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u3, u5} T M₂ (MulZeroClass.toHasZero.{u3} T (MulZeroOneClass.toMulZeroClass.{u3} T (MonoidWithZero.toMulZeroOneClass.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_18 : SMulCommClass.{u1, u3, u5} R T M₂ (SMulZeroClass.toHasSmul.{u1, u5} R M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u1, u5} R M₂ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u1, u5} R M₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u1, u5} R M₂ _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u3, u5} T M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u3, u5} T M₂ (MulZeroClass.toHasZero.{u3} T (MulZeroOneClass.toMulZeroClass.{u3} T (MonoidWithZero.toMulZeroOneClass.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_19 : SMulCommClass.{u2, u3, u5} S T M₂ (SMulZeroClass.toHasSmul.{u2, u5} S M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u2, u5} S M₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toHasSmul.{u3, u5} T M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u3, u5} T M₂ (MulZeroClass.toHasZero.{u3} T (MulZeroOneClass.toMulZeroClass.{u3} T (MonoidWithZero.toMulZeroOneClass.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))], (ContinuousLinearMap.{u1, u1, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 S _inst_9 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_14 _inst_4) -> (LinearMap.{u3, u3, u5, max u4 u5} T T _inst_3 _inst_3 (RingHom.id.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3)) M₂ (ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_5 (ContinuousLinearMap.addCommMonoid.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u1, u1, u3, u4, u5} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_15))
-but is expected to have type
- forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} {M : Type.{u4}} {M₂ : Type.{u5}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : Semiring.{u3} T] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : AddCommMonoid.{u5} M₂] [_inst_6 : Module.{u1, u5} R M₂ _inst_1 _inst_5] [_inst_7 : Module.{u2, u5} S M₂ _inst_2 _inst_5] [_inst_8 : IsScalarTower.{u1, u2, u5} R S M₂ (SMulZeroClass.toSMul.{u1, u2} R S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R S (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toSMul.{u2, u5} S M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u2, u5} S M₂ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toSMul.{u1, u5} R M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u5} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u5} R M₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (Module.toMulActionWithZero.{u1, u5} R M₂ _inst_1 _inst_5 _inst_6))))] [_inst_9 : TopologicalSpace.{u2} S] [_inst_10 : TopologicalSpace.{u5} M₂] [_inst_11 : ContinuousSMul.{u2, u5} S M₂ (SMulZeroClass.toSMul.{u2, u5} S M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u2, u5} S M₂ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) _inst_9 _inst_10] [_inst_12 : TopologicalSpace.{u4} M] [_inst_13 : AddCommMonoid.{u4} M] [_inst_14 : Module.{u1, u4} R M _inst_1 _inst_13] [_inst_15 : ContinuousAdd.{u5} M₂ _inst_10 (AddZeroClass.toAdd.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)))] [_inst_16 : Module.{u3, u5} T M₂ _inst_3 _inst_5] [_inst_17 : ContinuousConstSMul.{u3, u5} T M₂ _inst_10 (SMulZeroClass.toSMul.{u3, u5} T M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u5} T M₂ (MonoidWithZero.toZero.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_18 : SMulCommClass.{u1, u3, u5} R T M₂ (SMulZeroClass.toSMul.{u1, u5} R M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u5} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u5} R M₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (Module.toMulActionWithZero.{u1, u5} R M₂ _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u3, u5} T M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u5} T M₂ (MonoidWithZero.toZero.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_19 : SMulCommClass.{u2, u3, u5} S T M₂ (SMulZeroClass.toSMul.{u2, u5} S M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u2, u5} S M₂ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toSMul.{u3, u5} T M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u5} T M₂ (MonoidWithZero.toZero.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))], (ContinuousLinearMap.{u1, u1, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 S _inst_9 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_14 _inst_4) -> (LinearMap.{u3, u3, u5, max u5 u4} T T _inst_3 _inst_3 (RingHom.id.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3)) M₂ (ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_5 (ContinuousLinearMap.addCommMonoid.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u1, u1, u3, u4, u5} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_15))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_rightₗ ContinuousLinearMap.smulRightₗₓ'. -/
/-- Given `c : E →L[𝕜] 𝕜`, `c.smul_rightₗ` is the linear map from `F` to `E →L[𝕜] F`
sending `f` to `λ e, c e • f`. See also `continuous_linear_map.smul_rightL`. -/
@@ -2742,10 +2322,7 @@ def smulRightₗ (c : M →L[R] S) : M₂ →ₗ[T] M →L[R] M₂
#align continuous_linear_map.smul_rightₗ ContinuousLinearMap.smulRightₗ
/- warning: continuous_linear_map.coe_smul_rightₗ -> ContinuousLinearMap.coe_smulRightₗ is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} {M : Type.{u4}} {M₂ : Type.{u5}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : Semiring.{u3} T] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : AddCommMonoid.{u5} M₂] [_inst_6 : Module.{u1, u5} R M₂ _inst_1 _inst_5] [_inst_7 : Module.{u2, u5} S M₂ _inst_2 _inst_5] [_inst_8 : IsScalarTower.{u1, u2, u5} R S M₂ (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u5} S M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u2, u5} S M₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u5} R M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u1, u5} R M₂ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u1, u5} R M₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u1, u5} R M₂ _inst_1 _inst_5 _inst_6))))] [_inst_9 : TopologicalSpace.{u2} S] [_inst_10 : TopologicalSpace.{u5} M₂] [_inst_11 : ContinuousSMul.{u2, u5} S M₂ (SMulZeroClass.toHasSmul.{u2, u5} S M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u2, u5} S M₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) _inst_9 _inst_10] [_inst_12 : TopologicalSpace.{u4} M] [_inst_13 : AddCommMonoid.{u4} M] [_inst_14 : Module.{u1, u4} R M _inst_1 _inst_13] [_inst_15 : ContinuousAdd.{u5} M₂ _inst_10 (AddZeroClass.toHasAdd.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)))] [_inst_16 : Module.{u3, u5} T M₂ _inst_3 _inst_5] [_inst_17 : ContinuousConstSMul.{u3, u5} T M₂ _inst_10 (SMulZeroClass.toHasSmul.{u3, u5} T M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u3, u5} T M₂ (MulZeroClass.toHasZero.{u3} T (MulZeroOneClass.toMulZeroClass.{u3} T (MonoidWithZero.toMulZeroOneClass.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_18 : SMulCommClass.{u1, u3, u5} R T M₂ (SMulZeroClass.toHasSmul.{u1, u5} R M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u1, u5} R M₂ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u1, u5} R M₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u1, u5} R M₂ _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u3, u5} T M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u3, u5} T M₂ (MulZeroClass.toHasZero.{u3} T (MulZeroOneClass.toMulZeroClass.{u3} T (MonoidWithZero.toMulZeroOneClass.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_19 : SMulCommClass.{u2, u3, u5} S T M₂ (SMulZeroClass.toHasSmul.{u2, u5} S M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u2, u5} S M₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toHasSmul.{u3, u5} T M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u3, u5} T M₂ (MulZeroClass.toHasZero.{u3} T (MulZeroOneClass.toMulZeroClass.{u3} T (MonoidWithZero.toMulZeroOneClass.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))] (c : ContinuousLinearMap.{u1, u1, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 S _inst_9 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_14 _inst_4), Eq.{max (succ u5) (succ (max u4 u5))} (M₂ -> (ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6)) (coeFn.{max 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R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_5 (ContinuousLinearMap.addCommMonoid.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u1, u1, u3, u4, u5} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_15)) => M₂ -> (ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6)) (LinearMap.hasCoeToFun.{u3, u3, u5, max u4 u5} T T M₂ (ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_3 _inst_3 _inst_5 (ContinuousLinearMap.addCommMonoid.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u1, u1, u3, u4, u5} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_15) (RingHom.id.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3))) (ContinuousLinearMap.smulRightₗ.{u1, u2, u3, u4, u5} R S T M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 _inst_19 c)) (ContinuousLinearMap.smulRight.{u4, u5, u1, u2} M _inst_12 _inst_13 M₂ _inst_10 _inst_5 R S _inst_1 _inst_2 _inst_14 _inst_6 _inst_4 _inst_7 _inst_8 _inst_9 _inst_11 c)
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- forall {R : Type.{u5}} {S : Type.{u3}} {T : Type.{u1}} {M : Type.{u4}} {M₂ : Type.{u2}} [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u3} S] [_inst_3 : Semiring.{u1} T] [_inst_4 : Module.{u5, u3} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2)))] [_inst_5 : AddCommMonoid.{u2} M₂] [_inst_6 : Module.{u5, u2} R M₂ _inst_1 _inst_5] [_inst_7 : Module.{u3, u2} S M₂ _inst_2 _inst_5] [_inst_8 : IsScalarTower.{u5, u3, u2} R S M₂ (SMulZeroClass.toSMul.{u5, u3} R S (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (SMulWithZero.toSMulZeroClass.{u5, u3} R S (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (MulActionWithZero.toSMulWithZero.{u5, u3} R S (Semiring.toMonoidWithZero.{u5} R _inst_1) (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (Module.toMulActionWithZero.{u5, u3} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2))) _inst_4)))) (SMulZeroClass.toSMul.{u3, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u2} S M₂ (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u2} S M₂ (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u2} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toSMul.{u5, u2} R M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R M₂ (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R M₂ (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u5, u2} R M₂ _inst_1 _inst_5 _inst_6))))] [_inst_9 : TopologicalSpace.{u3} S] [_inst_10 : TopologicalSpace.{u2} M₂] [_inst_11 : ContinuousSMul.{u3, u2} S M₂ (SMulZeroClass.toSMul.{u3, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u2} S M₂ (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u2} S M₂ (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u2} S M₂ _inst_2 _inst_5 _inst_7)))) _inst_9 _inst_10] [_inst_12 : TopologicalSpace.{u4} M] [_inst_13 : AddCommMonoid.{u4} M] [_inst_14 : Module.{u5, u4} R M _inst_1 _inst_13] [_inst_15 : ContinuousAdd.{u2} M₂ _inst_10 (AddZeroClass.toAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)))] [_inst_16 : Module.{u1, u2} T M₂ _inst_3 _inst_5] [_inst_17 : ContinuousConstSMul.{u1, u2} T M₂ _inst_10 (SMulZeroClass.toSMul.{u1, u2} T M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} T M₂ (MonoidWithZero.toZero.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} T M₂ (Semiring.toMonoidWithZero.{u1} T _inst_3) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u1, u2} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_18 : SMulCommClass.{u5, u1, u2} R T M₂ (SMulZeroClass.toSMul.{u5, u2} R M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R M₂ (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R M₂ (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u5, u2} R M₂ _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u2} T M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} T M₂ (MonoidWithZero.toZero.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} T M₂ (Semiring.toMonoidWithZero.{u1} T _inst_3) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u1, u2} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_19 : SMulCommClass.{u3, u1, u2} S T M₂ (SMulZeroClass.toSMul.{u3, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u2} S M₂ (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u2} S M₂ (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u2} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toSMul.{u1, u2} T M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} T M₂ (MonoidWithZero.toZero.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} T M₂ (Semiring.toMonoidWithZero.{u1} T _inst_3) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u1, u2} T M₂ _inst_3 _inst_5 _inst_16))))] (c : ContinuousLinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 S _inst_9 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2))) _inst_14 _inst_4), Eq.{max (succ u4) (succ u2)} (forall (ᾰ : M₂), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₂) => ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) ᾰ) (FunLike.coe.{max (succ u4) (succ u2), succ u2, max (succ u4) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u4} T T _inst_3 _inst_3 (RingHom.id.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3)) M₂ (ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_5 (ContinuousLinearMap.addCommMonoid.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u5, u5, u1, u4, u2} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_15)) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₂) => ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u4 u2} T T M₂ (ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_3 _inst_3 _inst_5 (ContinuousLinearMap.addCommMonoid.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u5, u5, u1, u4, u2} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_15) (RingHom.id.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3))) (ContinuousLinearMap.smulRightₗ.{u5, u3, u1, u4, u2} R S T M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 _inst_19 c)) (ContinuousLinearMap.smulRight.{u4, u2, u5, u3} M _inst_12 _inst_13 M₂ _inst_10 _inst_5 R S _inst_1 _inst_2 _inst_14 _inst_6 _inst_4 _inst_7 _inst_8 _inst_9 _inst_11 c)
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_smul_rightₗ ContinuousLinearMap.coe_smulRightₗₓ'. -/
@[simp]
theorem coe_smulRightₗ (c : M →L[R] S) : ⇑(smulRightₗ c : M₂ →ₗ[T] M →L[R] M₂) = c.smul_right :=
@@ -2785,10 +2362,7 @@ def restrictScalars (f : M →L[A] M₂) : M →L[R] M₂ :=
variable {R}
/- warning: continuous_linear_map.coe_restrict_scalars -> ContinuousLinearMap.coe_restrictScalars is a dubious translation:
-lean 3 declaration is
- forall {A : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u4}} [_inst_8 : Ring.{u4} R] [_inst_9 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_10 : Module.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u2, u3, u4, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toHasSmul.{u4, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u4, u2} R M (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u4, u2} R M (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5] (f : ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A 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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_restrict_scalars ContinuousLinearMap.coe_restrictScalarsₓ'. -/
@[simp, norm_cast]
theorem coe_restrictScalars (f : M →L[A] M₂) :
@@ -2797,10 +2371,7 @@ theorem coe_restrictScalars (f : M →L[A] M₂) :
#align continuous_linear_map.coe_restrict_scalars ContinuousLinearMap.coe_restrictScalars
/- warning: continuous_linear_map.coe_restrict_scalars' -> ContinuousLinearMap.coe_restrictScalars' is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_restrict_scalars' ContinuousLinearMap.coe_restrictScalars'ₓ'. -/
@[simp]
theorem coe_restrictScalars' (f : M →L[A] M₂) : ⇑(f.restrictScalars R) = f :=
@@ -2808,10 +2379,7 @@ theorem coe_restrictScalars' (f : M →L[A] M₂) : ⇑(f.restrictScalars R) = f
#align continuous_linear_map.coe_restrict_scalars' ContinuousLinearMap.coe_restrictScalars'
/- warning: continuous_linear_map.restrict_scalars_zero -> ContinuousLinearMap.restrictScalars_zero is a dubious translation:
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(Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10))))
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- forall {A : Type.{u1}} {M : Type.{u4}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u4} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u4} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u4} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u2}} [_inst_8 : Ring.{u2} R] [_inst_9 : Module.{u2, u4} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] [_inst_10 : Module.{u2, u3} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u4, u3, u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toSMul.{u2, u4} R M (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (Module.toMulActionWithZero.{u2, u4} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u2, u3} R M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u3} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u3} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5], Eq.{max (succ u4) (succ u3)} (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u1, u4, u3, u2} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (OfNat.ofNat.{max u4 u3} (ContinuousLinearMap.{u1, u1, u4, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) 0 (Zero.toOfNat0.{max u4 u3} (ContinuousLinearMap.{u1, u1, u4, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.zero.{u1, u1, u4, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5)))) (OfNat.ofNat.{max u4 u3} (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) 0 (Zero.toOfNat0.{max u4 u3} (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.zero.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10)))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.restrict_scalars_zero ContinuousLinearMap.restrictScalars_zeroₓ'. -/
@[simp]
theorem restrictScalars_zero : (0 : M →L[A] M₂).restrictScalars R = 0 :=
@@ -2823,10 +2391,7 @@ section
variable [TopologicalAddGroup M₂]
/- warning: continuous_linear_map.restrict_scalars_add -> ContinuousLinearMap.restrictScalars_add is a dubious translation:
-lean 3 declaration is
- forall {A : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u4}} [_inst_8 : Ring.{u4} R] [_inst_9 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_10 : Module.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u2, u3, u4, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toHasSmul.{u4, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u4, u2} R M (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u4, u2} R M (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5] [_inst_12 : TopologicalAddGroup.{u3} M₂ _inst_7 (AddCommGroup.toAddGroup.{u3} M₂ _inst_3)] (f : ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (g : ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u1, 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_inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.add.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5 (TopologicalAddGroup.to_continuousAdd.{u3} M₂ _inst_7 (AddCommGroup.toAddGroup.{u3} M₂ _inst_3) _inst_12))) f g)) (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.add.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10 (TopologicalAddGroup.to_continuousAdd.{u3} M₂ _inst_7 (AddCommGroup.toAddGroup.{u3} M₂ _inst_3) _inst_12))) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 g))
-but is expected to have type
- forall {A : Type.{u4}} {M : Type.{u3}} {M₂ : Type.{u2}} [_inst_1 : Ring.{u4} A] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u2} M₂] [_inst_4 : Module.{u4, u3} A M (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_5 : Module.{u4, u2} A M₂ (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : TopologicalSpace.{u2} M₂] {R : Type.{u1}} [_inst_8 : Ring.{u1} R] [_inst_9 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_10 : Module.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u3, u2, u1, u4} M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) R A (Ring.toSemiring.{u4} A _inst_1) (SMulZeroClass.toSMul.{u1, u3} R M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (Module.toMulActionWithZero.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u1, u2} R M₂ (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_10)))) _inst_5] [_inst_12 : TopologicalAddGroup.{u2} M₂ _inst_7 (AddCommGroup.toAddGroup.{u2} M₂ _inst_3)] (f : ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) (g : ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R 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(AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) (instHAdd.{max u3 u2} (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.add.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5 (TopologicalAddGroup.toContinuousAdd.{u2} M₂ _inst_7 (AddCommGroup.toAddGroup.{u2} M₂ _inst_3) _inst_12))) f g)) (HAdd.hAdd.{max u3 u2, max u3 u2, max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (instHAdd.{max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.add.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10 (TopologicalAddGroup.toContinuousAdd.{u2} M₂ _inst_7 (AddCommGroup.toAddGroup.{u2} M₂ _inst_3) _inst_12))) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 g))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.restrict_scalars_add ContinuousLinearMap.restrictScalars_addₓ'. -/
@[simp]
theorem restrictScalars_add (f g : M →L[A] M₂) :
@@ -2835,10 +2400,7 @@ theorem restrictScalars_add (f g : M →L[A] M₂) :
#align continuous_linear_map.restrict_scalars_add ContinuousLinearMap.restrictScalars_add
/- warning: continuous_linear_map.restrict_scalars_neg -> ContinuousLinearMap.restrictScalars_neg is a dubious translation:
-lean 3 declaration is
- forall {A : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u4}} [_inst_8 : Ring.{u4} R] [_inst_9 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_10 : Module.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u2, u3, u4, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toHasSmul.{u4, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u4, u2} R M (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u4, u2} R M (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5] [_inst_12 : TopologicalAddGroup.{u3} M₂ _inst_7 (AddCommGroup.toAddGroup.{u3} M₂ _inst_3)] (f : ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.neg.{u1, u1, u2, u3} A _inst_1 A _inst_1 M _inst_6 _inst_2 M₂ _inst_7 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) _inst_12) f)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.neg.{u4, u4, u2, u3} R _inst_8 R _inst_8 M _inst_6 _inst_2 M₂ _inst_7 _inst_3 _inst_9 _inst_10 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) _inst_12) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f))
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(SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (Module.toMulActionWithZero.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u1, u2} R M₂ (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_10)))) _inst_5] [_inst_12 : TopologicalAddGroup.{u2} M₂ _inst_7 (AddCommGroup.toAddGroup.{u2} M₂ _inst_3)] (f : ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (Neg.neg.{max u3 u2} (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.neg.{u4, u4, u3, u2} A _inst_1 A _inst_1 M _inst_6 _inst_2 M₂ _inst_7 _inst_3 _inst_4 _inst_5 (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) _inst_12) f)) (Neg.neg.{max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.neg.{u1, u1, u3, u2} R _inst_8 R _inst_8 M _inst_6 _inst_2 M₂ _inst_7 _inst_3 _inst_9 _inst_10 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) _inst_12) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.restrict_scalars_neg ContinuousLinearMap.restrictScalars_negₓ'. -/
@[simp]
theorem restrictScalars_neg (f : M →L[A] M₂) : (-f).restrictScalars R = -f.restrictScalars R :=
@@ -2851,10 +2413,7 @@ variable {S : Type _} [Ring S] [Module S M₂] [ContinuousConstSMul S M₂] [SMu
[SMulCommClass R S M₂]
/- warning: continuous_linear_map.restrict_scalars_smul -> ContinuousLinearMap.restrictScalars_smul is a dubious translation:
-lean 3 declaration is
- forall {A : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u4}} [_inst_8 : Ring.{u4} R] [_inst_9 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_10 : Module.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u2, u3, u4, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toHasSmul.{u4, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u4, u2} R M (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u4, u2} R M (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5] {S : Type.{u5}} [_inst_12 : Ring.{u5} S] [_inst_13 : Module.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_14 : ContinuousConstSMul.{u5, u3} S M₂ _inst_7 (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_15 : SMulCommClass.{u1, u5, u3} A S M₂ (SMulZeroClass.toHasSmul.{u1, u3} A M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u1, u3} A M₂ (MulZeroClass.toHasZero.{u1} A (MulZeroOneClass.toMulZeroClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A _inst_1))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u1, u3} A M₂ (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A _inst_1)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_16 : SMulCommClass.{u4, u5, u3} R S M₂ (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] (c : S) (f : ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (SMul.smul.{u5, max u2 u3} S (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (MulAction.toHasSmul.{u5, max u2 u3} S (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (Ring.toMonoid.{u5} S _inst_12) (ContinuousLinearMap.mulAction.{u1, u1, u2, u3, u5} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5 S (Ring.toMonoid.{u5} S _inst_12) (Module.toDistribMulAction.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13) _inst_15 _inst_14)) c f)) (SMul.smul.{u5, max u2 u3} S (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (MulAction.toHasSmul.{u5, max u2 u3} S (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (Ring.toMonoid.{u5} S _inst_12) (ContinuousLinearMap.mulAction.{u4, u4, u2, u3, u5} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10 S (Ring.toMonoid.{u5} S _inst_12) (Module.toDistribMulAction.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13) _inst_16 _inst_14)) c (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f))
-but is expected to have type
- forall {A : Type.{u5}} {M : Type.{u4}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u5} A] [_inst_2 : AddCommGroup.{u4} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u5, u4} A M (Ring.toSemiring.{u5} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] [_inst_5 : Module.{u5, u3} A M₂ (Ring.toSemiring.{u5} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u4} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u2}} [_inst_8 : Ring.{u2} R] [_inst_9 : Module.{u2, u4} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] [_inst_10 : Module.{u2, u3} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u4, u3, u2, u5} M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u5} A _inst_1) (SMulZeroClass.toSMul.{u2, u4} R M (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (Module.toMulActionWithZero.{u2, u4} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u2, u3} R M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u3} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u3} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5] {S : Type.{u1}} [_inst_12 : Ring.{u1} S] [_inst_13 : Module.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_14 : ContinuousConstSMul.{u1, u3} S M₂ _inst_7 (SMulZeroClass.toSMul.{u1, u3} S M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u3} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_15 : SMulCommClass.{u5, u1, u3} A S M₂ (SMulZeroClass.toSMul.{u5, u3} A M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u5, u3} A M₂ (MonoidWithZero.toZero.{u5} A (Semiring.toMonoidWithZero.{u5} A (Ring.toSemiring.{u5} A _inst_1))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u5, u3} A M₂ (Semiring.toMonoidWithZero.{u5} A (Ring.toSemiring.{u5} A _inst_1)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u5, u3} A M₂ (Ring.toSemiring.{u5} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} S M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u3} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_16 : SMulCommClass.{u2, u1, u3} R S M₂ (SMulZeroClass.toSMul.{u2, u3} R M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u3} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u3} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) (SMulZeroClass.toSMul.{u1, u3} S M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u3} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] (c : S) (f : ContinuousLinearMap.{u5, u5, u4, u3} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A (Ring.toSemiring.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u4) (succ u3)} (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u5, u4, u3, u2} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (HSMul.hSMul.{u1, max u3 u4, max u3 u4} S (ContinuousLinearMap.{u5, u5, u4, u3} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A (Ring.toSemiring.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u5, u5, u4, u3} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A (Ring.toSemiring.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (instHSMul.{u1, max u3 u4} S (ContinuousLinearMap.{u5, u5, u4, u3} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A (Ring.toSemiring.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (MulAction.toSMul.{u1, max u3 u4} S (ContinuousLinearMap.{u5, u5, u4, u3} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A (Ring.toSemiring.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (ContinuousLinearMap.mulAction.{u5, u5, u4, u3, u1} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A (Ring.toSemiring.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5 S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (Module.toDistribMulAction.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13) _inst_15 _inst_14))) c f)) (HSMul.hSMul.{u1, max u3 u4, max u3 u4} S (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (instHSMul.{u1, max u3 u4} S (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (MulAction.toSMul.{u1, max u3 u4} S (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (ContinuousLinearMap.mulAction.{u2, u2, u4, u3, u1} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10 S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (Module.toDistribMulAction.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13) _inst_16 _inst_14))) c (ContinuousLinearMap.restrictScalars.{u5, u4, u3, u2} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.restrict_scalars_smul ContinuousLinearMap.restrictScalars_smulₓ'. -/
@[simp]
theorem restrictScalars_smul (c : S) (f : M →L[A] M₂) :
@@ -2878,10 +2437,7 @@ def restrictScalarsₗ : (M →L[A] M₂) →ₗ[S] M →L[R] M₂
variable {A M M₂ R S}
/- warning: continuous_linear_map.coe_restrict_scalarsₗ -> ContinuousLinearMap.coe_restrictScalarsₗ is a dubious translation:
-lean 3 declaration is
- forall {A : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u4}} [_inst_8 : Ring.{u4} R] [_inst_9 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_10 : Module.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u2, u3, u4, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toHasSmul.{u4, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u4, u2} R M (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u4, u2} R M (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5] {S : Type.{u5}} [_inst_12 : Ring.{u5} S] [_inst_13 : Module.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_14 : ContinuousConstSMul.{u5, u3} S M₂ _inst_7 (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_15 : SMulCommClass.{u1, u5, u3} A S M₂ (SMulZeroClass.toHasSmul.{u1, u3} A M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u1, u3} A M₂ (MulZeroClass.toHasZero.{u1} A (MulZeroOneClass.toMulZeroClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A _inst_1))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u1, u3} A M₂ (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A _inst_1)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_16 : SMulCommClass.{u4, u5, u3} R S M₂ (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_17 : TopologicalAddGroup.{u3} M₂ _inst_7 (AddCommGroup.toAddGroup.{u3} M₂ _inst_3)], Eq.{succ (max u2 u3)} ((ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) -> (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10)) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (LinearMap.{u5, u5, max u2 u3, max u2 u3} S S (Ring.toSemiring.{u5} S _inst_12) (Ring.toSemiring.{u5} S 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(Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5 (ContinuousLinearMap.restrictScalarsₗ._proof_1.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.addCommMonoid.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10 _inst_13 _inst_16 _inst_14 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) (ContinuousLinearMap.restrictScalarsₗ._proof_4.{u3} M₂ _inst_3 _inst_7 _inst_17))) => (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) -> (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10)) (LinearMap.hasCoeToFun.{u5, u5, max u2 u3, max u2 u3} S S (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (Ring.toSemiring.{u5} S _inst_12) (Ring.toSemiring.{u5} S _inst_12) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5 (ContinuousLinearMap.restrictScalarsₗ._proof_1.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.addCommMonoid.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10 (ContinuousLinearMap.restrictScalarsₗ._proof_2.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.module.{u1, u1, u5, u2, u3} A A S (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u5} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5 _inst_13 _inst_15 _inst_14 (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) (ContinuousLinearMap.restrictScalarsₗ._proof_3.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.module.{u4, u4, u5, u2, u3} R R S (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u5} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10 _inst_13 _inst_16 _inst_14 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) (ContinuousLinearMap.restrictScalarsₗ._proof_4.{u3} M₂ _inst_3 _inst_7 _inst_17)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S (Ring.toSemiring.{u5} S _inst_12)))) (ContinuousLinearMap.restrictScalarsₗ.{u1, u2, u3, u4, u5} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 S _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17)) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11)
-but is expected to have type
- forall {A : Type.{u3}} {M : Type.{u5}} {M₂ : Type.{u4}} [_inst_1 : Ring.{u3} A] [_inst_2 : AddCommGroup.{u5} M] [_inst_3 : AddCommGroup.{u4} M₂] [_inst_4 : Module.{u3, u5} A M (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2)] [_inst_5 : Module.{u3, u4} A M₂ (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u5} M] [_inst_7 : TopologicalSpace.{u4} M₂] {R : Type.{u2}} [_inst_8 : Ring.{u2} R] [_inst_9 : Module.{u2, u5} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2)] [_inst_10 : Module.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u5, u4, u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) R A (Ring.toSemiring.{u3} A _inst_1) (SMulZeroClass.toSMul.{u2, u5} R M (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u5} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u5} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (Module.toMulActionWithZero.{u2, u5} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u2, u4} R M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10)))) _inst_5] {S : Type.{u1}} [_inst_12 : Ring.{u1} S] [_inst_13 : Module.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_14 : ContinuousConstSMul.{u1, u4} S M₂ _inst_7 (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_15 : SMulCommClass.{u3, u1, u4} A S M₂ (SMulZeroClass.toSMul.{u3, u4} A M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u3, u4} A M₂ (MonoidWithZero.toZero.{u3} A (Semiring.toMonoidWithZero.{u3} A (Ring.toSemiring.{u3} A _inst_1))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A M₂ (Semiring.toMonoidWithZero.{u3} A (Ring.toSemiring.{u3} A _inst_1)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u3, u4} A M₂ (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_16 : SMulCommClass.{u2, u1, u4} R S M₂ (SMulZeroClass.toSMul.{u2, u4} R M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10)))) (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_17 : TopologicalAddGroup.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3)], Eq.{max (succ u5) (succ u4)} (forall (ᾰ : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) => ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10) ᾰ) (FunLike.coe.{max (succ u5) (succ u4), max (succ u5) (succ u4), max (succ u5) (succ u4)} (LinearMap.{u1, u1, max u4 u5, max u4 u5} S S (Ring.toSemiring.{u1} S _inst_12) (Ring.toSemiring.{u1} S _inst_12) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) 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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_restrict_scalarsₗ ContinuousLinearMap.coe_restrictScalarsₗₓ'. -/
@[simp]
theorem coe_restrictScalarsₗ : ⇑(restrictScalarsₗ A M M₂ R S) = restrictScalars R :=
@@ -2943,10 +2499,7 @@ instance : CoeFun (M₁ ≃SL[σ₁₂] M₂) fun _ => M₁ → M₂ :=
/- warning: continuous_linear_equiv.coe_def_rev clashes with [anonymous] -> [anonymous]
warning: continuous_linear_equiv.coe_def_rev -> [anonymous] is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_def_rev [anonymous]ₓ'. -/
@[simp]
theorem [anonymous] (e : M₁ ≃SL[σ₁₂] M₂) : e.toContinuousLinearMap = e :=
@@ -2954,20 +2507,14 @@ theorem [anonymous] (e : M₁ ≃SL[σ₁₂] M₂) : e.toContinuousLinearMap =
#align continuous_linear_equiv.coe_def_rev [anonymous]
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_apply ContinuousLinearEquiv.coe_applyₓ'. -/
theorem coe_apply (e : M₁ ≃SL[σ₁₂] M₂) (b : M₁) : (e : M₁ →SL[σ₁₂] M₂) b = e b :=
rfl
#align continuous_linear_equiv.coe_apply ContinuousLinearEquiv.coe_apply
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_to_linear_equiv ContinuousLinearEquiv.coe_toLinearEquivₓ'. -/
@[simp]
theorem coe_toLinearEquiv (f : M₁ ≃SL[σ₁₂] M₂) : ⇑f.toLinearEquiv = f :=
@@ -2975,10 +2522,7 @@ theorem coe_toLinearEquiv (f : M₁ ≃SL[σ₁₂] M₂) : ⇑f.toLinearEquiv =
#align continuous_linear_equiv.coe_to_linear_equiv ContinuousLinearEquiv.coe_toLinearEquiv
/- warning: continuous_linear_equiv.coe_coe -> ContinuousLinearEquiv.coe_coe is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_coe ContinuousLinearEquiv.coe_coeₓ'. -/
@[simp, norm_cast]
theorem coe_coe (e : M₁ ≃SL[σ₁₂] M₂) : ⇑(e : M₁ →SL[σ₁₂] M₂) = e :=
@@ -2986,10 +2530,7 @@ theorem coe_coe (e : M₁ ≃SL[σ₁₂] M₂) : ⇑(e : M₁ →SL[σ₁₂] M
#align continuous_linear_equiv.coe_coe ContinuousLinearEquiv.coe_coe
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.to_linear_equiv_injective ContinuousLinearEquiv.toLinearEquiv_injectiveₓ'. -/
theorem toLinearEquiv_injective :
Function.Injective (toLinearEquiv : (M₁ ≃SL[σ₁₂] M₂) → M₁ ≃ₛₗ[σ₁₂] M₂)
@@ -2997,10 +2538,7 @@ theorem toLinearEquiv_injective :
#align continuous_linear_equiv.to_linear_equiv_injective ContinuousLinearEquiv.toLinearEquiv_injective
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.ext ContinuousLinearEquiv.extₓ'. -/
@[ext]
theorem ext {f g : M₁ ≃SL[σ₁₂] M₂} (h : (f : M₁ → M₂) = g) : f = g :=
@@ -3008,20 +2546,14 @@ theorem ext {f g : M₁ ≃SL[σ₁₂] M₂} (h : (f : M₁ → M₂) = g) : f
#align continuous_linear_equiv.ext ContinuousLinearEquiv.ext
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_injective ContinuousLinearEquiv.coe_injectiveₓ'. -/
theorem coe_injective : Function.Injective (coe : (M₁ ≃SL[σ₁₂] M₂) → M₁ →SL[σ₁₂] M₂) :=
fun e e' h => ext <| funext <| ContinuousLinearMap.ext_iff.1 h
#align continuous_linear_equiv.coe_injective ContinuousLinearEquiv.coe_injective
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@[simp, norm_cast]
theorem coe_inj {e e' : M₁ ≃SL[σ₁₂] M₂} : (e : M₁ →SL[σ₁₂] M₂) = e' ↔ e = e' :=
@@ -3036,10 +2568,7 @@ def toHomeomorph (e : M₁ ≃SL[σ₁₂] M₂) : M₁ ≃ₜ M₂ :=
-/
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_to_homeomorph ContinuousLinearEquiv.coe_toHomeomorphₓ'. -/
@[simp]
theorem coe_toHomeomorph (e : M₁ ≃SL[σ₁₂] M₂) : ⇑e.toHomeomorph = e :=
@@ -3047,30 +2576,21 @@ theorem coe_toHomeomorph (e : M₁ ≃SL[σ₁₂] M₂) : ⇑e.toHomeomorph = e
#align continuous_linear_equiv.coe_to_homeomorph ContinuousLinearEquiv.coe_toHomeomorph
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.image_closure ContinuousLinearEquiv.image_closureₓ'. -/
theorem image_closure (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₁) : e '' closure s = closure (e '' s) :=
e.toHomeomorph.image_closure s
#align continuous_linear_equiv.image_closure ContinuousLinearEquiv.image_closure
/- warning: continuous_linear_equiv.preimage_closure -> ContinuousLinearEquiv.preimage_closure is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.preimage_closure ContinuousLinearEquiv.preimage_closureₓ'. -/
theorem preimage_closure (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₂) : e ⁻¹' closure s = closure (e ⁻¹' s) :=
e.toHomeomorph.preimage_closure s
#align continuous_linear_equiv.preimage_closure ContinuousLinearEquiv.preimage_closure
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.is_closed_image ContinuousLinearEquiv.isClosed_imageₓ'. -/
@[simp]
theorem isClosed_image (e : M₁ ≃SL[σ₁₂] M₂) {s : Set M₁} : IsClosed (e '' s) ↔ IsClosed s :=
@@ -3078,20 +2598,14 @@ theorem isClosed_image (e : M₁ ≃SL[σ₁₂] M₂) {s : Set M₁} : IsClosed
#align continuous_linear_equiv.is_closed_image ContinuousLinearEquiv.isClosed_image
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_nhds_eq ContinuousLinearEquiv.map_nhds_eqₓ'. -/
theorem map_nhds_eq (e : M₁ ≃SL[σ₁₂] M₂) (x : M₁) : map e (𝓝 x) = 𝓝 (e x) :=
e.toHomeomorph.map_nhds_eq x
#align continuous_linear_equiv.map_nhds_eq ContinuousLinearEquiv.map_nhds_eq
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_zero ContinuousLinearEquiv.map_zeroₓ'. -/
-- Make some straightforward lemmas available to `simp`.
@[simp]
@@ -3100,10 +2614,7 @@ theorem map_zero (e : M₁ ≃SL[σ₁₂] M₂) : e (0 : M₁) = 0 :=
#align continuous_linear_equiv.map_zero ContinuousLinearEquiv.map_zero
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_add ContinuousLinearEquiv.map_addₓ'. -/
@[simp]
theorem map_add (e : M₁ ≃SL[σ₁₂] M₂) (x y : M₁) : e (x + y) = e x + e y :=
@@ -3111,10 +2622,7 @@ theorem map_add (e : M₁ ≃SL[σ₁₂] M₂) (x y : M₁) : e (x + y) = e x +
#align continuous_linear_equiv.map_add ContinuousLinearEquiv.map_add
/- warning: continuous_linear_equiv.map_smulₛₗ -> ContinuousLinearEquiv.map_smulₛₗ is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_smulₛₗ ContinuousLinearEquiv.map_smulₛₗₓ'. -/
@[simp]
theorem map_smulₛₗ (e : M₁ ≃SL[σ₁₂] M₂) (c : R₁) (x : M₁) : e (c • x) = σ₁₂ c • e x :=
@@ -3124,10 +2632,7 @@ theorem map_smulₛₗ (e : M₁ ≃SL[σ₁₂] M₂) (c : R₁) (x : M₁) : e
omit σ₂₁
/- warning: continuous_linear_equiv.map_smul -> ContinuousLinearEquiv.map_smul is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_smul ContinuousLinearEquiv.map_smulₓ'. -/
@[simp]
theorem map_smul [Module R₁ M₂] (e : M₁ ≃L[R₁] M₂) (c : R₁) (x : M₁) : e (c • x) = c • e x :=
@@ -3137,10 +2642,7 @@ theorem map_smul [Module R₁ M₂] (e : M₁ ≃L[R₁] M₂) (c : R₁) (x : M
include σ₂₁
/- warning: continuous_linear_equiv.map_eq_zero_iff -> ContinuousLinearEquiv.map_eq_zero_iff is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_eq_zero_iff ContinuousLinearEquiv.map_eq_zero_iffₓ'. -/
@[simp]
theorem map_eq_zero_iff (e : M₁ ≃SL[σ₁₂] M₂) {x : M₁} : e x = 0 ↔ x = 0 :=
@@ -3151,10 +2653,7 @@ attribute [continuity]
ContinuousLinearEquiv.continuous_toFun ContinuousLinearEquiv.continuous_invFun
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.continuous ContinuousLinearEquiv.continuousₓ'. -/
@[continuity]
protected theorem continuous (e : M₁ ≃SL[σ₁₂] M₂) : Continuous (e : M₁ → M₂) :=
@@ -3162,30 +2661,21 @@ protected theorem continuous (e : M₁ ≃SL[σ₁₂] M₂) : Continuous (e : M
#align continuous_linear_equiv.continuous ContinuousLinearEquiv.continuous
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.continuous_on ContinuousLinearEquiv.continuousOnₓ'. -/
protected theorem continuousOn (e : M₁ ≃SL[σ₁₂] M₂) {s : Set M₁} : ContinuousOn (e : M₁ → M₂) s :=
e.Continuous.ContinuousOn
#align continuous_linear_equiv.continuous_on ContinuousLinearEquiv.continuousOn
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.continuous_at ContinuousLinearEquiv.continuousAtₓ'. -/
protected theorem continuousAt (e : M₁ ≃SL[σ₁₂] M₂) {x : M₁} : ContinuousAt (e : M₁ → M₂) x :=
e.Continuous.ContinuousAt
#align continuous_linear_equiv.continuous_at ContinuousLinearEquiv.continuousAt
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.continuous_within_at ContinuousLinearEquiv.continuousWithinAtₓ'. -/
protected theorem continuousWithinAt (e : M₁ ≃SL[σ₁₂] M₂) {s : Set M₁} {x : M₁} :
ContinuousWithinAt (e : M₁ → M₂) s x :=
@@ -3193,10 +2683,7 @@ protected theorem continuousWithinAt (e : M₁ ≃SL[σ₁₂] M₂) {s : Set M
#align continuous_linear_equiv.continuous_within_at ContinuousLinearEquiv.continuousWithinAt
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.comp_continuous_on_iff ContinuousLinearEquiv.comp_continuousOn_iffₓ'. -/
theorem comp_continuousOn_iff {α : Type _} [TopologicalSpace α] (e : M₁ ≃SL[σ₁₂] M₂) {f : α → M₁}
{s : Set α} : ContinuousOn (e ∘ f) s ↔ ContinuousOn f s :=
@@ -3204,10 +2691,7 @@ theorem comp_continuousOn_iff {α : Type _} [TopologicalSpace α] (e : M₁ ≃S
#align continuous_linear_equiv.comp_continuous_on_iff ContinuousLinearEquiv.comp_continuousOn_iff
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.comp_continuous_iff ContinuousLinearEquiv.comp_continuous_iffₓ'. -/
theorem comp_continuous_iff {α : Type _} [TopologicalSpace α] (e : M₁ ≃SL[σ₁₂] M₂) {f : α → M₁} :
Continuous (e ∘ f) ↔ Continuous f :=
@@ -3217,10 +2701,7 @@ theorem comp_continuous_iff {α : Type _} [TopologicalSpace α] (e : M₁ ≃SL[
omit σ₂₁
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.ext₁ ContinuousLinearEquiv.ext₁ₓ'. -/
/-- An extensionality lemma for `R ≃L[R] M`. -/
theorem ext₁ [TopologicalSpace R₁] {f g : R₁ ≃L[R₁] M₁} (h : f 1 = g 1) : f = g :=
@@ -3270,10 +2751,7 @@ protected def symm (e : M₁ ≃SL[σ₁₂] M₂) : M₂ ≃SL[σ₂₁] M₁ :
include σ₂₁
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_to_linear_equiv ContinuousLinearEquiv.symm_toLinearEquivₓ'. -/
@[simp]
theorem symm_toLinearEquiv (e : M₁ ≃SL[σ₁₂] M₂) : e.symm.toLinearEquiv = e.toLinearEquiv.symm :=
@@ -3283,10 +2761,7 @@ theorem symm_toLinearEquiv (e : M₁ ≃SL[σ₁₂] M₂) : e.symm.toLinearEqui
#align continuous_linear_equiv.symm_to_linear_equiv ContinuousLinearEquiv.symm_toLinearEquiv
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_to_homeomorph ContinuousLinearEquiv.symm_toHomeomorphₓ'. -/
@[simp]
theorem symm_toHomeomorph (e : M₁ ≃SL[σ₁₂] M₂) : e.toHomeomorph.symm = e.symm.toHomeomorph :=
@@ -3312,10 +2787,7 @@ initialize_simps_projections ContinuousLinearEquiv (to_linear_equiv_to_fun → a
to_linear_equiv_inv_fun → symm_apply)
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_map_nhds_eq ContinuousLinearEquiv.symm_map_nhds_eqₓ'. -/
theorem symm_map_nhds_eq (e : M₁ ≃SL[σ₁₂] M₂) (x : M₁) : map e.symm (𝓝 (e x)) = 𝓝 x :=
e.toHomeomorph.symm_map_nhds_eq x
@@ -3340,10 +2812,7 @@ protected def trans (e₁ : M₁ ≃SL[σ₁₂] M₂) (e₂ : M₂ ≃SL[σ₂
include σ₁₃
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.trans_to_linear_equiv ContinuousLinearEquiv.trans_toLinearEquivₓ'. -/
@[simp]
theorem trans_toLinearEquiv (e₁ : M₁ ≃SL[σ₁₂] M₂) (e₂ : M₂ ≃SL[σ₂₃] M₃) :
@@ -3356,10 +2825,7 @@ theorem trans_toLinearEquiv (e₁ : M₁ ≃SL[σ₁₂] M₂) (e₂ : M₂ ≃S
omit σ₁₃ σ₂₁ σ₃₂ σ₃₁
/- warning: continuous_linear_equiv.prod -> ContinuousLinearEquiv.prod is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.prod ContinuousLinearEquiv.prodₓ'. -/
/-- Product of two continuous linear equivalences. The map comes from `equiv.prod_congr`. -/
def prod [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M₁ ≃L[R₁] M₂) (e' : M₃ ≃L[R₁] M₄) :
@@ -3372,10 +2838,7 @@ def prod [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M₁ ≃L
#align continuous_linear_equiv.prod ContinuousLinearEquiv.prod
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(ContinuousLinearEquiv.{u5, u5, max u3 u1, max u2 u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHomInvPair.ids.{u5} R₁ _inst_1) (RingHomInvPair.ids.{u5} R₁ _inst_1) (Prod.{u1, u3} M₁ M₃) (instTopologicalSpaceProd.{u1, u3} M₁ M₃ _inst_12 _inst_18) (Prod.instAddCommMonoidSum.{u1, u3} M₁ M₃ _inst_13 _inst_19) (Prod.{u4, u2} M₂ M₄) (instTopologicalSpaceProd.{u4, u2} M₂ M₄ _inst_16 _inst_20) (Prod.instAddCommMonoidSum.{u4, u2} M₂ M₄ _inst_17 _inst_21) (Prod.module.{u5, u1, u3} R₁ M₁ M₃ _inst_1 _inst_13 _inst_19 _inst_22 _inst_27) (Prod.module.{u5, u4, u2} R₁ M₂ M₄ _inst_1 _inst_17 _inst_21 _inst_26 _inst_28)) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHomInvPair.ids.{u5} R₁ _inst_1) (RingHomInvPair.ids.{u5} R₁ _inst_1) (Prod.{u1, u3} M₁ M₃) 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M₂ M₄ _inst_17 _inst_21) (Prod.module.{u5, u1, u3} R₁ M₁ M₃ _inst_1 _inst_13 _inst_19 _inst_22 _inst_27) (Prod.module.{u5, u4, u2} R₁ M₂ M₄ _inst_1 _inst_17 _inst_21 _inst_26 _inst_28))))) (ContinuousLinearEquiv.prod.{u5, u1, u4, u3, u2} R₁ _inst_1 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 M₄ _inst_20 _inst_21 _inst_22 _inst_26 _inst_27 _inst_28 e e') x) (Prod.mk.{u4, u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) (Prod.fst.{u1, u3} M₁ M₃ x)) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₃) => M₄) (Prod.snd.{u1, u3} M₁ M₃ x)) (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (ContinuousLinearEquiv.{u5, u5, u1, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHomInvPair.ids.{u5} R₁ _inst_1) (RingHomInvPair.ids.{u5} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26) M₁ 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(RingHomInvPair.ids.{u5} R₁ _inst_1) (RingHomInvPair.ids.{u5} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26)))) e (Prod.fst.{u1, u3} M₁ M₃ x)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (ContinuousLinearEquiv.{u5, u5, u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHomInvPair.ids.{u5} R₁ _inst_1) (RingHomInvPair.ids.{u5} R₁ _inst_1) M₃ _inst_18 _inst_19 M₄ _inst_20 _inst_21 _inst_27 _inst_28) M₃ (fun (_x : M₃) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₃) => M₄) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u3, u2} (ContinuousLinearEquiv.{u5, u5, u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHomInvPair.ids.{u5} R₁ _inst_1) (RingHomInvPair.ids.{u5} R₁ _inst_1) M₃ _inst_18 _inst_19 M₄ 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M₄ _inst_20 _inst_21 _inst_27 _inst_28) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHomInvPair.ids.{u5} R₁ _inst_1) (RingHomInvPair.ids.{u5} R₁ _inst_1) M₃ _inst_18 _inst_19 M₄ _inst_20 _inst_21 _inst_27 _inst_28 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u5, u5, u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHomInvPair.ids.{u5} R₁ _inst_1) (RingHomInvPair.ids.{u5} R₁ _inst_1) M₃ _inst_18 _inst_19 M₄ _inst_20 _inst_21 _inst_27 _inst_28)))) e' (Prod.snd.{u1, u3} M₁ M₃ x)))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.prod_apply ContinuousLinearEquiv.prod_applyₓ'. -/
@[simp, norm_cast]
theorem prod_apply [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M₁ ≃L[R₁] M₂)
@@ -3384,10 +2847,7 @@ theorem prod_apply [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e :
#align continuous_linear_equiv.prod_apply ContinuousLinearEquiv.prod_apply
/- warning: continuous_linear_equiv.coe_prod -> ContinuousLinearEquiv.coe_prod is a dubious translation:
-lean 3 declaration is
- forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_16 : TopologicalSpace.{u3} M₂] [_inst_17 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u4}} [_inst_18 : TopologicalSpace.{u4} M₃] [_inst_19 : AddCommMonoid.{u4} M₃] {M₄ : Type.{u5}} [_inst_20 : TopologicalSpace.{u5} M₄] [_inst_21 : AddCommMonoid.{u5} M₄] [_inst_22 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_13] [_inst_26 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_17] [_inst_27 : Module.{u1, u4} R₁ M₃ _inst_1 _inst_19] [_inst_28 : Module.{u1, u5} R₁ M₄ _inst_1 _inst_21] (e : ContinuousLinearEquiv.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHomInvPair.ids.{u1} R₁ _inst_1) (RingHomInvPair.ids.{u1} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26) (e' : ContinuousLinearEquiv.{u1, u1, u4, u5} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHomInvPair.ids.{u1} R₁ _inst_1) (RingHomInvPair.ids.{u1} R₁ _inst_1) M₃ _inst_18 _inst_19 M₄ _inst_20 _inst_21 _inst_27 _inst_28), Eq.{max (succ (max u2 u4)) (succ (max u3 u5))} (ContinuousLinearMap.{u1, u1, max u2 u4, max u3 u5} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u4} M₁ M₃) (Prod.topologicalSpace.{u2, u4} M₁ M₃ _inst_12 _inst_18) (Prod.addCommMonoid.{u2, u4} M₁ M₃ _inst_13 _inst_19) (Prod.{u3, u5} M₂ M₄) (Prod.topologicalSpace.{u3, u5} M₂ M₄ _inst_16 _inst_20) (Prod.addCommMonoid.{u3, u5} M₂ M₄ _inst_17 _inst_21) (Prod.module.{u1, u2, u4} R₁ M₁ M₃ _inst_1 _inst_13 _inst_19 _inst_22 _inst_27) (Prod.module.{u1, u3, u5} R₁ M₂ M₄ _inst_1 _inst_17 _inst_21 _inst_26 _inst_28)) ((fun (a : Sort.{max (succ (max u2 u4)) (succ (max u3 u5))}) (b : Sort.{max (succ (max u2 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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_prod ContinuousLinearEquiv.coe_prodₓ'. -/
@[simp, norm_cast]
theorem coe_prod [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M₁ ≃L[R₁] M₂)
@@ -3397,10 +2857,7 @@ theorem coe_prod [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M
#align continuous_linear_equiv.coe_prod ContinuousLinearEquiv.coe_prod
/- warning: continuous_linear_equiv.prod_symm -> ContinuousLinearEquiv.prod_symm is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.prod_symm ContinuousLinearEquiv.prod_symmₓ'. -/
theorem prod_symm [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M₁ ≃L[R₁] M₂)
(e' : M₃ ≃L[R₁] M₄) : (e.Prod e').symm = e.symm.Prod e'.symm :=
@@ -3410,30 +2867,21 @@ theorem prod_symm [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e :
include σ₂₁
/- warning: continuous_linear_equiv.bijective -> ContinuousLinearEquiv.bijective is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.bijective ContinuousLinearEquiv.bijectiveₓ'. -/
protected theorem bijective (e : M₁ ≃SL[σ₁₂] M₂) : Function.Bijective e :=
e.toLinearEquiv.toEquiv.Bijective
#align continuous_linear_equiv.bijective ContinuousLinearEquiv.bijective
/- warning: continuous_linear_equiv.injective -> ContinuousLinearEquiv.injective is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.injective ContinuousLinearEquiv.injectiveₓ'. -/
protected theorem injective (e : M₁ ≃SL[σ₁₂] M₂) : Function.Injective e :=
e.toLinearEquiv.toEquiv.Injective
#align continuous_linear_equiv.injective ContinuousLinearEquiv.injective
/- warning: continuous_linear_equiv.surjective -> ContinuousLinearEquiv.surjective is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.surjective ContinuousLinearEquiv.surjectiveₓ'. -/
protected theorem surjective (e : M₁ ≃SL[σ₁₂] M₂) : Function.Surjective e :=
e.toLinearEquiv.toEquiv.Surjective
@@ -3442,10 +2890,7 @@ protected theorem surjective (e : M₁ ≃SL[σ₁₂] M₂) : Function.Surjecti
include σ₃₂ σ₃₁ σ₁₃
/- warning: continuous_linear_equiv.trans_apply -> ContinuousLinearEquiv.trans_apply is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.trans_apply ContinuousLinearEquiv.trans_applyₓ'. -/
@[simp]
theorem trans_apply (e₁ : M₁ ≃SL[σ₁₂] M₂) (e₂ : M₂ ≃SL[σ₂₃] M₃) (c : M₁) :
@@ -3456,10 +2901,7 @@ theorem trans_apply (e₁ : M₁ ≃SL[σ₁₂] M₂) (e₂ : M₂ ≃SL[σ₂
omit σ₃₂ σ₃₁ σ₁₃
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.apply_symm_apply ContinuousLinearEquiv.apply_symm_applyₓ'. -/
@[simp]
theorem apply_symm_apply (e : M₁ ≃SL[σ₁₂] M₂) (c : M₂) : e (e.symm c) = c :=
@@ -3467,10 +2909,7 @@ theorem apply_symm_apply (e : M₁ ≃SL[σ₁₂] M₂) (c : M₂) : e (e.symm
#align continuous_linear_equiv.apply_symm_apply ContinuousLinearEquiv.apply_symm_apply
/- warning: continuous_linear_equiv.symm_apply_apply -> ContinuousLinearEquiv.symm_apply_apply is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_apply_apply ContinuousLinearEquiv.symm_apply_applyₓ'. -/
@[simp]
theorem symm_apply_apply (e : M₁ ≃SL[σ₁₂] M₂) (b : M₁) : e.symm (e b) = b :=
@@ -3480,10 +2919,7 @@ theorem symm_apply_apply (e : M₁ ≃SL[σ₁₂] M₂) (b : M₁) : e.symm (e
include σ₁₂ σ₂₃ σ₁₃ σ₃₁
/- warning: continuous_linear_equiv.symm_trans_apply -> ContinuousLinearEquiv.symm_trans_apply is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_trans_apply ContinuousLinearEquiv.symm_trans_applyₓ'. -/
@[simp]
theorem symm_trans_apply (e₁ : M₂ ≃SL[σ₂₁] M₁) (e₂ : M₃ ≃SL[σ₃₂] M₂) (c : M₁) :
@@ -3494,10 +2930,7 @@ theorem symm_trans_apply (e₁ : M₂ ≃SL[σ₂₁] M₁) (e₂ : M₃ ≃SL[
omit σ₁₂ σ₂₃ σ₁₃ σ₃₁
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_image_image ContinuousLinearEquiv.symm_image_imageₓ'. -/
@[simp]
theorem symm_image_image (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₁) : e.symm '' (e '' s) = s :=
@@ -3505,10 +2938,7 @@ theorem symm_image_image (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₁) : e.symm
#align continuous_linear_equiv.symm_image_image ContinuousLinearEquiv.symm_image_image
/- warning: continuous_linear_equiv.image_symm_image -> ContinuousLinearEquiv.image_symm_image is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.image_symm_image ContinuousLinearEquiv.image_symm_imageₓ'. -/
@[simp]
theorem image_symm_image (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₂) : e '' (e.symm '' s) = s :=
@@ -3518,10 +2948,7 @@ theorem image_symm_image (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₂) : e '' (
include σ₃₂ σ₃₁
/- warning: continuous_linear_equiv.comp_coe -> ContinuousLinearEquiv.comp_coe is a dubious translation:
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(Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {σ₃₁ : RingHom.{u3, u1} R₃ R₁ (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_8 : RingHomInvPair.{u1, u3} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁] [_inst_9 : RingHomInvPair.{u3, u1} R₃ R₁ _inst_3 _inst_1 σ₃₁ σ₁₃] [_inst_10 : RingHomCompTriple.{u1, u2, u3} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] [_inst_11 : RingHomCompTriple.{u3, u2, u1} R₃ R₂ R₁ _inst_3 _inst_2 _inst_1 σ₃₂ σ₂₁ σ₃₁] {M₁ : Type.{u4}} [_inst_12 : TopologicalSpace.{u4} M₁] [_inst_13 : AddCommMonoid.{u4} M₁] {M₂ : Type.{u5}} [_inst_16 : TopologicalSpace.{u5} M₂] [_inst_17 : AddCommMonoid.{u5} M₂] {M₃ : Type.{u6}} [_inst_18 : TopologicalSpace.{u6} M₃] [_inst_19 : AddCommMonoid.{u6} M₃] [_inst_22 : Module.{u1, u4} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u5} R₂ M₂ _inst_2 _inst_17] [_inst_25 : Module.{u3, u6} R₃ M₃ _inst_3 _inst_19] (f : ContinuousLinearEquiv.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (f' : ContinuousLinearEquiv.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25), Eq.{max (succ u4) (succ u6)} (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_22 _inst_24 _inst_25 _inst_10 ((fun (a : Sort.{max (succ u5) (succ u6)}) (b : Sort.{max (succ u5) (succ u6)}) [self : HasLiftT.{max (succ u5) (succ u6), max (succ u5) (succ u6)} a b] => self.0) (ContinuousLinearEquiv.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25) (ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25) 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-but is expected to have type
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.comp_coe ContinuousLinearEquiv.comp_coeₓ'. -/
@[simp, norm_cast]
theorem comp_coe (f : M₁ ≃SL[σ₁₂] M₂) (f' : M₂ ≃SL[σ₂₃] M₃) :
@@ -3532,10 +2959,7 @@ theorem comp_coe (f : M₁ ≃SL[σ₁₂] M₂) (f' : M₂ ≃SL[σ₂₃] M₃
omit σ₃₂ σ₃₁ σ₂₁
/- warning: continuous_linear_equiv.coe_comp_coe_symm -> ContinuousLinearEquiv.coe_comp_coe_symm is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_comp_coe_symm ContinuousLinearEquiv.coe_comp_coe_symmₓ'. -/
@[simp]
theorem coe_comp_coe_symm (e : M₁ ≃SL[σ₁₂] M₂) :
@@ -3544,10 +2968,7 @@ theorem coe_comp_coe_symm (e : M₁ ≃SL[σ₁₂] M₂) :
#align continuous_linear_equiv.coe_comp_coe_symm ContinuousLinearEquiv.coe_comp_coe_symm
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_symm_comp_coe ContinuousLinearEquiv.coe_symm_comp_coeₓ'. -/
@[simp]
theorem coe_symm_comp_coe (e : M₁ ≃SL[σ₁₂] M₂) :
@@ -3558,10 +2979,7 @@ theorem coe_symm_comp_coe (e : M₁ ≃SL[σ₁₂] M₂) :
include σ₂₁
/- warning: continuous_linear_equiv.symm_comp_self -> ContinuousLinearEquiv.symm_comp_self is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_comp_self ContinuousLinearEquiv.symm_comp_selfₓ'. -/
@[simp]
theorem symm_comp_self (e : M₁ ≃SL[σ₁₂] M₂) : (e.symm : M₂ → M₁) ∘ (e : M₁ → M₂) = id :=
@@ -3571,10 +2989,7 @@ theorem symm_comp_self (e : M₁ ≃SL[σ₁₂] M₂) : (e.symm : M₂ → M₁
#align continuous_linear_equiv.symm_comp_self ContinuousLinearEquiv.symm_comp_self
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.self_comp_symm ContinuousLinearEquiv.self_comp_symmₓ'. -/
@[simp]
theorem self_comp_symm (e : M₁ ≃SL[σ₁₂] M₂) : (e : M₁ → M₂) ∘ (e.symm : M₂ → M₁) = id :=
@@ -3584,10 +2999,7 @@ theorem self_comp_symm (e : M₁ ≃SL[σ₁₂] M₂) : (e : M₁ → M₂) ∘
#align continuous_linear_equiv.self_comp_symm ContinuousLinearEquiv.self_comp_symm
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_symm ContinuousLinearEquiv.symm_symmₓ'. -/
@[simp]
theorem symm_symm (e : M₁ ≃SL[σ₁₂] M₂) : e.symm.symm = e :=
@@ -3608,60 +3020,42 @@ theorem refl_symm : (ContinuousLinearEquiv.refl R₁ M₁).symm = ContinuousLine
include σ₂₁
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_symm_apply ContinuousLinearEquiv.symm_symm_applyₓ'. -/
theorem symm_symm_apply (e : M₁ ≃SL[σ₁₂] M₂) (x : M₁) : e.symm.symm x = e x :=
rfl
#align continuous_linear_equiv.symm_symm_apply ContinuousLinearEquiv.symm_symm_apply
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_apply_eq ContinuousLinearEquiv.symm_apply_eqₓ'. -/
theorem symm_apply_eq (e : M₁ ≃SL[σ₁₂] M₂) {x y} : e.symm x = y ↔ x = e y :=
e.toLinearEquiv.symm_apply_eq
#align continuous_linear_equiv.symm_apply_eq ContinuousLinearEquiv.symm_apply_eq
/- warning: continuous_linear_equiv.eq_symm_apply -> ContinuousLinearEquiv.eq_symm_apply is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.eq_symm_apply ContinuousLinearEquiv.eq_symm_applyₓ'. -/
theorem eq_symm_apply (e : M₁ ≃SL[σ₁₂] M₂) {x y} : y = e.symm x ↔ e y = x :=
e.toLinearEquiv.eq_symm_apply
#align continuous_linear_equiv.eq_symm_apply ContinuousLinearEquiv.eq_symm_apply
/- warning: continuous_linear_equiv.image_eq_preimage -> ContinuousLinearEquiv.image_eq_preimage is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.image_eq_preimage ContinuousLinearEquiv.image_eq_preimageₓ'. -/
protected theorem image_eq_preimage (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₁) : e '' s = e.symm ⁻¹' s :=
e.toLinearEquiv.toEquiv.image_eq_preimage s
#align continuous_linear_equiv.image_eq_preimage ContinuousLinearEquiv.image_eq_preimage
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.image_symm_eq_preimage ContinuousLinearEquiv.image_symm_eq_preimageₓ'. -/
protected theorem image_symm_eq_preimage (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₂) :
e.symm '' s = e ⁻¹' s := by rw [e.symm.image_eq_preimage, e.symm_symm]
#align continuous_linear_equiv.image_symm_eq_preimage ContinuousLinearEquiv.image_symm_eq_preimage
/- warning: continuous_linear_equiv.symm_preimage_preimage -> ContinuousLinearEquiv.symm_preimage_preimage is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_preimage_preimage ContinuousLinearEquiv.symm_preimage_preimageₓ'. -/
@[simp]
protected theorem symm_preimage_preimage (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₂) :
@@ -3670,10 +3064,7 @@ protected theorem symm_preimage_preimage (e : M₁ ≃SL[σ₁₂] M₂) (s : Se
#align continuous_linear_equiv.symm_preimage_preimage ContinuousLinearEquiv.symm_preimage_preimage
/- warning: continuous_linear_equiv.preimage_symm_preimage -> ContinuousLinearEquiv.preimage_symm_preimage is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.preimage_symm_preimage ContinuousLinearEquiv.preimage_symm_preimageₓ'. -/
@[simp]
protected theorem preimage_symm_preimage (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₁) :
@@ -3682,10 +3073,7 @@ protected theorem preimage_symm_preimage (e : M₁ ≃SL[σ₁₂] M₂) (s : Se
#align continuous_linear_equiv.preimage_symm_preimage ContinuousLinearEquiv.preimage_symm_preimage
/- warning: continuous_linear_equiv.uniform_embedding -> ContinuousLinearEquiv.uniformEmbedding is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.uniform_embedding ContinuousLinearEquiv.uniformEmbeddingₓ'. -/
protected theorem uniformEmbedding {E₁ E₂ : Type _} [UniformSpace E₁] [UniformSpace E₂]
[AddCommGroup E₁] [AddCommGroup E₂] [Module R₁ E₁] [Module R₂ E₂] [UniformAddGroup E₁]
@@ -3695,10 +3083,7 @@ protected theorem uniformEmbedding {E₁ E₂ : Type _} [UniformSpace E₁] [Uni
#align continuous_linear_equiv.uniform_embedding ContinuousLinearEquiv.uniformEmbedding
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(AddCommGroup.toAddCommMonoid.{u3} E₂ _inst_29) _inst_30 _inst_31 σ₁₂ σ₂₁ _inst_4 _inst_5))))) e))
+<too large>
Case conversion may be inaccurate. Consider using '#align linear_equiv.uniform_embedding LinearEquiv.uniformEmbeddingₓ'. -/
protected theorem LinearEquiv.uniformEmbedding {E₁ E₂ : Type _} [UniformSpace E₁] [UniformSpace E₂]
[AddCommGroup E₁] [AddCommGroup E₂] [Module R₁ E₁] [Module R₂ E₂] [UniformAddGroup E₁]
@@ -3714,10 +3099,7 @@ protected theorem LinearEquiv.uniformEmbedding {E₁ E₂ : Type _} [UniformSpac
omit σ₂₁
/- warning: continuous_linear_equiv.equiv_of_inverse -> ContinuousLinearEquiv.equivOfInverse is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.equiv_of_inverse ContinuousLinearEquiv.equivOfInverseₓ'. -/
/-- Create a `continuous_linear_equiv` from two `continuous_linear_map`s that are
inverse of each other. -/
@@ -3735,10 +3117,7 @@ def equivOfInverse (f₁ : M₁ →SL[σ₁₂] M₂) (f₂ : M₂ →SL[σ₂
include σ₂₁
/- warning: continuous_linear_equiv.equiv_of_inverse_apply -> ContinuousLinearEquiv.equivOfInverse_apply is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.equiv_of_inverse_apply ContinuousLinearEquiv.equivOfInverse_applyₓ'. -/
@[simp]
theorem equivOfInverse_apply (f₁ : M₁ →SL[σ₁₂] M₂) (f₂ h₁ h₂ x) :
@@ -3747,10 +3126,7 @@ theorem equivOfInverse_apply (f₁ : M₁ →SL[σ₁₂] M₂) (f₂ h₁ h₂
#align continuous_linear_equiv.equiv_of_inverse_apply ContinuousLinearEquiv.equivOfInverse_apply
/- warning: continuous_linear_equiv.symm_equiv_of_inverse -> ContinuousLinearEquiv.symm_equivOfInverse is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_equiv_of_inverse ContinuousLinearEquiv.symm_equivOfInverseₓ'. -/
@[simp]
theorem symm_equivOfInverse (f₁ : M₁ →SL[σ₁₂] M₂) (f₂ h₁ h₂) :
@@ -3831,10 +3207,7 @@ variable {R : Type _} [Semiring R] {M : Type _} [TopologicalSpace M] [AddCommGro
variable [TopologicalAddGroup M₄]
/- warning: continuous_linear_equiv.skew_prod -> ContinuousLinearEquiv.skewProd is a dubious translation:
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- forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommGroup.{u2} M] {M₂ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₂] [_inst_5 : AddCommGroup.{u3} M₂] {M₃ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₃] [_inst_7 : AddCommGroup.{u4} M₃] {M₄ : Type.{u5}} [_inst_8 : TopologicalSpace.{u5} M₄] [_inst_9 : AddCommGroup.{u5} M₄] [_inst_10 : Module.{u1, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] [_inst_11 : Module.{u1, u3} R M₂ _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5)] [_inst_12 : Module.{u1, u4} R M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_7)] [_inst_13 : Module.{u1, u5} R M₄ _inst_1 (AddCommGroup.toAddCommMonoid.{u5} M₄ _inst_9)] [_inst_14 : TopologicalAddGroup.{u5} M₄ _inst_8 (AddCommGroup.toAddGroup.{u5} M₄ _inst_9)], (ContinuousLinearEquiv.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_10 _inst_11) -> (ContinuousLinearEquiv.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M₃ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_7) M₄ _inst_8 (AddCommGroup.toAddCommMonoid.{u5} M₄ _inst_9) _inst_12 _inst_13) -> (ContinuousLinearMap.{u1, u1, u2, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₄ _inst_8 (AddCommGroup.toAddCommMonoid.{u5} M₄ _inst_9) _inst_10 _inst_13) -> (ContinuousLinearEquiv.{u1, u1, max u4 u2, max u5 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Prod.{u2, u4} M M₃) (instTopologicalSpaceProd.{u2, u4} M M₃ _inst_2 _inst_6) (Prod.instAddCommMonoidSum.{u2, u4} M M₃ (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_7)) (Prod.{u3, u5} M₂ M₄) (instTopologicalSpaceProd.{u3, u5} M₂ M₄ _inst_4 _inst_8) (Prod.instAddCommMonoidSum.{u3, u5} M₂ M₄ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₄ _inst_9)) (Prod.module.{u1, u2, u4} R M M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_7) _inst_10 _inst_12) (Prod.module.{u1, u3, u5} R M₂ M₄ _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₄ _inst_9) _inst_11 _inst_13))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.skew_prod ContinuousLinearEquiv.skewProdₓ'. -/
/-- Equivalence given by a block lower diagonal matrix. `e` and `e'` are diagonal square blocks,
and `f` is a rectangular block below the diagonal. -/
@@ -3852,10 +3225,7 @@ def skewProd (e : M ≃L[R] M₂) (e' : M₃ ≃L[R] M₄) (f : M →L[R] M₄)
#align continuous_linear_equiv.skew_prod ContinuousLinearEquiv.skewProd
/- warning: continuous_linear_equiv.skew_prod_apply -> ContinuousLinearEquiv.skewProd_apply is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.skew_prod_apply ContinuousLinearEquiv.skewProd_applyₓ'. -/
@[simp]
theorem skewProd_apply (e : M ≃L[R] M₂) (e' : M₃ ≃L[R] M₄) (f : M →L[R] M₄) (x) :
@@ -3864,10 +3234,7 @@ theorem skewProd_apply (e : M ≃L[R] M₂) (e' : M₃ ≃L[R] M₄) (f : M →L
#align continuous_linear_equiv.skew_prod_apply ContinuousLinearEquiv.skewProd_apply
/- warning: continuous_linear_equiv.skew_prod_symm_apply -> ContinuousLinearEquiv.skewProd_symm_apply is a dubious translation:
-lean 3 declaration is
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.skew_prod_symm_apply ContinuousLinearEquiv.skewProd_symm_applyₓ'. -/
@[simp]
theorem skewProd_symm_apply (e : M ≃L[R] M₂) (e' : M₃ ≃L[R] M₄) (f : M →L[R] M₄) (x) :
@@ -3887,10 +3254,7 @@ variable {σ₁₂ : R →+* R₂} {σ₂₁ : R₂ →+* R} [RingHomInvPair σ
include σ₂₁
/- warning: continuous_linear_equiv.map_sub -> ContinuousLinearEquiv.map_sub is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_sub ContinuousLinearEquiv.map_subₓ'. -/
@[simp]
theorem map_sub (e : M ≃SL[σ₁₂] M₂) (x y : M) : e (x - y) = e x - e y :=
@@ -3898,10 +3262,7 @@ theorem map_sub (e : M ≃SL[σ₁₂] M₂) (x y : M) : e (x - y) = e x - e y :
#align continuous_linear_equiv.map_sub ContinuousLinearEquiv.map_sub
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_neg ContinuousLinearEquiv.map_negₓ'. -/
@[simp]
theorem map_neg (e : M ≃SL[σ₁₂] M₂) (x : M) : e (-x) = -e x :=
@@ -3966,10 +3327,7 @@ def toUnit (f : M ≃L[R] M) : (M →L[R] M)ˣ where
variable (R M)
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv ContinuousLinearEquiv.unitsEquivₓ'. -/
/-- The units of the algebra of continuous `R`-linear endomorphisms of `M` is multiplicatively
equivalent to the type of continuous linear equivalences between `M` and itself. -/
@@ -3989,10 +3347,7 @@ def unitsEquiv : (M →L[R] M)ˣ ≃* M ≃L[R] M
#align continuous_linear_equiv.units_equiv ContinuousLinearEquiv.unitsEquiv
/- warning: continuous_linear_equiv.units_equiv_apply -> ContinuousLinearEquiv.unitsEquiv_apply is a dubious translation:
-lean 3 declaration is
- forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (M : Type.{u2}) [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_11 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)] (f : Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (x : M), Eq.{succ u2} M (coeFn.{succ u2, succ u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (fun (_x : ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) => M -> M) (ContinuousLinearEquiv.hasCoeToFun.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (coeFn.{succ u2, succ u2} (MulEquiv.{u2, u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MulOneClass.toHasMul.{u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (Units.mulOneClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11)))) (MulOneClass.toHasMul.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Monoid.toMulOneClass.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (DivInvMonoid.toMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Group.toDivInvMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearEquiv.automorphismGroup.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))))) (fun (_x : MulEquiv.{u2, u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MulOneClass.toHasMul.{u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (Units.mulOneClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11)))) (MulOneClass.toHasMul.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Monoid.toMulOneClass.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (DivInvMonoid.toMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Group.toDivInvMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearEquiv.automorphismGroup.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))))) => (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R 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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv_apply ContinuousLinearEquiv.unitsEquiv_applyₓ'. -/
@[simp]
theorem unitsEquiv_apply (f : (M →L[R] M)ˣ) (x : M) : unitsEquiv R M f x = f x :=
@@ -4027,10 +3382,7 @@ def unitsEquivAut : Rˣ ≃ R ≃L[R] R
variable {R}
/- warning: continuous_linear_equiv.units_equiv_aut_apply -> ContinuousLinearEquiv.unitsEquivAut_apply is a dubious translation:
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_inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u) R R _inst_11 _inst_11 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u1, u1, u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{u1, u1, u1, u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.unitsEquivAut.{u1} R _inst_1 _inst_11 _inst_12) u) x) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) x (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv_aut_apply ContinuousLinearEquiv.unitsEquivAut_applyₓ'. -/
@[simp]
theorem unitsEquivAut_apply (u : Rˣ) (x : R) : unitsEquivAut R u x = x * u :=
@@ -4038,10 +3390,7 @@ theorem unitsEquivAut_apply (u : Rˣ) (x : R) : unitsEquivAut R u x = x * u :=
#align continuous_linear_equiv.units_equiv_aut_apply ContinuousLinearEquiv.unitsEquivAut_apply
/- warning: continuous_linear_equiv.units_equiv_aut_apply_symm -> ContinuousLinearEquiv.unitsEquivAut_apply_symm is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))] (u : Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (x : R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R 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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv_aut_apply_symm ContinuousLinearEquiv.unitsEquivAut_apply_symmₓ'. -/
@[simp]
theorem unitsEquivAut_apply_symm (u : Rˣ) (x : R) : (unitsEquivAut R u).symm x = x * ↑u⁻¹ :=
@@ -4049,10 +3398,7 @@ theorem unitsEquivAut_apply_symm (u : Rˣ) (x : R) : (unitsEquivAut R u).symm x
#align continuous_linear_equiv.units_equiv_aut_apply_symm ContinuousLinearEquiv.unitsEquivAut_apply_symm
/- warning: continuous_linear_equiv.units_equiv_aut_symm_apply -> ContinuousLinearEquiv.unitsEquivAut_symm_apply is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv_aut_symm_apply ContinuousLinearEquiv.unitsEquivAut_symm_applyₓ'. -/
@[simp]
theorem unitsEquivAut_symm_apply (e : R ≃L[R] R) : ↑((unitsEquivAut R).symm e) = e 1 :=
@@ -4068,10 +3414,7 @@ open _Root_.ContinuousLinearMap (id fst snd)
open _Root_.LinearMap (mem_ker)
/- warning: continuous_linear_equiv.equiv_of_right_inverse -> ContinuousLinearEquiv.equivOfRightInverse is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.equiv_of_right_inverse ContinuousLinearEquiv.equivOfRightInverseₓ'. -/
/-- A pair of continuous linear maps such that `f₁ ∘ f₂ = id` generates a continuous
linear equivalence `e` between `M` and `M₂ × f₁.ker` such that `(e x).2 = x` for `x ∈ f₁.ker`,
@@ -4083,10 +3426,7 @@ def equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M) (h : Fun
#align continuous_linear_equiv.equiv_of_right_inverse ContinuousLinearEquiv.equivOfRightInverse
/- warning: continuous_linear_equiv.fst_equiv_of_right_inverse -> ContinuousLinearEquiv.fst_equivOfRightInverse is a dubious translation:
-lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁)))) _inst_3 (instTopologicalSpaceProd.{u1, u2} M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁)) _inst_3)) (Prod.instAddCommMonoidSum.{u1, u2} M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R 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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.fst_equiv_of_right_inverse ContinuousLinearEquiv.fst_equivOfRightInverseₓ'. -/
@[simp]
theorem fst_equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
@@ -4095,10 +3435,7 @@ theorem fst_equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
#align continuous_linear_equiv.fst_equiv_of_right_inverse ContinuousLinearEquiv.fst_equivOfRightInverse
/- warning: continuous_linear_equiv.snd_equiv_of_right_inverse -> ContinuousLinearEquiv.snd_equivOfRightInverse is a dubious translation:
-lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁)) _inst_3)) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u3, u2, max u2 u1} (ContinuousLinearEquiv.{u3, u3, u2, max u2 u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (Prod.{u1, u2} M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M 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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.snd_equiv_of_right_inverse ContinuousLinearEquiv.snd_equivOfRightInverseₓ'. -/
@[simp]
theorem snd_equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
@@ -4108,10 +3445,7 @@ theorem snd_equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
#align continuous_linear_equiv.snd_equiv_of_right_inverse ContinuousLinearEquiv.snd_equivOfRightInverse
/- warning: continuous_linear_equiv.equiv_of_right_inverse_symm_apply -> ContinuousLinearEquiv.equivOfRightInverse_symm_apply is a dubious translation:
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R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁)))) (instTopologicalSpaceProd.{u1, u2} M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) 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(AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (Submodule.addCommMonoid.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, 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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.equiv_of_right_inverse_symm_apply ContinuousLinearEquiv.equivOfRightInverse_symm_applyₓ'. -/
@[simp]
theorem equivOfRightInverse_symm_apply (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
@@ -4137,10 +3471,7 @@ def funUnique : (ι → M) ≃L[R] M :=
variable {ι R M}
/- warning: continuous_linear_equiv.coe_fun_unique -> ContinuousLinearEquiv.coe_funUnique is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_fun_unique ContinuousLinearEquiv.coe_funUniqueₓ'. -/
@[simp]
theorem coe_funUnique : ⇑(funUnique ι R M) = Function.eval default :=
@@ -4148,10 +3479,7 @@ theorem coe_funUnique : ⇑(funUnique ι R M) = Function.eval default :=
#align continuous_linear_equiv.coe_fun_unique ContinuousLinearEquiv.coe_funUnique
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_fun_unique_symm ContinuousLinearEquiv.coe_funUnique_symmₓ'. -/
@[simp]
theorem coe_funUnique_symm : ⇑(funUnique ι R M).symm = Function.const ι :=
@@ -4161,10 +3489,7 @@ theorem coe_funUnique_symm : ⇑(funUnique ι R M).symm = Function.const ι :=
variable (R M)
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(Zero.zero.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) ContinuousLinearEquiv.piFinTwo._proof_1))))) (M (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (One.one.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) ContinuousLinearEquiv.piFinTwo._proof_2)))))) (Prod.topologicalSpace.{u2, u2} (M (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) ContinuousLinearEquiv.piFinTwo._proof_1))))) (M (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (One.one.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) ContinuousLinearEquiv.piFinTwo._proof_2))))) (_inst_8 (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) ContinuousLinearEquiv.piFinTwo._proof_1))))) (_inst_8 (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (One.one.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) ContinuousLinearEquiv.piFinTwo._proof_2)))))) (Prod.addCommMonoid.{u2, u2} (M (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) ContinuousLinearEquiv.piFinTwo._proof_1))))) (M (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (One.one.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) ContinuousLinearEquiv.piFinTwo._proof_2))))) (_inst_6 (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) ContinuousLinearEquiv.piFinTwo._proof_1))))) (_inst_6 (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (One.one.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) ContinuousLinearEquiv.piFinTwo._proof_2)))))) (Pi.module.{0, u2, u1} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => M i) R _inst_2 (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => _inst_6 i) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => _inst_7 i)) (Prod.module.{u1, u2, u2} R (M (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) ContinuousLinearEquiv.piFinTwo._proof_1))))) (M (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (One.one.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) ContinuousLinearEquiv.piFinTwo._proof_2))))) _inst_2 (_inst_6 (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) ContinuousLinearEquiv.piFinTwo._proof_1))))) (_inst_6 (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (One.one.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) ContinuousLinearEquiv.piFinTwo._proof_2))))) (_inst_7 (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) ContinuousLinearEquiv.piFinTwo._proof_1))))) (_inst_7 (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (One.one.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) ContinuousLinearEquiv.piFinTwo._proof_2))))))
-but is expected to have type
- forall (R : Type.{u1}) [_inst_2 : Semiring.{u1} R] (M : (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> Type.{u2}) [_inst_6 : forall (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))), AddCommMonoid.{u2} (M i)] [_inst_7 : forall (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))), Module.{u1, u2} R (M i) _inst_2 (_inst_6 i)] [_inst_8 : forall (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))), TopologicalSpace.{u2} (M i)], ContinuousLinearEquiv.{u1, u1, u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (forall (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))), M i) (Pi.topologicalSpace.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M i) (fun (a : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_8 a)) (Pi.addCommMonoid.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M i) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_6 i)) (Prod.{u2, u2} (M (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (M (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (instTopologicalSpaceProd.{u2, u2} (M (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (M (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (_inst_8 (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (_inst_8 (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (Prod.instAddCommMonoidSum.{u2, u2} (M (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (M (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (_inst_6 (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (_inst_6 (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (Pi.module.{0, u2, u1} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M i) R _inst_2 (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_6 i) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_7 i)) (Prod.module.{u1, u2, u2} R (M (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (M (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) _inst_2 (_inst_6 (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (_inst_6 (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (_inst_7 (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (_inst_7 (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.pi_fin_two ContinuousLinearEquiv.piFinTwoₓ'. -/
/-- Continuous linear equivalence between dependent functions `Π i : fin 2, M i` and `M 0 × M 1`. -/
@[simps (config := { fullyApplied := false })]
@@ -4177,7 +3502,7 @@ def piFinTwo (M : Fin 2 → Type _) [∀ i, AddCommMonoid (M i)] [∀ i, Module
lean 3 declaration is
forall (R : Type.{u1}) (M : Type.{u2}) [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], ContinuousLinearEquiv.{u1, u1, u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) ((Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> M) (Pi.topologicalSpace.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => M) (fun (a : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => _inst_5)) (Pi.addCommMonoid.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => M) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => _inst_3)) (Prod.{u2, u2} M M) (Prod.topologicalSpace.{u2, u2} M M _inst_5 _inst_5) (Prod.addCommMonoid.{u2, u2} M M _inst_3 _inst_3) (Pi.Function.module.{0, u1, u2} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) R M _inst_2 _inst_3 _inst_4) (Prod.module.{u1, u2, u2} R M M _inst_2 _inst_3 _inst_3 _inst_4 _inst_4)
but is expected to have type
- forall (R : Type.{u1}) (M : Type.{u2}) [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], ContinuousLinearEquiv.{u1, u1, u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) ((Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> M) (Pi.topologicalSpace.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M) (fun (a : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_5)) (Pi.addCommMonoid.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_3)) (Prod.{u2, u2} M M) (instTopologicalSpaceProd.{u2, u2} M M _inst_5 _inst_5) (Prod.instAddCommMonoidSum.{u2, u2} M M _inst_3 _inst_3) (Pi.module.{0, u2, u1} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61449 : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M) R _inst_2 (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_3) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_4)) (Prod.module.{u1, u2, u2} R M M _inst_2 _inst_3 _inst_3 _inst_4 _inst_4)
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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.fin_two_arrow ContinuousLinearEquiv.finTwoArrowₓ'. -/
/-- Continuous linear equivalence between vectors in `M² = fin 2 → M` and `M × M`. -/
@[simps (config := { fullyApplied := false })]
@@ -4214,10 +3539,7 @@ noncomputable def inverse : (M →L[R] M₂) → M₂ →L[R] M := fun f =>
-/
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.inverse_equiv ContinuousLinearMap.inverse_equivₓ'. -/
/-- By definition, if `f` is invertible then `inverse f = f.symm`. -/
@[simp]
@@ -4230,10 +3552,7 @@ theorem inverse_equiv (e : M ≃L[R] M₂) : inverse (e : M →L[R] M₂) = e.sy
#align continuous_linear_map.inverse_equiv ContinuousLinearMap.inverse_equiv
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.inverse_non_equiv ContinuousLinearMap.inverse_non_equivₓ'. -/
/-- By definition, if `f` is not invertible then `inverse f = 0`. -/
@[simp]
@@ -4252,10 +3571,7 @@ variable [AddCommGroup M] [TopologicalAddGroup M] [Module R M]
variable [AddCommGroup M₂] [Module R M₂]
/- warning: continuous_linear_map.ring_inverse_equiv -> ContinuousLinearMap.ring_inverse_equiv is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ring_inverse_equiv ContinuousLinearMap.ring_inverse_equivₓ'. -/
@[simp]
theorem ring_inverse_equiv (e : M ≃L[R] M) : Ring.inverse ↑e = inverse (e : M →L[R] M) :=
@@ -4267,10 +3583,7 @@ theorem ring_inverse_equiv (e : M ≃L[R] M) : Ring.inverse ↑e = inverse (e :
#align continuous_linear_map.ring_inverse_equiv ContinuousLinearMap.ring_inverse_equiv
/- warning: continuous_linear_map.to_ring_inverse -> ContinuousLinearMap.to_ring_inverse is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.to_ring_inverse ContinuousLinearMap.to_ring_inverseₓ'. -/
/-- The function `continuous_linear_equiv.inverse` can be written in terms of `ring.inverse` for the
ring of self-maps of the domain. -/
@@ -4369,10 +3682,7 @@ theorem closedComplemented_top : ClosedComplemented (⊤ : Submodule R M) :=
end Submodule
/- warning: continuous_linear_map.closed_complemented_ker_of_right_inverse -> ContinuousLinearMap.closedComplemented_ker_of_rightInverse is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.closed_complemented_ker_of_right_inverse ContinuousLinearMap.closedComplemented_ker_of_rightInverseₓ'. -/
theorem ContinuousLinearMap.closedComplemented_ker_of_rightInverse {R : Type _} [Ring R]
{M : Type _} [TopologicalSpace M] [AddCommGroup M] {M₂ : Type _} [TopologicalSpace M₂]
mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b
@@ -179,7 +179,7 @@ variable {ι R M₁ M₂ : Type _} [Semiring R] [AddCommMonoid M₁] [AddCommMon
lean 3 declaration is
forall {R : Type.{u1}} {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : AddCommMonoid.{u3} M₂] [_inst_4 : Module.{u1, u2} R M₁ _inst_1 _inst_2] [_inst_5 : Module.{u1, u3} R M₂ _inst_1 _inst_3] [u : TopologicalSpace.{u1} R] {t : TopologicalSpace.{u3} M₂} [_inst_6 : ContinuousSMul.{u1, u3} R M₂ (SMulZeroClass.toHasSmul.{u1, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M₂ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_3))) (Module.toMulActionWithZero.{u1, u3} R M₂ _inst_1 _inst_3 _inst_5)))) u t] (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5), ContinuousSMul.{u1, u2} R M₁ (SMulZeroClass.toHasSmul.{u1, u2} R M₁ (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M₁ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M₁ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2))) (Module.toMulActionWithZero.{u1, u2} R M₁ _inst_1 _inst_2 _inst_4)))) u (TopologicalSpace.induced.{u2, u3} M₁ M₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M₁ M₂ _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f) t)
but is expected to have type
- forall {R : Type.{u3}} {M₁ : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : AddCommMonoid.{u1} M₂] [_inst_4 : Module.{u3, u2} R M₁ _inst_1 _inst_2] [_inst_5 : Module.{u3, u1} R M₂ _inst_1 _inst_3] [u : TopologicalSpace.{u3} R] {t : TopologicalSpace.{u1} M₂} [_inst_6 : ContinuousSMul.{u3, u1} R M₂ (SMulZeroClass.toSMul.{u3, u1} R M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u1} R M₂ (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u1} R M₂ (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_3)) (Module.toMulActionWithZero.{u3, u1} R M₂ _inst_1 _inst_3 _inst_5)))) u t] (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5), ContinuousSMul.{u3, u2} R M₁ (SMulZeroClass.toSMul.{u3, u2} R M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M₁ (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M₁ (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (Module.toMulActionWithZero.{u3, u2} R M₁ _inst_1 _inst_2 _inst_4)))) u (TopologicalSpace.induced.{u2, u1} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M₁ M₂ _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) t)
+ forall {R : Type.{u3}} {M₁ : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : AddCommMonoid.{u1} M₂] [_inst_4 : Module.{u3, u2} R M₁ _inst_1 _inst_2] [_inst_5 : Module.{u3, u1} R M₂ _inst_1 _inst_3] [u : TopologicalSpace.{u3} R] {t : TopologicalSpace.{u1} M₂} [_inst_6 : ContinuousSMul.{u3, u1} R M₂ (SMulZeroClass.toSMul.{u3, u1} R M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u1} R M₂ (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u1} R M₂ (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_3)) (Module.toMulActionWithZero.{u3, u1} R M₂ _inst_1 _inst_3 _inst_5)))) u t] (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5), ContinuousSMul.{u3, u2} R M₁ (SMulZeroClass.toSMul.{u3, u2} R M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M₁ (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M₁ (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (Module.toMulActionWithZero.{u3, u2} R M₁ _inst_1 _inst_2 _inst_4)))) u (TopologicalSpace.induced.{u2, u1} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M₁ M₂ _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) t)
Case conversion may be inaccurate. Consider using '#align has_continuous_smul_induced continuousSMul_inducedₓ'. -/
theorem continuousSMul_induced : @ContinuousSMul R M₁ _ u (t.induced f) :=
{
@@ -365,7 +365,7 @@ section Pi
lean 3 declaration is
forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Finite.{succ u1} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : TopologicalSpace.{u2} R] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_2 _inst_4] [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : ContinuousAdd.{u3} M _inst_6 (AddZeroClass.toHasAdd.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)))] [_inst_8 : ContinuousSMul.{u2, u3} R M (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_4 _inst_5)))) _inst_3 _inst_6] (f : LinearMap.{u2, u2, max u1 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.Function.module.{u1, u2, u2} ι R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_5), Continuous.{max u1 u2, u3} (ι -> R) M (Pi.topologicalSpace.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (a : ι) => _inst_3)) _inst_6 (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.Function.module.{u1, u2, u2} ι R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.Function.module.{u1, u2, u2} ι R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_5) => (ι -> R) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (ι -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.Function.module.{u1, u2, u2} ι R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) f)
but is expected to have type
- forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Finite.{succ u3} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : TopologicalSpace.{u2} R] [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_2 _inst_4] [_inst_6 : TopologicalSpace.{u1} M] [_inst_7 : ContinuousAdd.{u1} M _inst_6 (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)))] [_inst_8 : ContinuousSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (Module.toMulActionWithZero.{u2, u1} R M _inst_2 _inst_4 _inst_5)))) _inst_3 _inst_6] (f : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5), Continuous.{max u3 u2, u1} (ι -> R) M (Pi.topologicalSpace.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (a : ι) => _inst_3)) _inst_6 (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5) (ι -> R) (fun (_x : ι -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (ι -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) f)
+ forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Finite.{succ u3} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : TopologicalSpace.{u2} R] [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_2 _inst_4] [_inst_6 : TopologicalSpace.{u1} M] [_inst_7 : ContinuousAdd.{u1} M _inst_6 (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)))] [_inst_8 : ContinuousSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (Module.toMulActionWithZero.{u2, u1} R M _inst_2 _inst_4 _inst_5)))) _inst_3 _inst_6] (f : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5), Continuous.{max u3 u2, u1} (ι -> R) M (Pi.topologicalSpace.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (a : ι) => _inst_3)) _inst_6 (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5) (ι -> R) (fun (_x : ι -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (ι -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) f)
Case conversion may be inaccurate. Consider using '#align linear_map.continuous_on_pi LinearMap.continuous_on_piₓ'. -/
theorem LinearMap.continuous_on_pi {ι : Type _} {R : Type _} {M : Type _} [Finite ι] [Semiring R]
[TopologicalSpace R] [AddCommMonoid M] [Module R M] [TopologicalSpace M] [ContinuousAdd M]
@@ -529,7 +529,7 @@ variable [ContinuousAdd M₂] {σ : R →+* S} {l : Filter α}
lean 3 declaration is
forall {M₁ : Type.{u1}} {M₂ : Type.{u2}} {R : Type.{u3}} {S : Type.{u4}} [_inst_1 : TopologicalSpace.{u2} M₂] [_inst_2 : T2Space.{u2} M₂ _inst_1] [_inst_3 : Semiring.{u3} R] [_inst_4 : Semiring.{u4} S] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_6 : AddCommMonoid.{u2} M₂] [_inst_7 : Module.{u3, u1} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u4, u2} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u4, u2} S M₂ _inst_1 (SMulZeroClass.toHasSmul.{u4, u2} S M₂ (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M₂ (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_4)))) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M₂ (Semiring.toMonoidWithZero.{u4} S _inst_4) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (Module.toMulActionWithZero.{u4, u2} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u2} M₂ _inst_1 (AddZeroClass.toHasAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)))] {σ : RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R _inst_3) (Semiring.toNonAssocSemiring.{u4} S _inst_4)} (f : M₁ -> M₂), (Membership.Mem.{max u1 u2, max u1 u2} (M₁ -> M₂) (Set.{max u1 u2} (M₁ -> M₂)) (Set.hasMem.{max u1 u2} (M₁ -> M₂)) f (closure.{max u1 u2} (M₁ -> M₂) (Pi.topologicalSpace.{u1, u2} M₁ (fun (ᾰ : M₁) => M₂) (fun (a : M₁) => _inst_1)) (Set.range.{max u1 u2, max (succ u1) (succ u2)} (M₁ -> M₂) (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (fun (ᾰ : LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u3, u4, u1, u2} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ))))) -> (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)
but is expected to have type
- forall {M₁ : Type.{u1}} {M₂ : Type.{u2}} {R : Type.{u3}} {S : Type.{u4}} [_inst_1 : TopologicalSpace.{u2} M₂] [_inst_2 : T2Space.{u2} M₂ _inst_1] [_inst_3 : Semiring.{u3} R] [_inst_4 : Semiring.{u4} S] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_6 : AddCommMonoid.{u2} M₂] [_inst_7 : Module.{u3, u1} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u4, u2} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u4, u2} S M₂ _inst_1 (SMulZeroClass.toSMul.{u4, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (SMulWithZero.toSMulZeroClass.{u4, u2} S M₂ (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_4)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (MulActionWithZero.toSMulWithZero.{u4, u2} S M₂ (Semiring.toMonoidWithZero.{u4} S _inst_4) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (Module.toMulActionWithZero.{u4, u2} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u2} M₂ _inst_1 (AddZeroClass.toAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)))] {σ : RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R _inst_3) (Semiring.toNonAssocSemiring.{u4} S _inst_4)} (f : M₁ -> M₂), (Membership.mem.{max u1 u2, max u1 u2} (M₁ -> M₂) (Set.{max u1 u2} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) ᾰ)) (Set.instMembershipSet.{max u1 u2} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) ᾰ)) f (closure.{max u1 u2} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) ᾰ) (Pi.topologicalSpace.{u1, u2} M₁ (fun (ᾰ : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) ᾰ) (fun (a : M₁) => _inst_1)) (Set.range.{max u1 u2, max (succ u1) (succ u2)} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) ᾰ) (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) M₁ (fun (ᾰ : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) ᾰ) (LinearMap.instFunLikeLinearMap.{u3, u4, u1, u2} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ))))) -> (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)
+ forall {M₁ : Type.{u1}} {M₂ : Type.{u2}} {R : Type.{u3}} {S : Type.{u4}} [_inst_1 : TopologicalSpace.{u2} M₂] [_inst_2 : T2Space.{u2} M₂ _inst_1] [_inst_3 : Semiring.{u3} R] [_inst_4 : Semiring.{u4} S] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_6 : AddCommMonoid.{u2} M₂] [_inst_7 : Module.{u3, u1} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u4, u2} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u4, u2} S M₂ _inst_1 (SMulZeroClass.toSMul.{u4, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (SMulWithZero.toSMulZeroClass.{u4, u2} S M₂ (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_4)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (MulActionWithZero.toSMulWithZero.{u4, u2} S M₂ (Semiring.toMonoidWithZero.{u4} S _inst_4) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (Module.toMulActionWithZero.{u4, u2} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u2} M₂ _inst_1 (AddZeroClass.toAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)))] {σ : RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R _inst_3) (Semiring.toNonAssocSemiring.{u4} S _inst_4)} (f : M₁ -> M₂), (Membership.mem.{max u1 u2, max u1 u2} (M₁ -> M₂) (Set.{max u1 u2} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₁) => M₂) ᾰ)) (Set.instMembershipSet.{max u1 u2} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₁) => M₂) ᾰ)) f (closure.{max u1 u2} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₁) => M₂) ᾰ) (Pi.topologicalSpace.{u1, u2} M₁ (fun (ᾰ : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₁) => M₂) ᾰ) (fun (a : M₁) => _inst_1)) (Set.range.{max u1 u2, max (succ u1) (succ u2)} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₁) => M₂) ᾰ) (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) M₁ (fun (ᾰ : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₁) => M₂) ᾰ) (LinearMap.instFunLikeLinearMap.{u3, u4, u1, u2} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ))))) -> (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)
Case conversion may be inaccurate. Consider using '#align linear_map_of_mem_closure_range_coe linearMapOfMemClosureRangeCoeₓ'. -/
/-- Constructs a bundled linear map from a function and a proof that this function belongs to the
closure of the set of linear maps. -/
@@ -547,7 +547,7 @@ def linearMapOfMemClosureRangeCoe (f : M₁ → M₂)
lean 3 declaration is
forall {M₁ : Type.{u1}} {M₂ : Type.{u2}} {α : Type.{u3}} {R : Type.{u4}} {S : Type.{u5}} [_inst_1 : TopologicalSpace.{u2} M₂] [_inst_2 : T2Space.{u2} M₂ _inst_1] [_inst_3 : Semiring.{u4} R] [_inst_4 : Semiring.{u5} S] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_6 : AddCommMonoid.{u2} M₂] [_inst_7 : Module.{u4, u1} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u5, u2} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u5, u2} S M₂ _inst_1 (SMulZeroClass.toHasSmul.{u5, u2} S M₂ (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (SMulWithZero.toSmulZeroClass.{u5, u2} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_4)))) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (MulActionWithZero.toSMulWithZero.{u5, u2} S M₂ (Semiring.toMonoidWithZero.{u5} S _inst_4) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (Module.toMulActionWithZero.{u5, u2} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u2} M₂ _inst_1 (AddZeroClass.toHasAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)))] {σ : RingHom.{u4, u5} R S (Semiring.toNonAssocSemiring.{u4} R _inst_3) (Semiring.toNonAssocSemiring.{u5} S _inst_4)} {l : Filter.{u3} α} (f : M₁ -> M₂) (g : α -> (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)) [_inst_11 : Filter.NeBot.{u3} α l], (Filter.Tendsto.{u3, max u1 u2} α (M₁ -> M₂) (fun (a : α) (x : M₁) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (fun (_x : LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u4, u5, u1, u2} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ) (g a) x) l (nhds.{max u1 u2} (M₁ -> M₂) (Pi.topologicalSpace.{u1, u2} M₁ (fun (x : M₁) => M₂) (fun (a : M₁) => _inst_1)) f)) -> (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)
but is expected to have type
- forall {M₁ : Type.{u1}} {M₂ : Type.{u2}} {α : Type.{u3}} {R : Type.{u4}} {S : Type.{u5}} [_inst_1 : TopologicalSpace.{u2} M₂] [_inst_2 : T2Space.{u2} M₂ _inst_1] [_inst_3 : Semiring.{u4} R] [_inst_4 : Semiring.{u5} S] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_6 : AddCommMonoid.{u2} M₂] [_inst_7 : Module.{u4, u1} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u5, u2} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u5, u2} S M₂ _inst_1 (SMulZeroClass.toSMul.{u5, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (SMulWithZero.toSMulZeroClass.{u5, u2} S M₂ (MonoidWithZero.toZero.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_4)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (MulActionWithZero.toSMulWithZero.{u5, u2} S M₂ (Semiring.toMonoidWithZero.{u5} S _inst_4) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (Module.toMulActionWithZero.{u5, u2} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u2} M₂ _inst_1 (AddZeroClass.toAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)))] {σ : RingHom.{u4, u5} R S (Semiring.toNonAssocSemiring.{u4} R _inst_3) (Semiring.toNonAssocSemiring.{u5} S _inst_4)} {l : Filter.{u3} α} (f : M₁ -> M₂) (g : α -> (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)) [_inst_11 : Filter.NeBot.{u3} α l], (Filter.Tendsto.{u3, max u1 u2} α (forall (x : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) x) (fun (a : α) (x : M₁) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u5, u1, u2} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ) (g a) x) l (nhds.{max u1 u2} (forall (x : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) x) (Pi.topologicalSpace.{u1, u2} M₁ (fun (x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) x) (fun (a : M₁) => _inst_1)) f)) -> (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)
+ forall {M₁ : Type.{u1}} {M₂ : Type.{u2}} {α : Type.{u3}} {R : Type.{u4}} {S : Type.{u5}} [_inst_1 : TopologicalSpace.{u2} M₂] [_inst_2 : T2Space.{u2} M₂ _inst_1] [_inst_3 : Semiring.{u4} R] [_inst_4 : Semiring.{u5} S] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_6 : AddCommMonoid.{u2} M₂] [_inst_7 : Module.{u4, u1} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u5, u2} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u5, u2} S M₂ _inst_1 (SMulZeroClass.toSMul.{u5, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (SMulWithZero.toSMulZeroClass.{u5, u2} S M₂ (MonoidWithZero.toZero.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_4)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (MulActionWithZero.toSMulWithZero.{u5, u2} S M₂ (Semiring.toMonoidWithZero.{u5} S _inst_4) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (Module.toMulActionWithZero.{u5, u2} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u2} M₂ _inst_1 (AddZeroClass.toAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)))] {σ : RingHom.{u4, u5} R S (Semiring.toNonAssocSemiring.{u4} R _inst_3) (Semiring.toNonAssocSemiring.{u5} S _inst_4)} {l : Filter.{u3} α} (f : M₁ -> M₂) (g : α -> (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)) [_inst_11 : Filter.NeBot.{u3} α l], (Filter.Tendsto.{u3, max u1 u2} α (forall (x : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₁) => M₂) x) (fun (a : α) (x : M₁) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u5, u1, u2} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ) (g a) x) l (nhds.{max u1 u2} (forall (x : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₁) => M₂) x) (Pi.topologicalSpace.{u1, u2} M₁ (fun (x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₁) => M₂) x) (fun (a : M₁) => _inst_1)) f)) -> (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)
Case conversion may be inaccurate. Consider using '#align linear_map_of_tendsto linearMapOfTendstoₓ'. -/
/-- Construct a bundled linear map from a pointwise limit of linear maps -/
@[simps (config := { fullyApplied := false })]
@@ -563,7 +563,7 @@ variable (M₁ M₂ σ)
lean 3 declaration is
forall (M₁ : Type.{u1}) (M₂ : Type.{u2}) {R : Type.{u3}} {S : Type.{u4}} [_inst_1 : TopologicalSpace.{u2} M₂] [_inst_2 : T2Space.{u2} M₂ _inst_1] [_inst_3 : Semiring.{u3} R] [_inst_4 : Semiring.{u4} S] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_6 : AddCommMonoid.{u2} M₂] [_inst_7 : Module.{u3, u1} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u4, u2} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u4, u2} S M₂ _inst_1 (SMulZeroClass.toHasSmul.{u4, u2} S M₂ (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M₂ (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_4)))) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M₂ (Semiring.toMonoidWithZero.{u4} S _inst_4) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (Module.toMulActionWithZero.{u4, u2} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u2} M₂ _inst_1 (AddZeroClass.toHasAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)))] (σ : RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R _inst_3) (Semiring.toNonAssocSemiring.{u4} S _inst_4)), IsClosed.{max u1 u2} (M₁ -> M₂) (Pi.topologicalSpace.{u1, u2} M₁ (fun (ᾰ : M₁) => M₂) (fun (a : M₁) => _inst_1)) (Set.range.{max u1 u2, max (succ u1) (succ u2)} (M₁ -> M₂) (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (fun (ᾰ : LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u3, u4, u1, u2} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ)))
but is expected to have type
- forall (M₁ : Type.{u4}) (M₂ : Type.{u3}) {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} M₂] [_inst_2 : T2Space.{u3} M₂ _inst_1] [_inst_3 : Semiring.{u2} R] [_inst_4 : Semiring.{u1} S] [_inst_5 : AddCommMonoid.{u4} M₁] [_inst_6 : AddCommMonoid.{u3} M₂] [_inst_7 : Module.{u2, u4} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u1, u3} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u1, u3} S M₂ _inst_1 (SMulZeroClass.toSMul.{u1, u3} S M₂ (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_6)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_4)) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_6)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M₂ (Semiring.toMonoidWithZero.{u1} S _inst_4) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_6)) (Module.toMulActionWithZero.{u1, u3} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u3} M₂ _inst_1 (AddZeroClass.toAdd.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_6)))] (σ : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_3) (Semiring.toNonAssocSemiring.{u1} S _inst_4)), IsClosed.{max u4 u3} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) ᾰ) (Pi.topologicalSpace.{u4, u3} M₁ (fun (ᾰ : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) ᾰ) (fun (a : M₁) => _inst_1)) (Set.range.{max u4 u3, max (succ u4) (succ u3)} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) ᾰ) (LinearMap.{u2, u1, u4, u3} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u2, u1, u4, u3} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) M₁ (fun (ᾰ : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) ᾰ) (LinearMap.instFunLikeLinearMap.{u2, u1, u4, u3} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ)))
+ forall (M₁ : Type.{u4}) (M₂ : Type.{u3}) {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} M₂] [_inst_2 : T2Space.{u3} M₂ _inst_1] [_inst_3 : Semiring.{u2} R] [_inst_4 : Semiring.{u1} S] [_inst_5 : AddCommMonoid.{u4} M₁] [_inst_6 : AddCommMonoid.{u3} M₂] [_inst_7 : Module.{u2, u4} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u1, u3} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u1, u3} S M₂ _inst_1 (SMulZeroClass.toSMul.{u1, u3} S M₂ (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_6)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_4)) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_6)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M₂ (Semiring.toMonoidWithZero.{u1} S _inst_4) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_6)) (Module.toMulActionWithZero.{u1, u3} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u3} M₂ _inst_1 (AddZeroClass.toAdd.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_6)))] (σ : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_3) (Semiring.toNonAssocSemiring.{u1} S _inst_4)), IsClosed.{max u4 u3} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₁) => M₂) ᾰ) (Pi.topologicalSpace.{u4, u3} M₁ (fun (ᾰ : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₁) => M₂) ᾰ) (fun (a : M₁) => _inst_1)) (Set.range.{max u4 u3, max (succ u4) (succ u3)} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₁) => M₂) ᾰ) (LinearMap.{u2, u1, u4, u3} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u2, u1, u4, u3} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) M₁ (fun (ᾰ : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₁) => M₂) ᾰ) (LinearMap.instFunLikeLinearMap.{u2, u1, u4, u3} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ)))
Case conversion may be inaccurate. Consider using '#align linear_map.is_closed_range_coe LinearMap.isClosed_range_coeₓ'. -/
theorem LinearMap.isClosed_range_coe : IsClosed (Set.range (coeFn : (M₁ →ₛₗ[σ] M₂) → M₁ → M₂)) :=
isClosed_of_closure_subset fun f hf => ⟨linearMapOfMemClosureRangeCoe f hf, rfl⟩
@@ -647,7 +647,7 @@ theorem coe_mk (f : M₁ →ₛₗ[σ₁₂] M₂) (h) : (mk f h : M₁ →ₛ
lean 3 declaration is
forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] [_inst_14 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_9] (f : LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (h : autoParamₓ.{0} (Continuous.{u3, u4} M₁ M₂ _inst_4 _inst_8 (LinearMap.toFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16 f)) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 99 (OfNat.mk.{0} Nat 99 (bit1.{0} Nat 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(Char.ofNat (OfNat.ofNat.{0} Nat 99 (OfNat.mk.{0} Nat 99 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 99 (OfNat.mk.{0} Nat 99 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous)))), Eq.{max (succ u3) (succ u4)} ((fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) => M₁ -> M₂) (ContinuousLinearMap.mk.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f h)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) => M₁ -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.mk.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f h)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (fun (_x : LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) f)
but is expected to have type
- forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] (f : LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (h : Continuous.{u2, u1} M₁ M₂ _inst_4 _inst_8 (AddHom.toFun.{u2, u1} M₁ M₂ (AddZeroClass.toAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (AddZeroClass.toAdd.{u1} M₂ (AddMonoid.toAddZeroClass.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9))) (LinearMap.toAddHom.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16 f))), Eq.{max (succ u2) (succ u1)} (forall (a : M₁), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) (ContinuousLinearMap.mk.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f h)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) f)
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] (f : LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (h : Continuous.{u2, u1} M₁ M₂ _inst_4 _inst_8 (AddHom.toFun.{u2, u1} M₁ M₂ (AddZeroClass.toAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (AddZeroClass.toAdd.{u1} M₂ (AddMonoid.toAddZeroClass.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9))) (LinearMap.toAddHom.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16 f))), Eq.{max (succ u2) (succ u1)} (forall (a : M₁), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) (ContinuousLinearMap.mk.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f h)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) f)
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_mk' ContinuousLinearMap.coe_mk'ₓ'. -/
@[simp]
theorem coe_mk' (f : M₁ →ₛₗ[σ₁₂] M₂) (h) : (mk f h : M₁ → M₂) = f :=
@@ -842,7 +842,7 @@ protected theorem map_sum {ι : Type _} (f : M₁ →SL[σ₁₂] M₂) (s : Fin
lean 3 declaration is
forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] [_inst_14 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_9] (f : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u3) (succ u4)} (M₁ -> M₂) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (fun (_x : LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) ((fun (a : Sort.{max (succ u3) (succ u4)}) (b : Sort.{max (succ u3) (succ u4)}) [self : HasLiftT.{max (succ u3) (succ u4), max (succ u3) (succ u4)} a b] => self.0) (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (HasLiftT.mk.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (CoeTCₓ.coe.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (coeBase.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.LinearMap.coe.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16)))) f)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) => M₁ -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) f)
but is expected to have type
- forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] (f : ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) f)
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] (f : ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₁) => M₂) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) f)
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_coe ContinuousLinearMap.coe_coeₓ'. -/
@[simp, norm_cast]
theorem coe_coe (f : M₁ →SL[σ₁₂] M₂) : ⇑(f : M₁ →ₛₗ[σ₁₂] M₂) = f :=
@@ -1733,7 +1733,7 @@ theorem Submodule.coe_subtypeL (p : Submodule R₁ M₁) : (p.subtypeL : p →
lean 3 declaration is
forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] (p : Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14), Eq.{succ u2} ((coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) p) -> M₁) (coeFn.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) p) (Subtype.topologicalSpace.{u2} M₁ (fun (x : M₁) => Membership.Mem.{u2, u2} M₁ 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but is expected to have type
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_inst_5 _inst_14)) x p)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) => M₁) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R₁ R₁ (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) M₁ _inst_1 _inst_1 (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) (Submodule.subtype.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p))
+ forall {R₁ : Type.{u2}} [_inst_1 : Semiring.{u2} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_14 : Module.{u2, u1} R₁ M₁ _inst_1 _inst_5] (p : Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14), Eq.{succ u1} (forall (ᾰ : Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) => M₁) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (instTopologicalSpaceSubtype.{u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (fun (_x : Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) => M₁) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (instTopologicalSpaceSubtype.{u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) M₁ (instTopologicalSpaceSubtype.{u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (instTopologicalSpaceSubtype.{u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (instTopologicalSpaceSubtype.{u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (instTopologicalSpaceSubtype.{u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14))) (Submodule.subtypeL.{u2, u1} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 p)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) M₁ (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (fun (_x : Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) => M₁) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R₁ R₁ (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) M₁ _inst_1 _inst_1 (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) (Submodule.subtype.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p))
Case conversion may be inaccurate. Consider using '#align submodule.coe_subtypeL' Submodule.coe_subtypeL'ₓ'. -/
@[simp]
theorem Submodule.coe_subtypeL' (p : Submodule R₁ M₁) : ⇑p.subtypeL = p.Subtype :=
@@ -2177,7 +2177,7 @@ def iInfKerProjEquiv {I J : Set ι} [DecidablePred fun i => i ∈ I] (hd : Disjo
continuous_invFun :=
Continuous.subtype_mk
(continuous_pi fun i => by dsimp;
- split_ifs <;> [apply continuous_apply, exact continuous_zero])
+ split_ifs <;> [apply continuous_apply;exact continuous_zero])
_
#align continuous_linear_map.infi_ker_proj_equiv ContinuousLinearMap.iInfKerProjEquiv
@@ -2217,7 +2217,7 @@ protected theorem map_sub (f : M →SL[σ₁₂] M₂) (x y : M) : f (x - y) = f
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} (f : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (g : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R 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_inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) g x))
+ forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_13 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))} (f : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (g : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (instHSub.{max u2 u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (LinearMap.instSubLinearMapToAddCommMonoid.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_7 _inst_12 _inst_13 σ₁₂)) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 f) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 g)) x) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (instHSub.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubNegMonoid.toSub.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) _inst_7)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) f x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) g x))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.sub_apply' ContinuousLinearMap.sub_apply'ₓ'. -/
@[simp]
theorem sub_apply' (f g : M →SL[σ₁₂] M₂) (x : M) : ((f : M →ₛₗ[σ₁₂] M₂) - g) x = f x - g x :=
@@ -2745,7 +2745,7 @@ def smulRightₗ (c : M →L[R] S) : M₂ →ₗ[T] M →L[R] M₂
lean 3 declaration is
forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} {M : Type.{u4}} {M₂ : Type.{u5}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : Semiring.{u3} T] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : AddCommMonoid.{u5} M₂] [_inst_6 : Module.{u1, u5} R M₂ _inst_1 _inst_5] [_inst_7 : Module.{u2, u5} S M₂ _inst_2 _inst_5] [_inst_8 : IsScalarTower.{u1, u2, u5} R S M₂ (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u5} S M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u2, u5} S M₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u5} R M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u1, u5} R M₂ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u1, u5} R M₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u1, u5} R M₂ _inst_1 _inst_5 _inst_6))))] [_inst_9 : TopologicalSpace.{u2} S] [_inst_10 : TopologicalSpace.{u5} M₂] [_inst_11 : ContinuousSMul.{u2, u5} S M₂ (SMulZeroClass.toHasSmul.{u2, u5} S M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u2, u5} S M₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) _inst_9 _inst_10] [_inst_12 : TopologicalSpace.{u4} M] [_inst_13 : AddCommMonoid.{u4} M] [_inst_14 : Module.{u1, u4} R M _inst_1 _inst_13] [_inst_15 : ContinuousAdd.{u5} M₂ _inst_10 (AddZeroClass.toHasAdd.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)))] [_inst_16 : Module.{u3, u5} T M₂ _inst_3 _inst_5] [_inst_17 : ContinuousConstSMul.{u3, u5} T M₂ _inst_10 (SMulZeroClass.toHasSmul.{u3, u5} T M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u3, u5} T M₂ (MulZeroClass.toHasZero.{u3} T (MulZeroOneClass.toMulZeroClass.{u3} T (MonoidWithZero.toMulZeroOneClass.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_18 : SMulCommClass.{u1, u3, u5} R T M₂ (SMulZeroClass.toHasSmul.{u1, u5} R M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u1, u5} R M₂ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u1, u5} R M₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u1, u5} R M₂ _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u3, u5} T M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u3, u5} T M₂ (MulZeroClass.toHasZero.{u3} T (MulZeroOneClass.toMulZeroClass.{u3} T (MonoidWithZero.toMulZeroOneClass.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_19 : SMulCommClass.{u2, u3, u5} S T M₂ (SMulZeroClass.toHasSmul.{u2, u5} S M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u2, u5} S M₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toHasSmul.{u3, u5} T M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u3, u5} T M₂ (MulZeroClass.toHasZero.{u3} T (MulZeroOneClass.toMulZeroClass.{u3} T (MonoidWithZero.toMulZeroOneClass.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))] (c : ContinuousLinearMap.{u1, u1, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 S _inst_9 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_14 _inst_4), Eq.{max (succ u5) (succ (max u4 u5))} (M₂ -> (ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6)) (coeFn.{max (succ u5) (succ (max u4 u5)), max (succ u5) (succ (max u4 u5))} (LinearMap.{u3, u3, u5, max u4 u5} T T _inst_3 _inst_3 (RingHom.id.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3)) M₂ (ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_5 (ContinuousLinearMap.addCommMonoid.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u1, u1, u3, u4, u5} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_15)) (fun (_x : LinearMap.{u3, u3, u5, max u4 u5} T T _inst_3 _inst_3 (RingHom.id.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3)) M₂ (ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_5 (ContinuousLinearMap.addCommMonoid.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u1, u1, u3, u4, u5} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_15)) => M₂ -> (ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6)) (LinearMap.hasCoeToFun.{u3, u3, u5, max u4 u5} T T M₂ (ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_3 _inst_3 _inst_5 (ContinuousLinearMap.addCommMonoid.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u1, u1, u3, u4, u5} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_15) (RingHom.id.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3))) (ContinuousLinearMap.smulRightₗ.{u1, u2, u3, u4, u5} R S T M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 _inst_19 c)) (ContinuousLinearMap.smulRight.{u4, u5, u1, u2} M _inst_12 _inst_13 M₂ _inst_10 _inst_5 R S _inst_1 _inst_2 _inst_14 _inst_6 _inst_4 _inst_7 _inst_8 _inst_9 _inst_11 c)
but is expected to have type
- forall {R : Type.{u5}} {S : Type.{u3}} {T : Type.{u1}} {M : Type.{u4}} {M₂ : Type.{u2}} [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u3} S] [_inst_3 : Semiring.{u1} T] [_inst_4 : Module.{u5, u3} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2)))] [_inst_5 : AddCommMonoid.{u2} M₂] [_inst_6 : Module.{u5, u2} R M₂ _inst_1 _inst_5] [_inst_7 : Module.{u3, u2} S M₂ _inst_2 _inst_5] [_inst_8 : IsScalarTower.{u5, u3, u2} R S M₂ (SMulZeroClass.toSMul.{u5, u3} R S (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (SMulWithZero.toSMulZeroClass.{u5, u3} R S (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (MulActionWithZero.toSMulWithZero.{u5, u3} R S (Semiring.toMonoidWithZero.{u5} R _inst_1) (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (Module.toMulActionWithZero.{u5, u3} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2))) _inst_4)))) (SMulZeroClass.toSMul.{u3, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u2} S M₂ (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u2} S M₂ (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u2} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toSMul.{u5, u2} R M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R M₂ (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R M₂ (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u5, u2} R M₂ _inst_1 _inst_5 _inst_6))))] [_inst_9 : TopologicalSpace.{u3} S] [_inst_10 : TopologicalSpace.{u2} M₂] [_inst_11 : ContinuousSMul.{u3, u2} S M₂ (SMulZeroClass.toSMul.{u3, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u2} S M₂ (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u2} S M₂ (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u2} S M₂ _inst_2 _inst_5 _inst_7)))) _inst_9 _inst_10] [_inst_12 : TopologicalSpace.{u4} M] [_inst_13 : AddCommMonoid.{u4} M] [_inst_14 : Module.{u5, u4} R M _inst_1 _inst_13] [_inst_15 : ContinuousAdd.{u2} M₂ _inst_10 (AddZeroClass.toAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)))] [_inst_16 : Module.{u1, u2} T M₂ _inst_3 _inst_5] [_inst_17 : ContinuousConstSMul.{u1, u2} T M₂ _inst_10 (SMulZeroClass.toSMul.{u1, u2} T M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} T M₂ (MonoidWithZero.toZero.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} T M₂ (Semiring.toMonoidWithZero.{u1} T _inst_3) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u1, u2} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_18 : SMulCommClass.{u5, u1, u2} R T M₂ (SMulZeroClass.toSMul.{u5, u2} R M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R M₂ (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R M₂ (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u5, u2} R M₂ _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u2} T M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} T M₂ (MonoidWithZero.toZero.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} T M₂ (Semiring.toMonoidWithZero.{u1} T _inst_3) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u1, u2} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_19 : SMulCommClass.{u3, u1, u2} S T M₂ (SMulZeroClass.toSMul.{u3, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u2} S M₂ (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u2} S M₂ (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u2} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toSMul.{u1, u2} T M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} T M₂ (MonoidWithZero.toZero.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} T M₂ (Semiring.toMonoidWithZero.{u1} T _inst_3) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u1, u2} T M₂ _inst_3 _inst_5 _inst_16))))] (c : ContinuousLinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 S _inst_9 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2))) _inst_14 _inst_4), Eq.{max (succ u4) (succ u2)} (forall (ᾰ : M₂), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₂) => ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) ᾰ) (FunLike.coe.{max (succ u4) (succ u2), succ u2, max (succ u4) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u4} T T _inst_3 _inst_3 (RingHom.id.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3)) M₂ (ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_5 (ContinuousLinearMap.addCommMonoid.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u5, u5, u1, u4, u2} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_15)) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₂) => ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u4 u2} T T M₂ (ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_3 _inst_3 _inst_5 (ContinuousLinearMap.addCommMonoid.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u5, u5, u1, u4, u2} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_15) (RingHom.id.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3))) (ContinuousLinearMap.smulRightₗ.{u5, u3, u1, u4, u2} R S T M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 _inst_19 c)) (ContinuousLinearMap.smulRight.{u4, u2, u5, u3} M _inst_12 _inst_13 M₂ _inst_10 _inst_5 R S _inst_1 _inst_2 _inst_14 _inst_6 _inst_4 _inst_7 _inst_8 _inst_9 _inst_11 c)
+ forall {R : Type.{u5}} {S : Type.{u3}} {T : Type.{u1}} {M : Type.{u4}} {M₂ : Type.{u2}} [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u3} S] [_inst_3 : Semiring.{u1} T] [_inst_4 : Module.{u5, u3} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2)))] [_inst_5 : AddCommMonoid.{u2} M₂] [_inst_6 : Module.{u5, u2} R M₂ _inst_1 _inst_5] [_inst_7 : Module.{u3, u2} S M₂ _inst_2 _inst_5] [_inst_8 : IsScalarTower.{u5, u3, u2} R S M₂ (SMulZeroClass.toSMul.{u5, u3} R S (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (SMulWithZero.toSMulZeroClass.{u5, u3} R S (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (MulActionWithZero.toSMulWithZero.{u5, u3} R S (Semiring.toMonoidWithZero.{u5} R _inst_1) (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (Module.toMulActionWithZero.{u5, u3} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2))) _inst_4)))) (SMulZeroClass.toSMul.{u3, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u2} S M₂ (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u2} S M₂ (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u2} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toSMul.{u5, u2} R M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R M₂ (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R M₂ (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u5, u2} R M₂ _inst_1 _inst_5 _inst_6))))] [_inst_9 : TopologicalSpace.{u3} S] [_inst_10 : TopologicalSpace.{u2} M₂] [_inst_11 : ContinuousSMul.{u3, u2} S M₂ (SMulZeroClass.toSMul.{u3, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u2} S M₂ (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u2} S M₂ (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u2} S M₂ _inst_2 _inst_5 _inst_7)))) _inst_9 _inst_10] [_inst_12 : TopologicalSpace.{u4} M] [_inst_13 : AddCommMonoid.{u4} M] [_inst_14 : Module.{u5, u4} R M _inst_1 _inst_13] [_inst_15 : ContinuousAdd.{u2} M₂ _inst_10 (AddZeroClass.toAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)))] [_inst_16 : Module.{u1, u2} T M₂ _inst_3 _inst_5] [_inst_17 : ContinuousConstSMul.{u1, u2} T M₂ _inst_10 (SMulZeroClass.toSMul.{u1, u2} T M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} T M₂ (MonoidWithZero.toZero.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} T M₂ (Semiring.toMonoidWithZero.{u1} T _inst_3) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u1, u2} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_18 : SMulCommClass.{u5, u1, u2} R T M₂ (SMulZeroClass.toSMul.{u5, u2} R M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R M₂ (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R M₂ (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u5, u2} R M₂ _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u2} T M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} T M₂ (MonoidWithZero.toZero.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} T M₂ (Semiring.toMonoidWithZero.{u1} T _inst_3) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u1, u2} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_19 : SMulCommClass.{u3, u1, u2} S T M₂ (SMulZeroClass.toSMul.{u3, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u2} S M₂ (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u2} S M₂ (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u2} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toSMul.{u1, u2} T M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} T M₂ (MonoidWithZero.toZero.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} T M₂ (Semiring.toMonoidWithZero.{u1} T _inst_3) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u1, u2} T M₂ _inst_3 _inst_5 _inst_16))))] (c : ContinuousLinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 S _inst_9 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2))) _inst_14 _inst_4), Eq.{max (succ u4) (succ u2)} (forall (ᾰ : M₂), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₂) => ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) ᾰ) (FunLike.coe.{max (succ u4) (succ u2), succ u2, max (succ u4) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u4} T T _inst_3 _inst_3 (RingHom.id.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3)) M₂ (ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_5 (ContinuousLinearMap.addCommMonoid.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u5, u5, u1, u4, u2} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_15)) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₂) => ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u4 u2} T T M₂ (ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_3 _inst_3 _inst_5 (ContinuousLinearMap.addCommMonoid.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u5, u5, u1, u4, u2} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_15) (RingHom.id.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3))) (ContinuousLinearMap.smulRightₗ.{u5, u3, u1, u4, u2} R S T M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 _inst_19 c)) (ContinuousLinearMap.smulRight.{u4, u2, u5, u3} M _inst_12 _inst_13 M₂ _inst_10 _inst_5 R S _inst_1 _inst_2 _inst_14 _inst_6 _inst_4 _inst_7 _inst_8 _inst_9 _inst_11 c)
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_smul_rightₗ ContinuousLinearMap.coe_smulRightₗₓ'. -/
@[simp]
theorem coe_smulRightₗ (c : M →L[R] S) : ⇑(smulRightₗ c : M₂ →ₗ[T] M →L[R] M₂) = c.smul_right :=
@@ -2881,7 +2881,7 @@ variable {A M M₂ R S}
lean 3 declaration is
forall {A : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u4}} [_inst_8 : Ring.{u4} R] [_inst_9 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_10 : Module.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u2, u3, u4, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toHasSmul.{u4, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u4, u2} R M (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u4, u2} R M (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5] {S : Type.{u5}} [_inst_12 : Ring.{u5} S] [_inst_13 : Module.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_14 : ContinuousConstSMul.{u5, u3} S M₂ _inst_7 (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_15 : SMulCommClass.{u1, u5, u3} A S M₂ (SMulZeroClass.toHasSmul.{u1, u3} A M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u1, u3} A M₂ (MulZeroClass.toHasZero.{u1} A (MulZeroOneClass.toMulZeroClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A _inst_1))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u1, u3} A M₂ (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A _inst_1)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_16 : SMulCommClass.{u4, u5, u3} R S M₂ (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_17 : TopologicalAddGroup.{u3} M₂ _inst_7 (AddCommGroup.toAddGroup.{u3} M₂ _inst_3)], Eq.{succ (max u2 u3)} ((ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) -> (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10)) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (LinearMap.{u5, u5, max u2 u3, max u2 u3} S S (Ring.toSemiring.{u5} S _inst_12) (Ring.toSemiring.{u5} S 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(LinearMap.hasCoeToFun.{u5, u5, max u2 u3, max u2 u3} S S (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (Ring.toSemiring.{u5} S _inst_12) (Ring.toSemiring.{u5} S _inst_12) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5 (ContinuousLinearMap.restrictScalarsₗ._proof_1.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.addCommMonoid.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10 (ContinuousLinearMap.restrictScalarsₗ._proof_2.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.module.{u1, u1, u5, u2, u3} A A S (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u5} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5 _inst_13 _inst_15 _inst_14 (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) (ContinuousLinearMap.restrictScalarsₗ._proof_3.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.module.{u4, u4, u5, u2, u3} R R S (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u5} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10 _inst_13 _inst_16 _inst_14 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) (ContinuousLinearMap.restrictScalarsₗ._proof_4.{u3} M₂ _inst_3 _inst_7 _inst_17)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S (Ring.toSemiring.{u5} S _inst_12)))) (ContinuousLinearMap.restrictScalarsₗ.{u1, u2, u3, u4, u5} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 S _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17)) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11)
but is expected to have type
- forall {A : Type.{u3}} {M : Type.{u5}} {M₂ : Type.{u4}} [_inst_1 : Ring.{u3} A] [_inst_2 : AddCommGroup.{u5} M] [_inst_3 : AddCommGroup.{u4} M₂] [_inst_4 : Module.{u3, u5} A M (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2)] [_inst_5 : Module.{u3, u4} A M₂ (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u5} M] [_inst_7 : TopologicalSpace.{u4} M₂] {R : Type.{u2}} [_inst_8 : Ring.{u2} R] [_inst_9 : Module.{u2, u5} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2)] [_inst_10 : Module.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u5, u4, u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) R A (Ring.toSemiring.{u3} A _inst_1) (SMulZeroClass.toSMul.{u2, u5} R M (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u5} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u5} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (Module.toMulActionWithZero.{u2, u5} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u2, u4} R M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10)))) _inst_5] {S : Type.{u1}} [_inst_12 : Ring.{u1} S] [_inst_13 : Module.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_14 : ContinuousConstSMul.{u1, u4} S M₂ _inst_7 (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_15 : SMulCommClass.{u3, u1, u4} A S M₂ (SMulZeroClass.toSMul.{u3, u4} A M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u3, u4} A M₂ (MonoidWithZero.toZero.{u3} A (Semiring.toMonoidWithZero.{u3} A (Ring.toSemiring.{u3} A _inst_1))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A M₂ (Semiring.toMonoidWithZero.{u3} A (Ring.toSemiring.{u3} A _inst_1)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u3, u4} A M₂ (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_16 : SMulCommClass.{u2, u1, u4} R S M₂ (SMulZeroClass.toSMul.{u2, u4} R M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10)))) (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_17 : TopologicalAddGroup.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3)], Eq.{max (succ u5) (succ u4)} (forall (ᾰ : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) => ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10) ᾰ) (FunLike.coe.{max (succ u5) (succ u4), max (succ u5) (succ u4), max (succ u5) (succ u4)} (LinearMap.{u1, u1, max u4 u5, max u4 u5} S S (Ring.toSemiring.{u1} S _inst_12) (Ring.toSemiring.{u1} S _inst_12) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.addCommMonoid.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5 (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.addCommMonoid.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10 (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.module.{u3, u3, u1, u5, u4} A A S (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u1} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_4 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_5 _inst_13 _inst_15 _inst_14 (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.module.{u2, u2, u1, u5, u4} R R S (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_9 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10 _inst_13 _inst_16 _inst_14 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17))) (ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) (fun (_x : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) => ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u5 u4, max u5 u4} S S (ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10) (Ring.toSemiring.{u1} S _inst_12) (Ring.toSemiring.{u1} S _inst_12) (ContinuousLinearMap.addCommMonoid.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5 (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.addCommMonoid.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10 (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.module.{u3, u3, u1, u5, u4} A A S (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u1} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_4 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_5 _inst_13 _inst_15 _inst_14 (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.module.{u2, u2, u1, u5, u4} R R S (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_9 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10 _inst_13 _inst_16 _inst_14 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_12)))) (ContinuousLinearMap.restrictScalarsₗ.{u3, u5, u4, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 S _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17)) (ContinuousLinearMap.restrictScalars.{u3, u5, u4, u2} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11)
+ forall {A : Type.{u3}} {M : Type.{u5}} {M₂ : Type.{u4}} [_inst_1 : Ring.{u3} A] [_inst_2 : AddCommGroup.{u5} M] [_inst_3 : AddCommGroup.{u4} M₂] [_inst_4 : Module.{u3, u5} A M (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2)] [_inst_5 : Module.{u3, u4} A M₂ (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u5} M] [_inst_7 : TopologicalSpace.{u4} M₂] {R : Type.{u2}} [_inst_8 : Ring.{u2} R] [_inst_9 : Module.{u2, u5} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2)] [_inst_10 : Module.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u5, u4, u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) R A (Ring.toSemiring.{u3} A _inst_1) (SMulZeroClass.toSMul.{u2, u5} R M (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u5} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u5} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (Module.toMulActionWithZero.{u2, u5} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u2, u4} R M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10)))) _inst_5] {S : Type.{u1}} [_inst_12 : Ring.{u1} S] [_inst_13 : Module.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_14 : ContinuousConstSMul.{u1, u4} S M₂ _inst_7 (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_15 : SMulCommClass.{u3, u1, u4} A S M₂ (SMulZeroClass.toSMul.{u3, u4} A M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u3, u4} A M₂ (MonoidWithZero.toZero.{u3} A (Semiring.toMonoidWithZero.{u3} A (Ring.toSemiring.{u3} A _inst_1))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A M₂ (Semiring.toMonoidWithZero.{u3} A (Ring.toSemiring.{u3} A _inst_1)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u3, u4} A M₂ (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_16 : SMulCommClass.{u2, u1, u4} R S M₂ (SMulZeroClass.toSMul.{u2, u4} R M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10)))) (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_17 : TopologicalAddGroup.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3)], Eq.{max (succ u5) (succ u4)} (forall (ᾰ : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) => ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10) ᾰ) (FunLike.coe.{max (succ u5) (succ u4), max (succ u5) (succ u4), max (succ u5) (succ u4)} (LinearMap.{u1, u1, max u4 u5, max u4 u5} S S (Ring.toSemiring.{u1} S _inst_12) (Ring.toSemiring.{u1} S _inst_12) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) 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(Ring.toSemiring.{u2} R _inst_8))) (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17))) (ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) (fun (_x : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) => ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u5 u4, max u5 u4} S S (ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10) (Ring.toSemiring.{u1} S _inst_12) (Ring.toSemiring.{u1} S _inst_12) (ContinuousLinearMap.addCommMonoid.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5 (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.addCommMonoid.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10 (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.module.{u3, u3, u1, u5, u4} A A S (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u1} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_4 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_5 _inst_13 _inst_15 _inst_14 (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.module.{u2, u2, u1, u5, u4} R R S (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_9 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10 _inst_13 _inst_16 _inst_14 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_12)))) (ContinuousLinearMap.restrictScalarsₗ.{u3, u5, u4, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 S _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17)) (ContinuousLinearMap.restrictScalars.{u3, u5, u4, u2} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11)
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_restrict_scalarsₗ ContinuousLinearMap.coe_restrictScalarsₗₓ'. -/
@[simp]
theorem coe_restrictScalarsₗ : ⇑(restrictScalarsₗ A M M₂ R S) = restrictScalars R :=
@@ -4392,7 +4392,7 @@ variable {R M : Type _} [Ring R] [AddCommGroup M] [Module R M] [TopologicalSpace
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : TopologicalSpace.{u2} M] (S : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : TopologicalAddGroup.{u2} M _inst_4 (AddCommGroup.toAddGroup.{u2} M _inst_2)], IsOpenMap.{u2, u2} M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) _inst_4 (Quotient.topologicalSpace.{u2} M (Submodule.quotientRel.{u1, u2} R M _inst_1 _inst_2 _inst_3 S) _inst_4) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) => M -> (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 S))
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : TopologicalSpace.{u2} M] (S : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : TopologicalAddGroup.{u2} M _inst_4 (AddCommGroup.toAddGroup.{u2} M _inst_2)], IsOpenMap.{u2, u2} M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) _inst_4 (QuotientModule.Quotient.topologicalSpace.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 S) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 S))
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : TopologicalSpace.{u2} M] (S : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : TopologicalAddGroup.{u2} M _inst_4 (AddCommGroup.toAddGroup.{u2} M _inst_2)], IsOpenMap.{u2, u2} M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) _inst_4 (QuotientModule.Quotient.topologicalSpace.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 S) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 S))
Case conversion may be inaccurate. Consider using '#align submodule.is_open_map_mkq Submodule.isOpenMap_mkQₓ'. -/
theorem isOpenMap_mkQ [TopologicalAddGroup M] : IsOpenMap S.mkQ :=
QuotientAddGroup.isOpenMap_coe S.toAddSubgroup
mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4
@@ -796,7 +796,7 @@ protected theorem map_add (f : M₁ →SL[σ₁₂] M₂) (x y : M₁) : f (x +
lean 3 declaration is
forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] [_inst_14 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_9] (f : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (c : R₁) (x : M₁), Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) => M₁ -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) f (SMul.smul.{u1, u3} R₁ M₁ (SMulZeroClass.toHasSmul.{u1, u3} R₁ M₁ (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5))) (SMulWithZero.toSmulZeroClass.{u1, u3} R₁ M₁ (MulZeroClass.toHasZero.{u1} R₁ (MulZeroOneClass.toMulZeroClass.{u1} R₁ (MonoidWithZero.toMulZeroOneClass.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)))) (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5))) (MulActionWithZero.toSMulWithZero.{u1, u3} R₁ M₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5))) (Module.toMulActionWithZero.{u1, u3} R₁ M₁ _inst_1 _inst_5 _inst_14)))) c x)) (SMul.smul.{u2, u4} R₂ M₂ (SMulZeroClass.toHasSmul.{u2, u4} R₂ M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (SMulWithZero.toSmulZeroClass.{u2, u4} R₂ M₂ (MulZeroClass.toHasZero.{u2} R₂ (MulZeroOneClass.toMulZeroClass.{u2} R₂ (MonoidWithZero.toMulZeroOneClass.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)))) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (MulActionWithZero.toSMulWithZero.{u2, u4} R₂ M₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (Module.toMulActionWithZero.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)) (fun (_x : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)) => R₁ -> R₂) (RingHom.hasCoeToFun.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)) σ₁₂ c) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) => M₁ -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) f x))
but is expected to have type
- forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] (f : ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (c : R₁) (x : M₁), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) (HSMul.hSMul.{u4, u2, u2} R₁ M₁ M₁ (instHSMul.{u4, u2} R₁ M₁ (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14))))) c x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) f (HSMul.hSMul.{u4, u2, u2} R₁ M₁ M₁ (instHSMul.{u4, u2} R₁ M₁ (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14))))) c x)) (HSMul.hSMul.{u3, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (instHSMul.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (SMulZeroClass.toSMul.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_9)) (SMulWithZero.toSMulZeroClass.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) _inst_2)) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_9)) (MulActionWithZero.toSMulWithZero.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) _inst_2) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_9)) (Module.toMulActionWithZero.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_2 _inst_9 _inst_16))))) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) R₁ (fun (_x : R₁) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) R₁ R₂ (NonUnitalNonAssocSemiring.toMul.{u4} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u3} R₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) R₁ R₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (RingHom.instRingHomClassRingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2))))) σ₁₂ c) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) f x))
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] (f : ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (c : R₁) (x : M₁), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) (HSMul.hSMul.{u4, u2, u2} R₁ M₁ M₁ (instHSMul.{u4, u2} R₁ M₁ (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14))))) c x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) f (HSMul.hSMul.{u4, u2, u2} R₁ M₁ M₁ (instHSMul.{u4, u2} R₁ M₁ (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14))))) c x)) (HSMul.hSMul.{u3, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (instHSMul.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (SMulZeroClass.toSMul.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_9)) (SMulWithZero.toSMulZeroClass.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => R₂) c) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => R₂) c) _inst_2)) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_9)) (MulActionWithZero.toSMulWithZero.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => R₂) c) _inst_2) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_9)) (Module.toMulActionWithZero.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_2 _inst_9 _inst_16))))) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) R₁ (fun (_x : R₁) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => R₂) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) R₁ R₂ (NonUnitalNonAssocSemiring.toMul.{u4} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u3} R₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) R₁ R₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (RingHom.instRingHomClassRingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2))))) σ₁₂ c) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) f x))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_smulₛₗ ContinuousLinearMap.map_smulₛₗₓ'. -/
@[simp]
protected theorem map_smulₛₗ (f : M₁ →SL[σ₁₂] M₂) (c : R₁) (x : M₁) : f (c • x) = σ₁₂ c • f x :=
@@ -2577,7 +2577,7 @@ include σ₁₃
lean 3 declaration is
forall {R : Type.{u1}} {R₂ : Type.{u2}} {R₃ : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : Semiring.{u3} R₃] {M : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M] [_inst_7 : AddCommMonoid.{u4} M] [_inst_8 : Module.{u1, u4} R M _inst_1 _inst_7] {M₂ : Type.{u5}} [_inst_9 : TopologicalSpace.{u5} M₂] [_inst_10 : AddCommMonoid.{u5} M₂] [_inst_11 : Module.{u2, u5} R₂ M₂ _inst_2 _inst_10] {M₃ : Type.{u6}} [_inst_12 : TopologicalSpace.{u6} M₃] [_inst_13 : AddCommMonoid.{u6} M₃] [_inst_14 : Module.{u3, u6} R₃ M₃ _inst_3 _inst_13] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₃ : RingHom.{u2, u3} R₂ R₃ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {σ₁₃ : RingHom.{u1, u3} R R₃ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} [_inst_27 : RingHomCompTriple.{u1, u2, u3} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] [_inst_34 : SMulCommClass.{u2, u2, u5} R₂ R₂ M₂ (SMulZeroClass.toHasSmul.{u2, u5} R₂ M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (SMulWithZero.toSmulZeroClass.{u2, u5} R₂ M₂ (MulZeroClass.toHasZero.{u2} R₂ (MulZeroOneClass.toMulZeroClass.{u2} R₂ (MonoidWithZero.toMulZeroOneClass.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (MulActionWithZero.toSMulWithZero.{u2, u5} R₂ M₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (Module.toMulActionWithZero.{u2, u5} R₂ M₂ _inst_2 _inst_10 _inst_11)))) (SMulZeroClass.toHasSmul.{u2, u5} R₂ M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (SMulWithZero.toSmulZeroClass.{u2, u5} R₂ M₂ (MulZeroClass.toHasZero.{u2} R₂ (MulZeroOneClass.toMulZeroClass.{u2} R₂ (MonoidWithZero.toMulZeroOneClass.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (MulActionWithZero.toSMulWithZero.{u2, u5} R₂ M₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (Module.toMulActionWithZero.{u2, u5} R₂ M₂ _inst_2 _inst_10 _inst_11))))] [_inst_35 : SMulCommClass.{u3, u3, u6} R₃ R₃ M₃ (SMulZeroClass.toHasSmul.{u3, u6} R₃ M₃ (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (SMulWithZero.toSmulZeroClass.{u3, u6} R₃ M₃ (MulZeroClass.toHasZero.{u3} R₃ (MulZeroOneClass.toMulZeroClass.{u3} R₃ (MonoidWithZero.toMulZeroOneClass.{u3} R₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3)))) (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (MulActionWithZero.toSMulWithZero.{u3, u6} R₃ M₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3) (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (Module.toMulActionWithZero.{u3, u6} R₃ M₃ _inst_3 _inst_13 _inst_14)))) (SMulZeroClass.toHasSmul.{u3, u6} R₃ M₃ (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (SMulWithZero.toSmulZeroClass.{u3, u6} R₃ M₃ (MulZeroClass.toHasZero.{u3} R₃ (MulZeroOneClass.toMulZeroClass.{u3} R₃ (MonoidWithZero.toMulZeroOneClass.{u3} R₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3)))) (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (MulActionWithZero.toSMulWithZero.{u3, u6} R₃ M₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3) (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (Module.toMulActionWithZero.{u3, u6} R₃ M₃ _inst_3 _inst_13 _inst_14))))] [_inst_36 : ContinuousConstSMul.{u2, u5} R₂ M₂ _inst_9 (SMulZeroClass.toHasSmul.{u2, u5} R₂ M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (SMulWithZero.toSmulZeroClass.{u2, u5} R₂ M₂ (MulZeroClass.toHasZero.{u2} R₂ (MulZeroOneClass.toMulZeroClass.{u2} R₂ (MonoidWithZero.toMulZeroOneClass.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (MulActionWithZero.toSMulWithZero.{u2, u5} R₂ M₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (Module.toMulActionWithZero.{u2, u5} R₂ M₂ _inst_2 _inst_10 _inst_11))))] [_inst_37 : ContinuousConstSMul.{u3, u6} R₃ M₃ _inst_12 (SMulZeroClass.toHasSmul.{u3, u6} R₃ M₃ (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (SMulWithZero.toSmulZeroClass.{u3, u6} R₃ M₃ (MulZeroClass.toHasZero.{u3} R₃ (MulZeroOneClass.toMulZeroClass.{u3} R₃ (MonoidWithZero.toMulZeroOneClass.{u3} R₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3)))) (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (MulActionWithZero.toSMulWithZero.{u3, u6} R₃ M₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3) (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (Module.toMulActionWithZero.{u3, u6} R₃ M₃ _inst_3 _inst_13 _inst_14))))] (h : ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14) (c : R₂) (f : ContinuousLinearMap.{u1, u2, u4, u5} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 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_inst_2 _inst_10 _inst_11) _inst_34 _inst_36)) c f)) (SMul.smul.{u3, max u4 u6} R₃ (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (MulAction.toHasSmul.{u3, max u4 u6} R₃ (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (MonoidWithZero.toMonoid.{u3} R₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3)) (ContinuousLinearMap.mulAction.{u1, u3, u4, u6, u3} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14 R₃ (MonoidWithZero.toMonoid.{u3} R₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3)) (Module.toDistribMulAction.{u3, u6} R₃ M₃ _inst_3 _inst_13 _inst_14) _inst_35 _inst_37)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} R₂ R₃ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)) (fun (_x : RingHom.{u2, u3} R₂ R₃ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)) => R₂ -> R₃) (RingHom.hasCoeToFun.{u2, u3} R₂ R₃ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)) σ₂₃ c) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_8 _inst_11 _inst_14 _inst_27 h f))
but is expected to have type
- forall {R : Type.{u2}} {R₂ : Type.{u6}} {R₃ : Type.{u4}} [_inst_1 : Semiring.{u2} R] [_inst_2 : Semiring.{u6} R₂] [_inst_3 : Semiring.{u4} R₃] {M : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M] [_inst_7 : AddCommMonoid.{u1} M] [_inst_8 : Module.{u2, u1} R M _inst_1 _inst_7] {M₂ : Type.{u5}} [_inst_9 : TopologicalSpace.{u5} M₂] [_inst_10 : AddCommMonoid.{u5} M₂] [_inst_11 : Module.{u6, u5} R₂ M₂ _inst_2 _inst_10] {M₃ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₃] [_inst_13 : AddCommMonoid.{u3} M₃] [_inst_14 : Module.{u4, u3} R₃ M₃ _inst_3 _inst_13] {σ₁₂ : RingHom.{u2, u6} R R₂ (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2)} {σ₂₃ : RingHom.{u6, u4} R₂ R₃ (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3)} {σ₁₃ : RingHom.{u2, u4} R R₃ (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3)} [_inst_27 : RingHomCompTriple.{u2, u6, u4} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] [_inst_34 : SMulCommClass.{u6, u6, u5} R₂ R₂ M₂ (SMulZeroClass.toSMul.{u6, u5} R₂ M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (SMulWithZero.toSMulZeroClass.{u6, u5} R₂ M₂ (MonoidWithZero.toZero.{u6} R₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (MulActionWithZero.toSMulWithZero.{u6, u5} R₂ M₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (Module.toMulActionWithZero.{u6, u5} R₂ M₂ _inst_2 _inst_10 _inst_11)))) (SMulZeroClass.toSMul.{u6, u5} R₂ M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (SMulWithZero.toSMulZeroClass.{u6, u5} R₂ M₂ (MonoidWithZero.toZero.{u6} R₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (MulActionWithZero.toSMulWithZero.{u6, u5} R₂ M₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (Module.toMulActionWithZero.{u6, u5} R₂ M₂ _inst_2 _inst_10 _inst_11))))] [_inst_35 : SMulCommClass.{u4, u4, u3} R₃ R₃ M₃ (SMulZeroClass.toSMul.{u4, u3} R₃ M₃ (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (SMulWithZero.toSMulZeroClass.{u4, u3} R₃ M₃ (MonoidWithZero.toZero.{u4} R₃ (Semiring.toMonoidWithZero.{u4} R₃ _inst_3)) (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (MulActionWithZero.toSMulWithZero.{u4, u3} R₃ M₃ (Semiring.toMonoidWithZero.{u4} R₃ _inst_3) (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (Module.toMulActionWithZero.{u4, u3} R₃ M₃ _inst_3 _inst_13 _inst_14)))) (SMulZeroClass.toSMul.{u4, u3} R₃ M₃ (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (SMulWithZero.toSMulZeroClass.{u4, u3} R₃ M₃ (MonoidWithZero.toZero.{u4} R₃ (Semiring.toMonoidWithZero.{u4} R₃ _inst_3)) (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (MulActionWithZero.toSMulWithZero.{u4, u3} R₃ M₃ (Semiring.toMonoidWithZero.{u4} R₃ _inst_3) (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (Module.toMulActionWithZero.{u4, u3} R₃ M₃ _inst_3 _inst_13 _inst_14))))] [_inst_36 : ContinuousConstSMul.{u6, u5} R₂ M₂ _inst_9 (SMulZeroClass.toSMul.{u6, u5} R₂ M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (SMulWithZero.toSMulZeroClass.{u6, u5} R₂ M₂ (MonoidWithZero.toZero.{u6} R₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (MulActionWithZero.toSMulWithZero.{u6, u5} R₂ M₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (Module.toMulActionWithZero.{u6, u5} R₂ M₂ _inst_2 _inst_10 _inst_11))))] [_inst_37 : ContinuousConstSMul.{u4, u3} R₃ M₃ _inst_12 (SMulZeroClass.toSMul.{u4, u3} R₃ M₃ (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (SMulWithZero.toSMulZeroClass.{u4, u3} R₃ M₃ (MonoidWithZero.toZero.{u4} R₃ (Semiring.toMonoidWithZero.{u4} R₃ _inst_3)) (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (MulActionWithZero.toSMulWithZero.{u4, u3} R₃ M₃ (Semiring.toMonoidWithZero.{u4} R₃ _inst_3) (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (Module.toMulActionWithZero.{u4, u3} R₃ M₃ _inst_3 _inst_13 _inst_14))))] (h : ContinuousLinearMap.{u6, u4, u5, u3} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14) (c : R₂) (f : ContinuousLinearMap.{u2, u6, u1, u5} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11), Eq.{max (succ u1) (succ u3)} (ContinuousLinearMap.{u2, u4, u1, u3} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (ContinuousLinearMap.comp.{u2, u6, u4, u1, u5, u3} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M _inst_6 _inst_7 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_inst_2 _inst_10 _inst_11) _inst_34 _inst_36))) c f)) (HSMul.hSMul.{u4, max u3 u1, max u3 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₂) => R₃) c) (ContinuousLinearMap.{u2, u4, u1, u3} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (ContinuousLinearMap.{u2, u4, u1, u3} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (instHSMul.{u4, max u3 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₂) => R₃) c) (ContinuousLinearMap.{u2, u4, u1, u3} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (MulAction.toSMul.{u4, max u3 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₂) => R₃) c) (ContinuousLinearMap.{u2, u4, u1, u3} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (MonoidWithZero.toMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₂) => R₃) c) (Semiring.toMonoidWithZero.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₂) => R₃) c) _inst_3)) (ContinuousLinearMap.mulAction.{u2, u4, u1, u3, u4} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₂) => R₃) c) (MonoidWithZero.toMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₂) => R₃) c) (Semiring.toMonoidWithZero.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₂) => R₃) c) _inst_3)) (Module.toDistribMulAction.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₂) => R₃) c) M₃ _inst_3 _inst_13 _inst_14) _inst_35 _inst_37))) (FunLike.coe.{max (succ u6) (succ u4), succ u6, succ u4} (RingHom.{u6, u4} R₂ R₃ (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3)) R₂ (fun (_x : R₂) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₂) => R₃) _x) (MulHomClass.toFunLike.{max u6 u4, u6, u4} (RingHom.{u6, u4} R₂ R₃ (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3)) R₂ R₃ (NonUnitalNonAssocSemiring.toMul.{u6} R₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R₂ (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u4} R₃ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R₃ (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u6 u4, u6, u4} (RingHom.{u6, u4} R₂ R₃ (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3)) R₂ R₃ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R₂ (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R₃ (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u6 u4, u6, u4} (RingHom.{u6, u4} R₂ R₃ (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3)) R₂ R₃ (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3) (RingHom.instRingHomClassRingHom.{u6, u4} R₂ R₃ (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3))))) σ₂₃ c) (ContinuousLinearMap.comp.{u2, u6, u4, u1, u5, u3} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_8 _inst_11 _inst_14 _inst_27 h f))
+ forall {R : Type.{u2}} {R₂ : Type.{u6}} {R₃ : Type.{u4}} [_inst_1 : Semiring.{u2} R] [_inst_2 : Semiring.{u6} R₂] [_inst_3 : Semiring.{u4} R₃] {M : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M] [_inst_7 : AddCommMonoid.{u1} M] [_inst_8 : Module.{u2, u1} R M _inst_1 _inst_7] {M₂ : Type.{u5}} [_inst_9 : TopologicalSpace.{u5} M₂] [_inst_10 : AddCommMonoid.{u5} M₂] [_inst_11 : Module.{u6, u5} R₂ M₂ _inst_2 _inst_10] {M₃ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₃] [_inst_13 : AddCommMonoid.{u3} M₃] [_inst_14 : Module.{u4, u3} R₃ M₃ _inst_3 _inst_13] {σ₁₂ : RingHom.{u2, u6} R R₂ (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2)} {σ₂₃ : RingHom.{u6, u4} R₂ R₃ (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3)} {σ₁₃ : RingHom.{u2, u4} R R₃ (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3)} [_inst_27 : RingHomCompTriple.{u2, u6, u4} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] [_inst_34 : SMulCommClass.{u6, u6, u5} R₂ R₂ M₂ (SMulZeroClass.toSMul.{u6, u5} R₂ M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (SMulWithZero.toSMulZeroClass.{u6, u5} R₂ M₂ (MonoidWithZero.toZero.{u6} R₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (MulActionWithZero.toSMulWithZero.{u6, u5} R₂ M₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (Module.toMulActionWithZero.{u6, u5} R₂ M₂ _inst_2 _inst_10 _inst_11)))) (SMulZeroClass.toSMul.{u6, u5} R₂ M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (SMulWithZero.toSMulZeroClass.{u6, u5} R₂ M₂ (MonoidWithZero.toZero.{u6} R₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (MulActionWithZero.toSMulWithZero.{u6, u5} R₂ M₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (Module.toMulActionWithZero.{u6, u5} R₂ M₂ _inst_2 _inst_10 _inst_11))))] [_inst_35 : SMulCommClass.{u4, u4, u3} R₃ R₃ M₃ (SMulZeroClass.toSMul.{u4, u3} R₃ M₃ (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (SMulWithZero.toSMulZeroClass.{u4, u3} R₃ M₃ (MonoidWithZero.toZero.{u4} R₃ (Semiring.toMonoidWithZero.{u4} R₃ _inst_3)) (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (MulActionWithZero.toSMulWithZero.{u4, u3} R₃ M₃ (Semiring.toMonoidWithZero.{u4} R₃ _inst_3) (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (Module.toMulActionWithZero.{u4, u3} R₃ M₃ _inst_3 _inst_13 _inst_14)))) (SMulZeroClass.toSMul.{u4, u3} R₃ M₃ (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (SMulWithZero.toSMulZeroClass.{u4, u3} R₃ M₃ (MonoidWithZero.toZero.{u4} R₃ (Semiring.toMonoidWithZero.{u4} R₃ _inst_3)) (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (MulActionWithZero.toSMulWithZero.{u4, u3} R₃ M₃ (Semiring.toMonoidWithZero.{u4} R₃ _inst_3) (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (Module.toMulActionWithZero.{u4, u3} R₃ M₃ _inst_3 _inst_13 _inst_14))))] [_inst_36 : ContinuousConstSMul.{u6, u5} R₂ M₂ _inst_9 (SMulZeroClass.toSMul.{u6, u5} R₂ M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (SMulWithZero.toSMulZeroClass.{u6, u5} R₂ M₂ (MonoidWithZero.toZero.{u6} R₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (MulActionWithZero.toSMulWithZero.{u6, u5} R₂ M₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (Module.toMulActionWithZero.{u6, u5} R₂ M₂ _inst_2 _inst_10 _inst_11))))] [_inst_37 : ContinuousConstSMul.{u4, u3} R₃ M₃ _inst_12 (SMulZeroClass.toSMul.{u4, u3} R₃ M₃ (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (SMulWithZero.toSMulZeroClass.{u4, u3} R₃ M₃ (MonoidWithZero.toZero.{u4} R₃ (Semiring.toMonoidWithZero.{u4} R₃ _inst_3)) (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (MulActionWithZero.toSMulWithZero.{u4, u3} R₃ M₃ (Semiring.toMonoidWithZero.{u4} R₃ _inst_3) (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (Module.toMulActionWithZero.{u4, u3} R₃ M₃ _inst_3 _inst_13 _inst_14))))] (h : ContinuousLinearMap.{u6, u4, u5, u3} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14) (c : R₂) (f : ContinuousLinearMap.{u2, u6, u1, u5} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11), Eq.{max (succ u1) (succ u3)} (ContinuousLinearMap.{u2, u4, u1, u3} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (ContinuousLinearMap.comp.{u2, u6, u4, u1, u5, u3} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_8 _inst_11 _inst_14 _inst_27 h (HSMul.hSMul.{u6, max u5 u1, max u5 u1} R₂ (ContinuousLinearMap.{u2, u6, u1, u5} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11) (ContinuousLinearMap.{u2, u6, u1, u5} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11) (instHSMul.{u6, max u5 u1} R₂ (ContinuousLinearMap.{u2, u6, u1, u5} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11) (MulAction.toSMul.{u6, max u5 u1} R₂ (ContinuousLinearMap.{u2, u6, u1, u5} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11) (MonoidWithZero.toMonoid.{u6} R₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2)) (ContinuousLinearMap.mulAction.{u2, u6, u1, u5, u6} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11 R₂ (MonoidWithZero.toMonoid.{u6} R₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2)) (Module.toDistribMulAction.{u6, u5} R₂ M₂ _inst_2 _inst_10 _inst_11) _inst_34 _inst_36))) c f)) (HSMul.hSMul.{u4, max u3 u1, max u3 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₂) => R₃) c) (ContinuousLinearMap.{u2, u4, u1, u3} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (ContinuousLinearMap.{u2, u4, u1, u3} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (instHSMul.{u4, max u3 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₂) => R₃) c) (ContinuousLinearMap.{u2, u4, u1, u3} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (MulAction.toSMul.{u4, max u3 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₂) => R₃) c) (ContinuousLinearMap.{u2, u4, u1, u3} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (MonoidWithZero.toMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₂) => R₃) c) (Semiring.toMonoidWithZero.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₂) => R₃) c) _inst_3)) (ContinuousLinearMap.mulAction.{u2, u4, u1, u3, u4} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₂) => R₃) c) (MonoidWithZero.toMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₂) => R₃) c) (Semiring.toMonoidWithZero.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₂) => R₃) c) _inst_3)) (Module.toDistribMulAction.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₂) => R₃) c) M₃ _inst_3 _inst_13 _inst_14) _inst_35 _inst_37))) (FunLike.coe.{max (succ u6) (succ u4), succ u6, succ u4} (RingHom.{u6, u4} R₂ R₃ (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3)) R₂ (fun (_x : R₂) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₂) => R₃) _x) (MulHomClass.toFunLike.{max u6 u4, u6, u4} (RingHom.{u6, u4} R₂ R₃ (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3)) R₂ R₃ (NonUnitalNonAssocSemiring.toMul.{u6} R₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R₂ (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u4} R₃ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R₃ (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u6 u4, u6, u4} (RingHom.{u6, u4} R₂ R₃ (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3)) R₂ R₃ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R₂ (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R₃ (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u6 u4, u6, u4} (RingHom.{u6, u4} R₂ R₃ (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3)) R₂ R₃ (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3) (RingHom.instRingHomClassRingHom.{u6, u4} R₂ R₃ (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3))))) σ₂₃ c) (ContinuousLinearMap.comp.{u2, u6, u4, u1, u5, u3} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_8 _inst_11 _inst_14 _inst_27 h f))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_smulₛₗ ContinuousLinearMap.comp_smulₛₗₓ'. -/
@[simp]
theorem comp_smulₛₗ [SMulCommClass R₂ R₂ M₂] [SMulCommClass R₃ R₃ M₃] [ContinuousConstSMul R₂ M₂]
@@ -3114,7 +3114,7 @@ theorem map_add (e : M₁ ≃SL[σ₁₂] M₂) (x y : M₁) : e (x + y) = e x +
lean 3 declaration is
forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (c : R₁) (x : M₁), Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e (SMul.smul.{u1, u3} R₁ M₁ (SMulZeroClass.toHasSmul.{u1, u3} R₁ M₁ (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_13))) (SMulWithZero.toSmulZeroClass.{u1, u3} R₁ M₁ (MulZeroClass.toHasZero.{u1} R₁ (MulZeroOneClass.toMulZeroClass.{u1} R₁ (MonoidWithZero.toMulZeroOneClass.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)))) (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_13))) (MulActionWithZero.toSMulWithZero.{u1, u3} R₁ M₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_13))) (Module.toMulActionWithZero.{u1, u3} R₁ M₁ _inst_1 _inst_13 _inst_22)))) c x)) (SMul.smul.{u2, u4} R₂ M₂ (SMulZeroClass.toHasSmul.{u2, u4} R₂ M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_17))) (SMulWithZero.toSmulZeroClass.{u2, u4} R₂ M₂ (MulZeroClass.toHasZero.{u2} R₂ (MulZeroOneClass.toMulZeroClass.{u2} R₂ (MonoidWithZero.toMulZeroOneClass.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)))) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_17))) (MulActionWithZero.toSMulWithZero.{u2, u4} R₂ M₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_17))) (Module.toMulActionWithZero.{u2, u4} R₂ M₂ _inst_2 _inst_17 _inst_24)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)) (fun (_x : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)) => R₁ -> R₂) (RingHom.hasCoeToFun.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)) σ₁₂ c) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e x))
but is expected to have type
- forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (c : R₁) (x : M₁), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) (HSMul.hSMul.{u4, u2, u2} R₁ M₁ M₁ (instHSMul.{u4, u2} R₁ M₁ (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_13)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_13)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_13)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_13 _inst_22))))) c x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e (HSMul.hSMul.{u4, u2, u2} R₁ M₁ M₁ (instHSMul.{u4, u2} R₁ M₁ (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_13)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_13)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_13)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_13 _inst_22))))) c x)) (HSMul.hSMul.{u3, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (instHSMul.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (SMulZeroClass.toSMul.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_17)) (SMulWithZero.toSMulZeroClass.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) _inst_2)) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_17)) (MulActionWithZero.toSMulWithZero.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) _inst_2) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_17)) (Module.toMulActionWithZero.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_2 _inst_17 _inst_24))))) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) R₁ (fun (_x : R₁) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) R₁ R₂ (NonUnitalNonAssocSemiring.toMul.{u4} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u3} R₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) R₁ R₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (RingHom.instRingHomClassRingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2))))) σ₁₂ c) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e x))
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (c : R₁) (x : M₁), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) (HSMul.hSMul.{u4, u2, u2} R₁ M₁ M₁ (instHSMul.{u4, u2} R₁ M₁ (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_13)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_13)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_13)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_13 _inst_22))))) c x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e (HSMul.hSMul.{u4, u2, u2} R₁ M₁ M₁ (instHSMul.{u4, u2} R₁ M₁ (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_13)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_13)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_13)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_13 _inst_22))))) c x)) (HSMul.hSMul.{u3, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (instHSMul.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (SMulZeroClass.toSMul.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_17)) (SMulWithZero.toSMulZeroClass.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => R₂) c) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => R₂) c) _inst_2)) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_17)) (MulActionWithZero.toSMulWithZero.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => R₂) c) _inst_2) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_17)) (Module.toMulActionWithZero.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_2 _inst_17 _inst_24))))) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) R₁ (fun (_x : R₁) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => R₂) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) R₁ R₂ (NonUnitalNonAssocSemiring.toMul.{u4} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u3} R₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) R₁ R₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (RingHom.instRingHomClassRingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2))))) σ₁₂ c) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e x))
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_smulₛₗ ContinuousLinearEquiv.map_smulₛₗₓ'. -/
@[simp]
theorem map_smulₛₗ (e : M₁ ≃SL[σ₁₂] M₂) (c : R₁) (x : M₁) : e (c • x) = σ₁₂ c • e x :=
@@ -4030,7 +4030,7 @@ variable {R}
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))] (u : Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (x : R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (_x : ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => R -> R) (ContinuousLinearEquiv.hasCoeToFun.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : Equiv.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) -> (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Equiv.hasCoeToFun.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.unitsEquivAut.{u1} R _inst_1 _inst_11 _inst_12) u) x) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))) x ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (coeBase.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (Units.hasCoe.{u1} R (Ring.toMonoid.{u1} R _inst_1))))) u))
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))] (u : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) x) (FunLike.coe.{succ u1, succ u1, succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u) R (fun (_x : R) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u) R R _inst_11 _inst_11 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u1, u1, u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{u1, u1, u1, u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.unitsEquivAut.{u1} R _inst_1 _inst_11 _inst_12) u) x) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) x (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u))
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))] (u : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) x) (FunLike.coe.{succ u1, succ u1, succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u) R (fun (_x : R) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u) R R _inst_11 _inst_11 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u1, u1, u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{u1, u1, u1, u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R 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R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv_aut_apply ContinuousLinearEquiv.unitsEquivAut_applyₓ'. -/
@[simp]
theorem unitsEquivAut_apply (u : Rˣ) (x : R) : unitsEquivAut R u x = x * u :=
@@ -4041,7 +4041,7 @@ theorem unitsEquivAut_apply (u : Rˣ) (x : R) : unitsEquivAut R u x = x * u :=
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))] (u : Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (x : R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R 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(Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.symm.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : Equiv.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R 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(Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Equiv.hasCoeToFun.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.unitsEquivAut.{u1} R _inst_1 _inst_11 _inst_12) u)) x) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))) x ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (coeBase.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (Units.hasCoe.{u1} R (Ring.toMonoid.{u1} R _inst_1))))) (Inv.inv.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (Units.hasInv.{u1} R (Ring.toMonoid.{u1} R _inst_1)) u)))
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))] (u : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) x) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R _inst_11 _inst_11 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u1, u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{u1, u1, u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (ContinuousLinearEquiv.symm.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.unitsEquivAut.{u1} R _inst_1 _inst_11 _inst_12) u)) x) (HMul.hMul.{u1, u1, u1} R ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) x) R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) x (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Inv.inv.{u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Units.instInv.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) u)))
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))] (u : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) x) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R _inst_11 _inst_11 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u1, u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{u1, u1, u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (ContinuousLinearEquiv.symm.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.unitsEquivAut.{u1} R _inst_1 _inst_11 _inst_12) u)) x) (HMul.hMul.{u1, u1, u1} R ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) x) R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) x (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Inv.inv.{u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Units.instInv.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) u)))
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv_aut_apply_symm ContinuousLinearEquiv.unitsEquivAut_apply_symmₓ'. -/
@[simp]
theorem unitsEquivAut_apply_symm (u : Rˣ) (x : R) : (unitsEquivAut R u).symm x = x * ↑u⁻¹ :=
@@ -4052,7 +4052,7 @@ theorem unitsEquivAut_apply_symm (u : Rˣ) (x : R) : (unitsEquivAut R u).symm x
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))] (e : ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))), Eq.{succ u1} R ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (coeBase.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (Units.hasCoe.{u1} R (Ring.toMonoid.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1))) (fun (_x : Equiv.{succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1))) => (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) -> (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1))) (Equiv.hasCoeToFun.{succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1))) (Equiv.symm.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut.{u1} R _inst_1 _inst_11 _inst_12)) e)) (coeFn.{succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (_x : ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => R -> R) (ContinuousLinearEquiv.hasCoeToFun.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) e (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))))))
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))] (e : ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (_x : ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R 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(RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Equiv.symm.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut.{u1} R _inst_1 _inst_11 _inst_12)) e)) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R _inst_11 _inst_11 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u1, u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{u1, u1, u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) e (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))] (e : ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (_x : ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Equiv.symm.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut.{u1} R _inst_1 _inst_11 _inst_12)) e)) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R _inst_11 _inst_11 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u1, u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{u1, u1, u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) e (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv_aut_symm_apply ContinuousLinearEquiv.unitsEquivAut_symm_applyₓ'. -/
@[simp]
theorem unitsEquivAut_symm_apply (e : R ≃L[R] R) : ↑((unitsEquivAut R).symm e) = e 1 :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e
@@ -179,7 +179,7 @@ variable {ι R M₁ M₂ : Type _} [Semiring R] [AddCommMonoid M₁] [AddCommMon
lean 3 declaration is
forall {R : Type.{u1}} {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : AddCommMonoid.{u3} M₂] [_inst_4 : Module.{u1, u2} R M₁ _inst_1 _inst_2] [_inst_5 : Module.{u1, u3} R M₂ _inst_1 _inst_3] [u : TopologicalSpace.{u1} R] {t : TopologicalSpace.{u3} M₂} [_inst_6 : ContinuousSMul.{u1, u3} R M₂ (SMulZeroClass.toHasSmul.{u1, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M₂ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_3))) (Module.toMulActionWithZero.{u1, u3} R M₂ _inst_1 _inst_3 _inst_5)))) u t] (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5), ContinuousSMul.{u1, u2} R M₁ (SMulZeroClass.toHasSmul.{u1, u2} R M₁ (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M₁ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M₁ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2))) (Module.toMulActionWithZero.{u1, u2} R M₁ _inst_1 _inst_2 _inst_4)))) u (TopologicalSpace.induced.{u2, u3} M₁ M₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M₁ M₂ _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f) t)
but is expected to have type
- forall {R : Type.{u3}} {M₁ : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : AddCommMonoid.{u1} M₂] [_inst_4 : Module.{u3, u2} R M₁ _inst_1 _inst_2] [_inst_5 : Module.{u3, u1} R M₂ _inst_1 _inst_3] [u : TopologicalSpace.{u3} R] {t : TopologicalSpace.{u1} M₂} [_inst_6 : ContinuousSMul.{u3, u1} R M₂ (SMulZeroClass.toSMul.{u3, u1} R M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u1} R M₂ (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u1} R M₂ (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_3)) (Module.toMulActionWithZero.{u3, u1} R M₂ _inst_1 _inst_3 _inst_5)))) u t] (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5), ContinuousSMul.{u3, u2} R M₁ (SMulZeroClass.toSMul.{u3, u2} R M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M₁ (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M₁ (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (Module.toMulActionWithZero.{u3, u2} R M₁ _inst_1 _inst_2 _inst_4)))) u (TopologicalSpace.induced.{u2, u1} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M₁ M₂ _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) t)
+ forall {R : Type.{u3}} {M₁ : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : AddCommMonoid.{u1} M₂] [_inst_4 : Module.{u3, u2} R M₁ _inst_1 _inst_2] [_inst_5 : Module.{u3, u1} R M₂ _inst_1 _inst_3] [u : TopologicalSpace.{u3} R] {t : TopologicalSpace.{u1} M₂} [_inst_6 : ContinuousSMul.{u3, u1} R M₂ (SMulZeroClass.toSMul.{u3, u1} R M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u1} R M₂ (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u1} R M₂ (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_3)) (Module.toMulActionWithZero.{u3, u1} R M₂ _inst_1 _inst_3 _inst_5)))) u t] (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5), ContinuousSMul.{u3, u2} R M₁ (SMulZeroClass.toSMul.{u3, u2} R M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M₁ (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M₁ (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (Module.toMulActionWithZero.{u3, u2} R M₁ _inst_1 _inst_2 _inst_4)))) u (TopologicalSpace.induced.{u2, u1} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M₁ M₂ _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) t)
Case conversion may be inaccurate. Consider using '#align has_continuous_smul_induced continuousSMul_inducedₓ'. -/
theorem continuousSMul_induced : @ContinuousSMul R M₁ _ u (t.induced f) :=
{
@@ -365,7 +365,7 @@ section Pi
lean 3 declaration is
forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Finite.{succ u1} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : TopologicalSpace.{u2} R] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_2 _inst_4] [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : ContinuousAdd.{u3} M _inst_6 (AddZeroClass.toHasAdd.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)))] [_inst_8 : ContinuousSMul.{u2, u3} R M (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_4 _inst_5)))) _inst_3 _inst_6] (f : LinearMap.{u2, u2, max u1 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.Function.module.{u1, u2, u2} ι R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_5), Continuous.{max u1 u2, u3} (ι -> R) M (Pi.topologicalSpace.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (a : ι) => _inst_3)) _inst_6 (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.Function.module.{u1, u2, u2} ι R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.Function.module.{u1, u2, u2} ι R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_5) => (ι -> R) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (ι -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.Function.module.{u1, u2, u2} ι R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) f)
but is expected to have type
- forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Finite.{succ u3} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : TopologicalSpace.{u2} R] [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_2 _inst_4] [_inst_6 : TopologicalSpace.{u1} M] [_inst_7 : ContinuousAdd.{u1} M _inst_6 (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)))] [_inst_8 : ContinuousSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (Module.toMulActionWithZero.{u2, u1} R M _inst_2 _inst_4 _inst_5)))) _inst_3 _inst_6] (f : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5), Continuous.{max u3 u2, u1} (ι -> R) M (Pi.topologicalSpace.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (a : ι) => _inst_3)) _inst_6 (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5) (ι -> R) (fun (_x : ι -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (ι -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) f)
+ forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Finite.{succ u3} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : TopologicalSpace.{u2} R] [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_2 _inst_4] [_inst_6 : TopologicalSpace.{u1} M] [_inst_7 : ContinuousAdd.{u1} M _inst_6 (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)))] [_inst_8 : ContinuousSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (Module.toMulActionWithZero.{u2, u1} R M _inst_2 _inst_4 _inst_5)))) _inst_3 _inst_6] (f : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5), Continuous.{max u3 u2, u1} (ι -> R) M (Pi.topologicalSpace.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (a : ι) => _inst_3)) _inst_6 (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5) (ι -> R) (fun (_x : ι -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (ι -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) f)
Case conversion may be inaccurate. Consider using '#align linear_map.continuous_on_pi LinearMap.continuous_on_piₓ'. -/
theorem LinearMap.continuous_on_pi {ι : Type _} {R : Type _} {M : Type _} [Finite ι] [Semiring R]
[TopologicalSpace R] [AddCommMonoid M] [Module R M] [TopologicalSpace M] [ContinuousAdd M]
@@ -529,7 +529,7 @@ variable [ContinuousAdd M₂] {σ : R →+* S} {l : Filter α}
lean 3 declaration is
forall {M₁ : Type.{u1}} {M₂ : Type.{u2}} {R : Type.{u3}} {S : Type.{u4}} [_inst_1 : TopologicalSpace.{u2} M₂] [_inst_2 : T2Space.{u2} M₂ _inst_1] [_inst_3 : Semiring.{u3} R] [_inst_4 : Semiring.{u4} S] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_6 : AddCommMonoid.{u2} M₂] [_inst_7 : Module.{u3, u1} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u4, u2} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u4, u2} S M₂ _inst_1 (SMulZeroClass.toHasSmul.{u4, u2} S M₂ (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M₂ (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_4)))) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M₂ (Semiring.toMonoidWithZero.{u4} S _inst_4) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (Module.toMulActionWithZero.{u4, u2} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u2} M₂ _inst_1 (AddZeroClass.toHasAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)))] {σ : RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R _inst_3) (Semiring.toNonAssocSemiring.{u4} S _inst_4)} (f : M₁ -> M₂), (Membership.Mem.{max u1 u2, max u1 u2} (M₁ -> M₂) (Set.{max u1 u2} (M₁ -> M₂)) (Set.hasMem.{max u1 u2} (M₁ -> M₂)) f (closure.{max u1 u2} (M₁ -> M₂) (Pi.topologicalSpace.{u1, u2} M₁ (fun (ᾰ : M₁) => M₂) (fun (a : M₁) => _inst_1)) (Set.range.{max u1 u2, max (succ u1) (succ u2)} (M₁ -> M₂) (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (fun (ᾰ : LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u3, u4, u1, u2} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ))))) -> (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)
but is expected to have type
- forall {M₁ : Type.{u1}} {M₂ : Type.{u2}} {R : Type.{u3}} {S : Type.{u4}} [_inst_1 : TopologicalSpace.{u2} M₂] [_inst_2 : T2Space.{u2} M₂ _inst_1] [_inst_3 : Semiring.{u3} R] [_inst_4 : Semiring.{u4} S] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_6 : AddCommMonoid.{u2} M₂] [_inst_7 : Module.{u3, u1} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u4, u2} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u4, u2} S M₂ _inst_1 (SMulZeroClass.toSMul.{u4, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (SMulWithZero.toSMulZeroClass.{u4, u2} S M₂ (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_4)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (MulActionWithZero.toSMulWithZero.{u4, u2} S M₂ (Semiring.toMonoidWithZero.{u4} S _inst_4) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (Module.toMulActionWithZero.{u4, u2} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u2} M₂ _inst_1 (AddZeroClass.toAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)))] {σ : RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R _inst_3) (Semiring.toNonAssocSemiring.{u4} S _inst_4)} (f : M₁ -> M₂), (Membership.mem.{max u1 u2, max u1 u2} (M₁ -> M₂) (Set.{max u1 u2} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) ᾰ)) (Set.instMembershipSet.{max u1 u2} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) ᾰ)) f (closure.{max u1 u2} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) ᾰ) (Pi.topologicalSpace.{u1, u2} M₁ (fun (ᾰ : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) ᾰ) (fun (a : M₁) => _inst_1)) (Set.range.{max u1 u2, max (succ u1) (succ u2)} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) ᾰ) (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) M₁ (fun (ᾰ : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) ᾰ) (LinearMap.instFunLikeLinearMap.{u3, u4, u1, u2} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ))))) -> (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)
+ forall {M₁ : Type.{u1}} {M₂ : Type.{u2}} {R : Type.{u3}} {S : Type.{u4}} [_inst_1 : TopologicalSpace.{u2} M₂] [_inst_2 : T2Space.{u2} M₂ _inst_1] [_inst_3 : Semiring.{u3} R] [_inst_4 : Semiring.{u4} S] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_6 : AddCommMonoid.{u2} M₂] [_inst_7 : Module.{u3, u1} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u4, u2} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u4, u2} S M₂ _inst_1 (SMulZeroClass.toSMul.{u4, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (SMulWithZero.toSMulZeroClass.{u4, u2} S M₂ (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_4)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (MulActionWithZero.toSMulWithZero.{u4, u2} S M₂ (Semiring.toMonoidWithZero.{u4} S _inst_4) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (Module.toMulActionWithZero.{u4, u2} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u2} M₂ _inst_1 (AddZeroClass.toAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)))] {σ : RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R _inst_3) (Semiring.toNonAssocSemiring.{u4} S _inst_4)} (f : M₁ -> M₂), (Membership.mem.{max u1 u2, max u1 u2} (M₁ -> M₂) (Set.{max u1 u2} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) ᾰ)) (Set.instMembershipSet.{max u1 u2} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) ᾰ)) f (closure.{max u1 u2} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) ᾰ) (Pi.topologicalSpace.{u1, u2} M₁ (fun (ᾰ : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) ᾰ) (fun (a : M₁) => _inst_1)) (Set.range.{max u1 u2, max (succ u1) (succ u2)} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) ᾰ) (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) M₁ (fun (ᾰ : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) ᾰ) (LinearMap.instFunLikeLinearMap.{u3, u4, u1, u2} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ))))) -> (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)
Case conversion may be inaccurate. Consider using '#align linear_map_of_mem_closure_range_coe linearMapOfMemClosureRangeCoeₓ'. -/
/-- Constructs a bundled linear map from a function and a proof that this function belongs to the
closure of the set of linear maps. -/
@@ -547,7 +547,7 @@ def linearMapOfMemClosureRangeCoe (f : M₁ → M₂)
lean 3 declaration is
forall {M₁ : Type.{u1}} {M₂ : Type.{u2}} {α : Type.{u3}} {R : Type.{u4}} {S : Type.{u5}} [_inst_1 : TopologicalSpace.{u2} M₂] [_inst_2 : T2Space.{u2} M₂ _inst_1] [_inst_3 : Semiring.{u4} R] [_inst_4 : Semiring.{u5} S] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_6 : AddCommMonoid.{u2} M₂] [_inst_7 : Module.{u4, u1} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u5, u2} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u5, u2} S M₂ _inst_1 (SMulZeroClass.toHasSmul.{u5, u2} S M₂ (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (SMulWithZero.toSmulZeroClass.{u5, u2} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_4)))) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (MulActionWithZero.toSMulWithZero.{u5, u2} S M₂ (Semiring.toMonoidWithZero.{u5} S _inst_4) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (Module.toMulActionWithZero.{u5, u2} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u2} M₂ _inst_1 (AddZeroClass.toHasAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)))] {σ : RingHom.{u4, u5} R S (Semiring.toNonAssocSemiring.{u4} R _inst_3) (Semiring.toNonAssocSemiring.{u5} S _inst_4)} {l : Filter.{u3} α} (f : M₁ -> M₂) (g : α -> (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)) [_inst_11 : Filter.NeBot.{u3} α l], (Filter.Tendsto.{u3, max u1 u2} α (M₁ -> M₂) (fun (a : α) (x : M₁) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (fun (_x : LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u4, u5, u1, u2} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ) (g a) x) l (nhds.{max u1 u2} (M₁ -> M₂) (Pi.topologicalSpace.{u1, u2} M₁ (fun (x : M₁) => M₂) (fun (a : M₁) => _inst_1)) f)) -> (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)
but is expected to have type
- forall {M₁ : Type.{u1}} {M₂ : Type.{u2}} {α : Type.{u3}} {R : Type.{u4}} {S : Type.{u5}} [_inst_1 : TopologicalSpace.{u2} M₂] [_inst_2 : T2Space.{u2} M₂ _inst_1] [_inst_3 : Semiring.{u4} R] [_inst_4 : Semiring.{u5} S] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_6 : AddCommMonoid.{u2} M₂] [_inst_7 : Module.{u4, u1} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u5, u2} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u5, u2} S M₂ _inst_1 (SMulZeroClass.toSMul.{u5, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (SMulWithZero.toSMulZeroClass.{u5, u2} S M₂ (MonoidWithZero.toZero.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_4)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (MulActionWithZero.toSMulWithZero.{u5, u2} S M₂ (Semiring.toMonoidWithZero.{u5} S _inst_4) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (Module.toMulActionWithZero.{u5, u2} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u2} M₂ _inst_1 (AddZeroClass.toAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)))] {σ : RingHom.{u4, u5} R S (Semiring.toNonAssocSemiring.{u4} R _inst_3) (Semiring.toNonAssocSemiring.{u5} S _inst_4)} {l : Filter.{u3} α} (f : M₁ -> M₂) (g : α -> (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)) [_inst_11 : Filter.NeBot.{u3} α l], (Filter.Tendsto.{u3, max u1 u2} α (forall (x : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) x) (fun (a : α) (x : M₁) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u5, u1, u2} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ) (g a) x) l (nhds.{max u1 u2} (forall (x : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) x) (Pi.topologicalSpace.{u1, u2} M₁ (fun (x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) x) (fun (a : M₁) => _inst_1)) f)) -> (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)
+ forall {M₁ : Type.{u1}} {M₂ : Type.{u2}} {α : Type.{u3}} {R : Type.{u4}} {S : Type.{u5}} [_inst_1 : TopologicalSpace.{u2} M₂] [_inst_2 : T2Space.{u2} M₂ _inst_1] [_inst_3 : Semiring.{u4} R] [_inst_4 : Semiring.{u5} S] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_6 : AddCommMonoid.{u2} M₂] [_inst_7 : Module.{u4, u1} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u5, u2} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u5, u2} S M₂ _inst_1 (SMulZeroClass.toSMul.{u5, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (SMulWithZero.toSMulZeroClass.{u5, u2} S M₂ (MonoidWithZero.toZero.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_4)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (MulActionWithZero.toSMulWithZero.{u5, u2} S M₂ (Semiring.toMonoidWithZero.{u5} S _inst_4) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (Module.toMulActionWithZero.{u5, u2} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u2} M₂ _inst_1 (AddZeroClass.toAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)))] {σ : RingHom.{u4, u5} R S (Semiring.toNonAssocSemiring.{u4} R _inst_3) (Semiring.toNonAssocSemiring.{u5} S _inst_4)} {l : Filter.{u3} α} (f : M₁ -> M₂) (g : α -> (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)) [_inst_11 : Filter.NeBot.{u3} α l], (Filter.Tendsto.{u3, max u1 u2} α (forall (x : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) x) (fun (a : α) (x : M₁) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u5, u1, u2} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ) (g a) x) l (nhds.{max u1 u2} (forall (x : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) x) (Pi.topologicalSpace.{u1, u2} M₁ (fun (x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) x) (fun (a : M₁) => _inst_1)) f)) -> (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)
Case conversion may be inaccurate. Consider using '#align linear_map_of_tendsto linearMapOfTendstoₓ'. -/
/-- Construct a bundled linear map from a pointwise limit of linear maps -/
@[simps (config := { fullyApplied := false })]
@@ -563,7 +563,7 @@ variable (M₁ M₂ σ)
lean 3 declaration is
forall (M₁ : Type.{u1}) (M₂ : Type.{u2}) {R : Type.{u3}} {S : Type.{u4}} [_inst_1 : TopologicalSpace.{u2} M₂] [_inst_2 : T2Space.{u2} M₂ _inst_1] [_inst_3 : Semiring.{u3} R] [_inst_4 : Semiring.{u4} S] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_6 : AddCommMonoid.{u2} M₂] [_inst_7 : Module.{u3, u1} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u4, u2} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u4, u2} S M₂ _inst_1 (SMulZeroClass.toHasSmul.{u4, u2} S M₂ (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M₂ (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_4)))) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M₂ (Semiring.toMonoidWithZero.{u4} S _inst_4) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (Module.toMulActionWithZero.{u4, u2} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u2} M₂ _inst_1 (AddZeroClass.toHasAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)))] (σ : RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R _inst_3) (Semiring.toNonAssocSemiring.{u4} S _inst_4)), IsClosed.{max u1 u2} (M₁ -> M₂) (Pi.topologicalSpace.{u1, u2} M₁ (fun (ᾰ : M₁) => M₂) (fun (a : M₁) => _inst_1)) (Set.range.{max u1 u2, max (succ u1) (succ u2)} (M₁ -> M₂) (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (fun (ᾰ : LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u3, u4, u1, u2} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ)))
but is expected to have type
- forall (M₁ : Type.{u4}) (M₂ : Type.{u3}) {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} M₂] [_inst_2 : T2Space.{u3} M₂ _inst_1] [_inst_3 : Semiring.{u2} R] [_inst_4 : Semiring.{u1} S] [_inst_5 : AddCommMonoid.{u4} M₁] [_inst_6 : AddCommMonoid.{u3} M₂] [_inst_7 : Module.{u2, u4} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u1, u3} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u1, u3} S M₂ _inst_1 (SMulZeroClass.toSMul.{u1, u3} S M₂ (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_6)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_4)) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_6)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M₂ (Semiring.toMonoidWithZero.{u1} S _inst_4) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_6)) (Module.toMulActionWithZero.{u1, u3} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u3} M₂ _inst_1 (AddZeroClass.toAdd.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_6)))] (σ : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_3) (Semiring.toNonAssocSemiring.{u1} S _inst_4)), IsClosed.{max u4 u3} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) ᾰ) (Pi.topologicalSpace.{u4, u3} M₁ (fun (ᾰ : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) ᾰ) (fun (a : M₁) => _inst_1)) (Set.range.{max u4 u3, max (succ u4) (succ u3)} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) ᾰ) (LinearMap.{u2, u1, u4, u3} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u2, u1, u4, u3} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) M₁ (fun (ᾰ : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) ᾰ) (LinearMap.instFunLikeLinearMap.{u2, u1, u4, u3} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ)))
+ forall (M₁ : Type.{u4}) (M₂ : Type.{u3}) {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} M₂] [_inst_2 : T2Space.{u3} M₂ _inst_1] [_inst_3 : Semiring.{u2} R] [_inst_4 : Semiring.{u1} S] [_inst_5 : AddCommMonoid.{u4} M₁] [_inst_6 : AddCommMonoid.{u3} M₂] [_inst_7 : Module.{u2, u4} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u1, u3} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u1, u3} S M₂ _inst_1 (SMulZeroClass.toSMul.{u1, u3} S M₂ (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_6)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_4)) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_6)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M₂ (Semiring.toMonoidWithZero.{u1} S _inst_4) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_6)) (Module.toMulActionWithZero.{u1, u3} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u3} M₂ _inst_1 (AddZeroClass.toAdd.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_6)))] (σ : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_3) (Semiring.toNonAssocSemiring.{u1} S _inst_4)), IsClosed.{max u4 u3} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) ᾰ) (Pi.topologicalSpace.{u4, u3} M₁ (fun (ᾰ : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) ᾰ) (fun (a : M₁) => _inst_1)) (Set.range.{max u4 u3, max (succ u4) (succ u3)} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) ᾰ) (LinearMap.{u2, u1, u4, u3} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u2, u1, u4, u3} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) M₁ (fun (ᾰ : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) ᾰ) (LinearMap.instFunLikeLinearMap.{u2, u1, u4, u3} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ)))
Case conversion may be inaccurate. Consider using '#align linear_map.is_closed_range_coe LinearMap.isClosed_range_coeₓ'. -/
theorem LinearMap.isClosed_range_coe : IsClosed (Set.range (coeFn : (M₁ →ₛₗ[σ] M₂) → M₁ → M₂)) :=
isClosed_of_closure_subset fun f hf => ⟨linearMapOfMemClosureRangeCoe f hf, rfl⟩
@@ -647,7 +647,7 @@ theorem coe_mk (f : M₁ →ₛₗ[σ₁₂] M₂) (h) : (mk f h : M₁ →ₛ
lean 3 declaration is
forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] [_inst_14 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_9] (f : LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (h : autoParamₓ.{0} (Continuous.{u3, u4} M₁ M₂ _inst_4 _inst_8 (LinearMap.toFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16 f)) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 99 (OfNat.mk.{0} Nat 99 (bit1.{0} Nat 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_inst_9 _inst_14 _inst_16 f h)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (fun (_x : LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) f)
but is expected to have type
- forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] (f : LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (h : Continuous.{u2, u1} M₁ M₂ _inst_4 _inst_8 (AddHom.toFun.{u2, u1} M₁ M₂ (AddZeroClass.toAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (AddZeroClass.toAdd.{u1} M₂ (AddMonoid.toAddZeroClass.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9))) (LinearMap.toAddHom.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16 f))), Eq.{max (succ u2) (succ u1)} (forall (a : M₁), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) (ContinuousLinearMap.mk.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f h)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) f)
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] (f : LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (h : Continuous.{u2, u1} M₁ M₂ _inst_4 _inst_8 (AddHom.toFun.{u2, u1} M₁ M₂ (AddZeroClass.toAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (AddZeroClass.toAdd.{u1} M₂ (AddMonoid.toAddZeroClass.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9))) (LinearMap.toAddHom.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16 f))), Eq.{max (succ u2) (succ u1)} (forall (a : M₁), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) (ContinuousLinearMap.mk.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f h)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) f)
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_mk' ContinuousLinearMap.coe_mk'ₓ'. -/
@[simp]
theorem coe_mk' (f : M₁ →ₛₗ[σ₁₂] M₂) (h) : (mk f h : M₁ → M₂) = f :=
@@ -842,7 +842,7 @@ protected theorem map_sum {ι : Type _} (f : M₁ →SL[σ₁₂] M₂) (s : Fin
lean 3 declaration is
forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] [_inst_14 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_9] (f : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u3) (succ u4)} (M₁ -> M₂) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (fun (_x : LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) ((fun (a : Sort.{max (succ u3) (succ u4)}) (b : Sort.{max (succ u3) (succ u4)}) [self : HasLiftT.{max (succ u3) (succ u4), max (succ u3) (succ u4)} a b] => self.0) (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (HasLiftT.mk.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (CoeTCₓ.coe.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (coeBase.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.LinearMap.coe.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16)))) f)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) => M₁ -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) f)
but is expected to have type
- forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] (f : ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) f)
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] (f : ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) f)
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_coe ContinuousLinearMap.coe_coeₓ'. -/
@[simp, norm_cast]
theorem coe_coe (f : M₁ →SL[σ₁₂] M₂) : ⇑(f : M₁ →ₛₗ[σ₁₂] M₂) = f :=
@@ -900,7 +900,7 @@ theorem ext_on [T2Space M₂] {s : Set M₁} (hs : Dense (Submodule.span R₁ s
lean 3 declaration is
forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] [_inst_14 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_9] [_inst_18 : RingHomSurjective.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂] [_inst_19 : TopologicalSpace.{u1} R₁] [_inst_20 : TopologicalSpace.{u2} R₂] [_inst_21 : ContinuousSMul.{u1, u3} R₁ M₁ (SMulZeroClass.toHasSmul.{u1, u3} R₁ M₁ (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5))) (SMulWithZero.toSmulZeroClass.{u1, u3} R₁ M₁ (MulZeroClass.toHasZero.{u1} R₁ (MulZeroOneClass.toMulZeroClass.{u1} R₁ (MonoidWithZero.toMulZeroOneClass.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)))) (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5))) (MulActionWithZero.toSMulWithZero.{u1, u3} R₁ M₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5))) (Module.toMulActionWithZero.{u1, u3} R₁ M₁ _inst_1 _inst_5 _inst_14)))) _inst_19 _inst_4] [_inst_22 : ContinuousAdd.{u3} M₁ _inst_4 (AddZeroClass.toHasAdd.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5)))] [_inst_23 : ContinuousSMul.{u2, u4} R₂ M₂ (SMulZeroClass.toHasSmul.{u2, u4} R₂ M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (SMulWithZero.toSmulZeroClass.{u2, u4} R₂ M₂ (MulZeroClass.toHasZero.{u2} R₂ (MulZeroOneClass.toMulZeroClass.{u2} R₂ (MonoidWithZero.toMulZeroOneClass.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)))) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (MulActionWithZero.toSMulWithZero.{u2, u4} R₂ M₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (Module.toMulActionWithZero.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)))) _inst_20 _inst_8] [_inst_24 : ContinuousAdd.{u4} M₂ _inst_8 (AddZeroClass.toHasAdd.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9)))] (f : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (s : Submodule.{u1, u3} R₁ M₁ _inst_1 _inst_5 _inst_14), LE.le.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) (Preorder.toHasLe.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) (PartialOrder.toPreorder.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) (SetLike.partialOrder.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)))) (Submodule.map.{u1, u2, u3, u4, max u3 u4} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂ _inst_18 (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) ((fun (a : Sort.{max (succ u3) (succ u4)}) (b : Sort.{max (succ u3) (succ u4)}) [self : HasLiftT.{max (succ u3) (succ u4), max (succ u3) (succ u4)} a b] => self.0) (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (HasLiftT.mk.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (CoeTCₓ.coe.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (coeBase.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.LinearMap.coe.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16)))) f) (Submodule.topologicalClosure.{u1, u3} R₁ M₁ _inst_1 _inst_19 _inst_4 _inst_5 _inst_14 _inst_21 _inst_22 s)) (Submodule.topologicalClosure.{u2, u4} R₂ M₂ _inst_2 _inst_20 _inst_8 _inst_9 _inst_16 _inst_23 _inst_24 (Submodule.map.{u1, u2, u3, u4, max u3 u4} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂ _inst_18 (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) ((fun (a : Sort.{max (succ u3) (succ u4)}) (b : Sort.{max (succ u3) (succ u4)}) [self : HasLiftT.{max (succ u3) (succ u4), max (succ u3) (succ u4)} a b] => self.0) (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (HasLiftT.mk.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (CoeTCₓ.coe.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (coeBase.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.LinearMap.coe.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16)))) f) s))
but is expected to have type
- forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] [_inst_18 : RingHomSurjective.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂] [_inst_19 : TopologicalSpace.{u4} R₁] [_inst_20 : TopologicalSpace.{u3} R₂] [_inst_21 : ContinuousSMul.{u4, u2} R₁ M₁ (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)))) _inst_19 _inst_4] [_inst_22 : ContinuousAdd.{u2} M₁ _inst_4 (AddZeroClass.toAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)))] [_inst_23 : ContinuousSMul.{u3, u1} R₂ M₂ (SMulZeroClass.toSMul.{u3, u1} R₂ M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u3, u1} R₂ M₂ (MonoidWithZero.toZero.{u3} R₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u3, u1} R₂ M₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16)))) _inst_20 _inst_8] [_inst_24 : ContinuousAdd.{u1} M₂ _inst_8 (AddZeroClass.toAdd.{u1} M₂ (AddMonoid.toAddZeroClass.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)))] (f : ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (s : Submodule.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14), LE.le.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (Preorder.toLE.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (PartialOrder.toPreorder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (Submodule.completeLattice.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16))))) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂ _inst_18 (LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f) (Submodule.topologicalClosure.{u4, u2} R₁ M₁ _inst_1 _inst_4 _inst_5 _inst_14 (ContinuousSMul.continuousConstSMul.{u4, u2} R₁ M₁ _inst_19 _inst_4 (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)))) _inst_21) _inst_22 s)) (Submodule.topologicalClosure.{u3, u1} R₂ M₂ _inst_2 _inst_8 _inst_9 _inst_16 (ContinuousSMul.continuousConstSMul.{u3, u1} R₂ M₂ _inst_20 _inst_8 (SMulZeroClass.toSMul.{u3, u1} R₂ M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u3, u1} R₂ M₂ (MonoidWithZero.toZero.{u3} R₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u3, u1} R₂ M₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16)))) _inst_23) _inst_24 (Submodule.map.{u4, u3, u2, u1, max u2 u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂ _inst_18 (LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f) s))
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] [_inst_18 : RingHomSurjective.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂] [_inst_19 : TopologicalSpace.{u4} R₁] [_inst_20 : TopologicalSpace.{u3} R₂] [_inst_21 : ContinuousSMul.{u4, u2} R₁ M₁ (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)))) _inst_19 _inst_4] [_inst_22 : ContinuousAdd.{u2} M₁ _inst_4 (AddZeroClass.toAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)))] [_inst_23 : ContinuousSMul.{u3, u1} R₂ M₂ (SMulZeroClass.toSMul.{u3, u1} R₂ M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u3, u1} R₂ M₂ (MonoidWithZero.toZero.{u3} R₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u3, u1} R₂ M₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16)))) _inst_20 _inst_8] [_inst_24 : ContinuousAdd.{u1} M₂ _inst_8 (AddZeroClass.toAdd.{u1} M₂ (AddMonoid.toAddZeroClass.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)))] (f : ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (s : Submodule.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14), LE.le.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (Preorder.toLE.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (PartialOrder.toPreorder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (Submodule.completeLattice.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16))))) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂ _inst_18 (LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f) (Submodule.topologicalClosure.{u4, u2} R₁ M₁ _inst_1 _inst_4 _inst_5 _inst_14 (ContinuousSMul.continuousConstSMul.{u4, u2} R₁ M₁ _inst_19 _inst_4 (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)))) _inst_21) _inst_22 s)) (Submodule.topologicalClosure.{u3, u1} R₂ M₂ _inst_2 _inst_8 _inst_9 _inst_16 (ContinuousSMul.continuousConstSMul.{u3, u1} R₂ M₂ _inst_20 _inst_8 (SMulZeroClass.toSMul.{u3, u1} R₂ M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u3, u1} R₂ M₂ (MonoidWithZero.toZero.{u3} R₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u3, u1} R₂ M₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16)))) _inst_23) _inst_24 (Submodule.map.{u4, u3, u2, u1, max u2 u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂ _inst_18 (LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f) s))
Case conversion may be inaccurate. Consider using '#align submodule.topological_closure_map Submodule.topologicalClosure_mapₓ'. -/
/-- Under a continuous linear map, the image of the `topological_closure` of a submodule is
contained in the `topological_closure` of its image. -/
@@ -916,7 +916,7 @@ theorem Submodule.topologicalClosure_map [RingHomSurjective σ₁₂] [Topologic
lean 3 declaration is
forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] [_inst_14 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_9] [_inst_18 : RingHomSurjective.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂] [_inst_19 : TopologicalSpace.{u1} R₁] [_inst_20 : TopologicalSpace.{u2} R₂] [_inst_21 : ContinuousSMul.{u1, u3} R₁ M₁ (SMulZeroClass.toHasSmul.{u1, u3} R₁ M₁ (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5))) (SMulWithZero.toSmulZeroClass.{u1, u3} R₁ M₁ (MulZeroClass.toHasZero.{u1} R₁ (MulZeroOneClass.toMulZeroClass.{u1} R₁ (MonoidWithZero.toMulZeroOneClass.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)))) (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5))) (MulActionWithZero.toSMulWithZero.{u1, u3} R₁ M₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5))) (Module.toMulActionWithZero.{u1, u3} R₁ M₁ _inst_1 _inst_5 _inst_14)))) _inst_19 _inst_4] [_inst_22 : ContinuousAdd.{u3} M₁ _inst_4 (AddZeroClass.toHasAdd.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5)))] [_inst_23 : ContinuousSMul.{u2, u4} R₂ M₂ (SMulZeroClass.toHasSmul.{u2, u4} R₂ M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (SMulWithZero.toSmulZeroClass.{u2, u4} R₂ M₂ (MulZeroClass.toHasZero.{u2} R₂ (MulZeroOneClass.toMulZeroClass.{u2} R₂ (MonoidWithZero.toMulZeroOneClass.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)))) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (MulActionWithZero.toSMulWithZero.{u2, u4} R₂ M₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (Module.toMulActionWithZero.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)))) _inst_20 _inst_8] [_inst_24 : ContinuousAdd.{u4} M₂ _inst_8 (AddZeroClass.toHasAdd.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9)))] {f : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16}, (DenseRange.{u4, u3} M₂ _inst_8 M₁ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) => M₁ -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) f)) -> (forall {s : Submodule.{u1, u3} R₁ M₁ _inst_1 _inst_5 _inst_14}, (Eq.{succ u3} (Submodule.{u1, u3} R₁ M₁ _inst_1 _inst_5 _inst_14) (Submodule.topologicalClosure.{u1, u3} R₁ M₁ _inst_1 _inst_19 _inst_4 _inst_5 _inst_14 _inst_21 _inst_22 s) (Top.top.{u3} (Submodule.{u1, u3} R₁ M₁ _inst_1 _inst_5 _inst_14) (Submodule.hasTop.{u1, u3} R₁ M₁ _inst_1 _inst_5 _inst_14))) -> (Eq.{succ u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) (Submodule.topologicalClosure.{u2, u4} R₂ M₂ _inst_2 _inst_20 _inst_8 _inst_9 _inst_16 _inst_23 _inst_24 (Submodule.map.{u1, u2, u3, u4, max u3 u4} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂ _inst_18 (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) ((fun (a : Sort.{max (succ u3) (succ u4)}) (b : Sort.{max (succ u3) (succ u4)}) [self : HasLiftT.{max (succ u3) (succ u4), max (succ u3) (succ u4)} a b] => self.0) (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (HasLiftT.mk.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (CoeTCₓ.coe.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (coeBase.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.LinearMap.coe.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16)))) f) s)) (Top.top.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) (Submodule.hasTop.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16))))
but is expected to have type
- forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] [_inst_18 : RingHomSurjective.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂] [_inst_19 : TopologicalSpace.{u4} R₁] [_inst_20 : TopologicalSpace.{u3} R₂] [_inst_21 : ContinuousSMul.{u4, u2} R₁ M₁ (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)))) _inst_19 _inst_4] [_inst_22 : ContinuousAdd.{u2} M₁ _inst_4 (AddZeroClass.toAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)))] [_inst_23 : ContinuousSMul.{u3, u1} R₂ M₂ (SMulZeroClass.toSMul.{u3, u1} R₂ M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u3, u1} R₂ M₂ (MonoidWithZero.toZero.{u3} R₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u3, u1} R₂ M₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16)))) _inst_20 _inst_8] [_inst_24 : ContinuousAdd.{u1} M₂ _inst_8 (AddZeroClass.toAdd.{u1} M₂ (AddMonoid.toAddZeroClass.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)))] {f : ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16}, (DenseRange.{u1, u2} M₂ _inst_8 M₁ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) f)) -> (forall {s : Submodule.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14}, (Eq.{succ u2} (Submodule.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) (Submodule.topologicalClosure.{u4, u2} R₁ M₁ _inst_1 _inst_4 _inst_5 _inst_14 (ContinuousSMul.continuousConstSMul.{u4, u2} R₁ M₁ _inst_19 _inst_4 (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)))) _inst_21) _inst_22 s) (Top.top.{u2} (Submodule.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) (Submodule.instTopSubmodule.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14))) -> (Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (Submodule.topologicalClosure.{u3, u1} R₂ M₂ _inst_2 _inst_8 _inst_9 _inst_16 (ContinuousSMul.continuousConstSMul.{u3, u1} R₂ M₂ _inst_20 _inst_8 (SMulZeroClass.toSMul.{u3, u1} R₂ M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u3, u1} R₂ M₂ (MonoidWithZero.toZero.{u3} R₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u3, u1} R₂ M₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16)))) _inst_23) _inst_24 (Submodule.map.{u4, u3, u2, u1, max u2 u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂ _inst_18 (LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f) s)) (Top.top.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (Submodule.instTopSubmodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16))))
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] [_inst_18 : RingHomSurjective.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂] [_inst_19 : TopologicalSpace.{u4} R₁] [_inst_20 : TopologicalSpace.{u3} R₂] [_inst_21 : ContinuousSMul.{u4, u2} R₁ M₁ (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)))) _inst_19 _inst_4] [_inst_22 : ContinuousAdd.{u2} M₁ _inst_4 (AddZeroClass.toAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)))] [_inst_23 : ContinuousSMul.{u3, u1} R₂ M₂ (SMulZeroClass.toSMul.{u3, u1} R₂ M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u3, u1} R₂ M₂ (MonoidWithZero.toZero.{u3} R₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u3, u1} R₂ M₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16)))) _inst_20 _inst_8] [_inst_24 : ContinuousAdd.{u1} M₂ _inst_8 (AddZeroClass.toAdd.{u1} M₂ (AddMonoid.toAddZeroClass.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)))] {f : ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16}, (DenseRange.{u1, u2} M₂ _inst_8 M₁ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) f)) -> (forall {s : Submodule.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14}, (Eq.{succ u2} (Submodule.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) (Submodule.topologicalClosure.{u4, u2} R₁ M₁ _inst_1 _inst_4 _inst_5 _inst_14 (ContinuousSMul.continuousConstSMul.{u4, u2} R₁ M₁ _inst_19 _inst_4 (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)))) _inst_21) _inst_22 s) (Top.top.{u2} (Submodule.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) (Submodule.instTopSubmodule.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14))) -> (Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (Submodule.topologicalClosure.{u3, u1} R₂ M₂ _inst_2 _inst_8 _inst_9 _inst_16 (ContinuousSMul.continuousConstSMul.{u3, u1} R₂ M₂ _inst_20 _inst_8 (SMulZeroClass.toSMul.{u3, u1} R₂ M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u3, u1} R₂ M₂ (MonoidWithZero.toZero.{u3} R₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u3, u1} R₂ M₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16)))) _inst_23) _inst_24 (Submodule.map.{u4, u3, u2, u1, max u2 u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂ _inst_18 (LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f) s)) (Top.top.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (Submodule.instTopSubmodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16))))
Case conversion may be inaccurate. Consider using '#align dense_range.topological_closure_map_submodule DenseRange.topologicalClosure_map_submoduleₓ'. -/
/-- Under a dense continuous linear map, a submodule whose `topological_closure` is `⊤` is sent to
another such submodule. That is, the image of a dense set under a map with dense range is dense.
@@ -1733,7 +1733,7 @@ theorem Submodule.coe_subtypeL (p : Submodule R₁ M₁) : (p.subtypeL : p →
lean 3 declaration is
forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] (p : Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14), Eq.{succ u2} ((coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) p) -> M₁) (coeFn.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) p) (Subtype.topologicalSpace.{u2} M₁ (fun (x : M₁) => Membership.Mem.{u2, u2} M₁ (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) p) (Subtype.topologicalSpace.{u2} M₁ (fun (x : M₁) => Membership.Mem.{u2, u2} M₁ (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14) => (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) p) -> M₁) (ContinuousLinearMap.toFun.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) p) (Subtype.topologicalSpace.{u2} M₁ (fun (x : M₁) => Membership.Mem.{u2, u2} M₁ (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14) (Submodule.subtypeL.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 p)) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) p) M₁ (Submodule.addCommMonoid.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_5 (Submodule.module.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14) (fun (_x : LinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) p) M₁ (Submodule.addCommMonoid.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_5 (Submodule.module.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14) => (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) p) -> M₁) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R₁ R₁ (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) p) M₁ _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_5 (Submodule.module.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Submodule.subtype.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14 p))
but is expected to have type
- forall {R₁ : Type.{u2}} [_inst_1 : Semiring.{u2} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_14 : Module.{u2, u1} R₁ M₁ _inst_1 _inst_5] (p : Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14), Eq.{succ u1} (forall (ᾰ : Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) => M₁) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (instTopologicalSpaceSubtype.{u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (fun (_x : Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) => M₁) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (instTopologicalSpaceSubtype.{u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) M₁ (instTopologicalSpaceSubtype.{u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (instTopologicalSpaceSubtype.{u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (instTopologicalSpaceSubtype.{u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (instTopologicalSpaceSubtype.{u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14))) (Submodule.subtypeL.{u2, u1} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 p)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) M₁ (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (fun (_x : Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) => M₁) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R₁ R₁ (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) M₁ _inst_1 _inst_1 (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) (Submodule.subtype.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p))
+ forall {R₁ : Type.{u2}} [_inst_1 : Semiring.{u2} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_14 : Module.{u2, u1} R₁ M₁ _inst_1 _inst_5] (p : Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14), Eq.{succ u1} (forall (ᾰ : Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) => M₁) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (instTopologicalSpaceSubtype.{u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (fun (_x : Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) => M₁) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (instTopologicalSpaceSubtype.{u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) M₁ (instTopologicalSpaceSubtype.{u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (instTopologicalSpaceSubtype.{u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (instTopologicalSpaceSubtype.{u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} 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Case conversion may be inaccurate. Consider using '#align submodule.coe_subtypeL' Submodule.coe_subtypeL'ₓ'. -/
@[simp]
theorem Submodule.coe_subtypeL' (p : Submodule R₁ M₁) : ⇑p.subtypeL = p.Subtype :=
@@ -2217,7 +2217,7 @@ protected theorem map_sub (f : M →SL[σ₁₂] M₂) (x y : M) : f (x - y) = f
lean 3 declaration is
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but is expected to have type
- forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_13 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))} (f : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (g : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_7 _inst_12 _inst_13 σ₁₂)) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 f) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 g)) x) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (instHSub.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubNegMonoid.toSub.{u1} ((fun 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_inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 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+ forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_13 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))} (f : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (g : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) 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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.sub_apply' ContinuousLinearMap.sub_apply'ₓ'. -/
@[simp]
theorem sub_apply' (f g : M →SL[σ₁₂] M₂) (x : M) : ((f : M →ₛₗ[σ₁₂] M₂) - g) x = f x - g x :=
@@ -2745,7 +2745,7 @@ def smulRightₗ (c : M →L[R] S) : M₂ →ₗ[T] M →L[R] M₂
lean 3 declaration is
forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} {M : Type.{u4}} {M₂ : Type.{u5}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : Semiring.{u3} T] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : AddCommMonoid.{u5} M₂] [_inst_6 : Module.{u1, u5} R M₂ _inst_1 _inst_5] [_inst_7 : Module.{u2, u5} S M₂ _inst_2 _inst_5] [_inst_8 : IsScalarTower.{u1, u2, u5} R S M₂ (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u5} S M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u2, u5} S M₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u5} R M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u1, u5} R M₂ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u1, u5} R M₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u1, u5} R M₂ _inst_1 _inst_5 _inst_6))))] [_inst_9 : TopologicalSpace.{u2} S] [_inst_10 : TopologicalSpace.{u5} M₂] [_inst_11 : ContinuousSMul.{u2, u5} S M₂ (SMulZeroClass.toHasSmul.{u2, u5} S M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u2, u5} S M₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) _inst_9 _inst_10] [_inst_12 : TopologicalSpace.{u4} M] [_inst_13 : AddCommMonoid.{u4} M] [_inst_14 : Module.{u1, u4} R M _inst_1 _inst_13] [_inst_15 : ContinuousAdd.{u5} M₂ _inst_10 (AddZeroClass.toHasAdd.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)))] [_inst_16 : Module.{u3, u5} T M₂ _inst_3 _inst_5] [_inst_17 : ContinuousConstSMul.{u3, u5} T M₂ _inst_10 (SMulZeroClass.toHasSmul.{u3, u5} T M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u3, u5} T M₂ (MulZeroClass.toHasZero.{u3} T (MulZeroOneClass.toMulZeroClass.{u3} T (MonoidWithZero.toMulZeroOneClass.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_18 : SMulCommClass.{u1, u3, u5} R T M₂ (SMulZeroClass.toHasSmul.{u1, u5} R M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u1, u5} R M₂ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u1, u5} R M₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u1, u5} R M₂ _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u3, u5} T M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u3, u5} T M₂ (MulZeroClass.toHasZero.{u3} T (MulZeroOneClass.toMulZeroClass.{u3} T (MonoidWithZero.toMulZeroOneClass.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_19 : SMulCommClass.{u2, u3, u5} S T M₂ (SMulZeroClass.toHasSmul.{u2, u5} S M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u2, u5} S M₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toHasSmul.{u3, u5} T M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u3, u5} T M₂ (MulZeroClass.toHasZero.{u3} T (MulZeroOneClass.toMulZeroClass.{u3} T (MonoidWithZero.toMulZeroOneClass.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))] (c : ContinuousLinearMap.{u1, u1, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 S _inst_9 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_14 _inst_4), Eq.{max (succ u5) (succ (max u4 u5))} (M₂ -> (ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6)) (coeFn.{max (succ u5) (succ (max u4 u5)), max (succ u5) (succ (max u4 u5))} (LinearMap.{u3, u3, u5, max u4 u5} T T _inst_3 _inst_3 (RingHom.id.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3)) M₂ (ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_5 (ContinuousLinearMap.addCommMonoid.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u1, u1, u3, u4, u5} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_15)) (fun (_x : LinearMap.{u3, u3, u5, max u4 u5} T T _inst_3 _inst_3 (RingHom.id.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3)) M₂ (ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_5 (ContinuousLinearMap.addCommMonoid.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u1, u1, u3, u4, u5} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_15)) => M₂ -> (ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6)) (LinearMap.hasCoeToFun.{u3, u3, u5, max u4 u5} T T M₂ (ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_3 _inst_3 _inst_5 (ContinuousLinearMap.addCommMonoid.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u1, u1, u3, u4, u5} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_15) (RingHom.id.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3))) (ContinuousLinearMap.smulRightₗ.{u1, u2, u3, u4, u5} R S T M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 _inst_19 c)) (ContinuousLinearMap.smulRight.{u4, u5, u1, u2} M _inst_12 _inst_13 M₂ _inst_10 _inst_5 R S _inst_1 _inst_2 _inst_14 _inst_6 _inst_4 _inst_7 _inst_8 _inst_9 _inst_11 c)
but is expected to have type
- forall {R : Type.{u5}} {S : Type.{u3}} {T : Type.{u1}} {M : Type.{u4}} {M₂ : Type.{u2}} [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u3} S] [_inst_3 : Semiring.{u1} T] [_inst_4 : Module.{u5, u3} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2)))] [_inst_5 : AddCommMonoid.{u2} M₂] [_inst_6 : Module.{u5, u2} R M₂ _inst_1 _inst_5] [_inst_7 : Module.{u3, u2} S M₂ _inst_2 _inst_5] [_inst_8 : IsScalarTower.{u5, u3, u2} R S M₂ (SMulZeroClass.toSMul.{u5, u3} R S (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (SMulWithZero.toSMulZeroClass.{u5, u3} R S (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (MulActionWithZero.toSMulWithZero.{u5, u3} R S (Semiring.toMonoidWithZero.{u5} R _inst_1) (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (Module.toMulActionWithZero.{u5, u3} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2))) _inst_4)))) (SMulZeroClass.toSMul.{u3, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u2} S M₂ (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u2} S M₂ (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u2} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toSMul.{u5, u2} R M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R M₂ (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R M₂ (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u5, u2} R M₂ _inst_1 _inst_5 _inst_6))))] [_inst_9 : TopologicalSpace.{u3} S] [_inst_10 : TopologicalSpace.{u2} M₂] [_inst_11 : ContinuousSMul.{u3, u2} S M₂ (SMulZeroClass.toSMul.{u3, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u2} S M₂ (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u2} S M₂ (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u2} S M₂ _inst_2 _inst_5 _inst_7)))) _inst_9 _inst_10] [_inst_12 : TopologicalSpace.{u4} M] [_inst_13 : AddCommMonoid.{u4} M] [_inst_14 : Module.{u5, u4} R M _inst_1 _inst_13] [_inst_15 : ContinuousAdd.{u2} M₂ _inst_10 (AddZeroClass.toAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)))] [_inst_16 : Module.{u1, u2} T M₂ _inst_3 _inst_5] [_inst_17 : ContinuousConstSMul.{u1, u2} T M₂ _inst_10 (SMulZeroClass.toSMul.{u1, u2} T M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} T M₂ (MonoidWithZero.toZero.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} T M₂ (Semiring.toMonoidWithZero.{u1} T _inst_3) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u1, u2} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_18 : SMulCommClass.{u5, u1, u2} R T M₂ (SMulZeroClass.toSMul.{u5, u2} R M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R M₂ (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R M₂ (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u5, u2} R M₂ _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u2} T M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} T M₂ (MonoidWithZero.toZero.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} T M₂ (Semiring.toMonoidWithZero.{u1} T _inst_3) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u1, u2} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_19 : SMulCommClass.{u3, u1, u2} S T M₂ (SMulZeroClass.toSMul.{u3, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u2} S M₂ (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u2} S M₂ (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u2} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toSMul.{u1, u2} T M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} T M₂ (MonoidWithZero.toZero.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} T M₂ (Semiring.toMonoidWithZero.{u1} T _inst_3) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u1, u2} T M₂ _inst_3 _inst_5 _inst_16))))] (c : ContinuousLinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 S _inst_9 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2))) _inst_14 _inst_4), Eq.{max (succ u4) (succ u2)} (forall (ᾰ : M₂), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₂) => ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) ᾰ) (FunLike.coe.{max (succ u4) (succ u2), succ u2, max (succ u4) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u4} T T _inst_3 _inst_3 (RingHom.id.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3)) M₂ (ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_5 (ContinuousLinearMap.addCommMonoid.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u5, u5, u1, u4, u2} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_15)) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₂) => ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u4 u2} T T M₂ (ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_3 _inst_3 _inst_5 (ContinuousLinearMap.addCommMonoid.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u5, u5, u1, u4, u2} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_15) (RingHom.id.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3))) (ContinuousLinearMap.smulRightₗ.{u5, u3, u1, u4, u2} R S T M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 _inst_19 c)) (ContinuousLinearMap.smulRight.{u4, u2, u5, u3} M _inst_12 _inst_13 M₂ _inst_10 _inst_5 R S _inst_1 _inst_2 _inst_14 _inst_6 _inst_4 _inst_7 _inst_8 _inst_9 _inst_11 c)
+ forall {R : Type.{u5}} {S : Type.{u3}} {T : Type.{u1}} {M : Type.{u4}} {M₂ : Type.{u2}} [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u3} S] [_inst_3 : Semiring.{u1} T] [_inst_4 : Module.{u5, u3} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2)))] [_inst_5 : AddCommMonoid.{u2} M₂] [_inst_6 : Module.{u5, u2} R M₂ _inst_1 _inst_5] [_inst_7 : Module.{u3, u2} S M₂ _inst_2 _inst_5] [_inst_8 : IsScalarTower.{u5, u3, u2} R S M₂ (SMulZeroClass.toSMul.{u5, u3} R S (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (SMulWithZero.toSMulZeroClass.{u5, u3} R S (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (MulActionWithZero.toSMulWithZero.{u5, u3} R S (Semiring.toMonoidWithZero.{u5} R _inst_1) (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (Module.toMulActionWithZero.{u5, u3} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2))) _inst_4)))) (SMulZeroClass.toSMul.{u3, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u2} S M₂ (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u2} S M₂ (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u2} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toSMul.{u5, u2} R M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R M₂ (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R M₂ (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u5, u2} R M₂ _inst_1 _inst_5 _inst_6))))] [_inst_9 : TopologicalSpace.{u3} S] [_inst_10 : TopologicalSpace.{u2} M₂] [_inst_11 : ContinuousSMul.{u3, u2} S M₂ (SMulZeroClass.toSMul.{u3, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u2} S M₂ (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u2} S M₂ (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u2} S M₂ _inst_2 _inst_5 _inst_7)))) _inst_9 _inst_10] [_inst_12 : TopologicalSpace.{u4} M] [_inst_13 : AddCommMonoid.{u4} M] [_inst_14 : Module.{u5, u4} R M _inst_1 _inst_13] [_inst_15 : ContinuousAdd.{u2} M₂ _inst_10 (AddZeroClass.toAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)))] [_inst_16 : Module.{u1, u2} T M₂ _inst_3 _inst_5] [_inst_17 : ContinuousConstSMul.{u1, u2} T M₂ _inst_10 (SMulZeroClass.toSMul.{u1, u2} T M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} T M₂ (MonoidWithZero.toZero.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} T M₂ (Semiring.toMonoidWithZero.{u1} T _inst_3) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u1, u2} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_18 : SMulCommClass.{u5, u1, u2} R T M₂ (SMulZeroClass.toSMul.{u5, u2} R M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R M₂ (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R M₂ (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u5, u2} R M₂ _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u2} T M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} T M₂ (MonoidWithZero.toZero.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} T M₂ (Semiring.toMonoidWithZero.{u1} T _inst_3) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u1, u2} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_19 : SMulCommClass.{u3, u1, u2} S T M₂ (SMulZeroClass.toSMul.{u3, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u2} S M₂ (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u2} S M₂ (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u2} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toSMul.{u1, u2} T M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} T M₂ (MonoidWithZero.toZero.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} T M₂ (Semiring.toMonoidWithZero.{u1} T _inst_3) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u1, u2} T M₂ _inst_3 _inst_5 _inst_16))))] (c : ContinuousLinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 S _inst_9 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2))) _inst_14 _inst_4), Eq.{max (succ u4) (succ u2)} (forall (ᾰ : M₂), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₂) => ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) ᾰ) (FunLike.coe.{max (succ u4) (succ u2), succ u2, max (succ u4) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u4} T T _inst_3 _inst_3 (RingHom.id.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3)) M₂ (ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_5 (ContinuousLinearMap.addCommMonoid.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u5, u5, u1, u4, u2} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_15)) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₂) => ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u4 u2} T T M₂ (ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_3 _inst_3 _inst_5 (ContinuousLinearMap.addCommMonoid.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u5, u5, u1, u4, u2} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_15) (RingHom.id.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3))) (ContinuousLinearMap.smulRightₗ.{u5, u3, u1, u4, u2} R S T M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 _inst_19 c)) (ContinuousLinearMap.smulRight.{u4, u2, u5, u3} M _inst_12 _inst_13 M₂ _inst_10 _inst_5 R S _inst_1 _inst_2 _inst_14 _inst_6 _inst_4 _inst_7 _inst_8 _inst_9 _inst_11 c)
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_smul_rightₗ ContinuousLinearMap.coe_smulRightₗₓ'. -/
@[simp]
theorem coe_smulRightₗ (c : M →L[R] S) : ⇑(smulRightₗ c : M₂ →ₗ[T] M →L[R] M₂) = c.smul_right :=
@@ -2881,7 +2881,7 @@ variable {A M M₂ R S}
lean 3 declaration is
forall {A : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u4}} [_inst_8 : Ring.{u4} R] [_inst_9 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_10 : Module.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u2, u3, u4, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toHasSmul.{u4, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u4, u2} R M (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u4, u2} R M (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5] {S : Type.{u5}} [_inst_12 : Ring.{u5} S] [_inst_13 : Module.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_14 : ContinuousConstSMul.{u5, u3} S M₂ _inst_7 (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_15 : SMulCommClass.{u1, u5, u3} A S M₂ (SMulZeroClass.toHasSmul.{u1, u3} A M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u1, u3} A M₂ (MulZeroClass.toHasZero.{u1} A (MulZeroOneClass.toMulZeroClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A _inst_1))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u1, u3} A M₂ (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A _inst_1)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_16 : SMulCommClass.{u4, u5, u3} R S M₂ (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_17 : TopologicalAddGroup.{u3} M₂ _inst_7 (AddCommGroup.toAddGroup.{u3} M₂ _inst_3)], Eq.{succ (max u2 u3)} ((ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) -> (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10)) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (LinearMap.{u5, u5, max u2 u3, max u2 u3} S S (Ring.toSemiring.{u5} S _inst_12) (Ring.toSemiring.{u5} S 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(Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5 (ContinuousLinearMap.restrictScalarsₗ._proof_1.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.addCommMonoid.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10 _inst_13 _inst_16 _inst_14 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) (ContinuousLinearMap.restrictScalarsₗ._proof_4.{u3} M₂ _inst_3 _inst_7 _inst_17))) => (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) -> (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10)) (LinearMap.hasCoeToFun.{u5, u5, max u2 u3, max u2 u3} S S (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (Ring.toSemiring.{u5} S _inst_12) (Ring.toSemiring.{u5} S _inst_12) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5 (ContinuousLinearMap.restrictScalarsₗ._proof_1.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.addCommMonoid.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10 (ContinuousLinearMap.restrictScalarsₗ._proof_2.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.module.{u1, u1, u5, u2, u3} A A S (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u5} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5 _inst_13 _inst_15 _inst_14 (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) (ContinuousLinearMap.restrictScalarsₗ._proof_3.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.module.{u4, u4, u5, u2, u3} R R S (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u5} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10 _inst_13 _inst_16 _inst_14 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) (ContinuousLinearMap.restrictScalarsₗ._proof_4.{u3} M₂ _inst_3 _inst_7 _inst_17)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S (Ring.toSemiring.{u5} S _inst_12)))) (ContinuousLinearMap.restrictScalarsₗ.{u1, u2, u3, u4, u5} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 S _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17)) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11)
but is expected to have type
- forall {A : Type.{u3}} {M : Type.{u5}} {M₂ : Type.{u4}} [_inst_1 : Ring.{u3} A] [_inst_2 : AddCommGroup.{u5} M] [_inst_3 : AddCommGroup.{u4} M₂] [_inst_4 : Module.{u3, u5} A M (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2)] [_inst_5 : Module.{u3, u4} A M₂ (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u5} M] [_inst_7 : TopologicalSpace.{u4} M₂] {R : Type.{u2}} [_inst_8 : Ring.{u2} R] [_inst_9 : Module.{u2, u5} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2)] [_inst_10 : Module.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u5, u4, u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) R A (Ring.toSemiring.{u3} A _inst_1) (SMulZeroClass.toSMul.{u2, u5} R M (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u5} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u5} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (Module.toMulActionWithZero.{u2, u5} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u2, u4} R M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10)))) _inst_5] {S : Type.{u1}} [_inst_12 : Ring.{u1} S] [_inst_13 : Module.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_14 : ContinuousConstSMul.{u1, u4} S M₂ _inst_7 (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_15 : SMulCommClass.{u3, u1, u4} A S M₂ (SMulZeroClass.toSMul.{u3, u4} A M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u3, u4} A M₂ (MonoidWithZero.toZero.{u3} A (Semiring.toMonoidWithZero.{u3} A (Ring.toSemiring.{u3} A _inst_1))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A M₂ (Semiring.toMonoidWithZero.{u3} A (Ring.toSemiring.{u3} A _inst_1)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u3, u4} A M₂ (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_16 : SMulCommClass.{u2, u1, u4} R S M₂ (SMulZeroClass.toSMul.{u2, u4} R M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10)))) (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_17 : TopologicalAddGroup.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3)], Eq.{max (succ u5) (succ u4)} (forall (ᾰ : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) => ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10) ᾰ) (FunLike.coe.{max (succ u5) (succ u4), max (succ u5) (succ u4), max (succ u5) (succ u4)} (LinearMap.{u1, u1, max u4 u5, max u4 u5} S S (Ring.toSemiring.{u1} S _inst_12) (Ring.toSemiring.{u1} S _inst_12) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.addCommMonoid.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5 (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.addCommMonoid.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10 (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.module.{u3, u3, u1, u5, u4} A A S (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u1} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_4 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_5 _inst_13 _inst_15 _inst_14 (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.module.{u2, u2, u1, u5, u4} R R S (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_9 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10 _inst_13 _inst_16 _inst_14 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17))) (ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) (fun (_x : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) => ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u5 u4, max u5 u4} S S (ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10) (Ring.toSemiring.{u1} S _inst_12) (Ring.toSemiring.{u1} S _inst_12) (ContinuousLinearMap.addCommMonoid.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5 (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.addCommMonoid.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10 (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.module.{u3, u3, u1, u5, u4} A A S (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u1} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_4 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_5 _inst_13 _inst_15 _inst_14 (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.module.{u2, u2, u1, u5, u4} R R S (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_9 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10 _inst_13 _inst_16 _inst_14 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_12)))) (ContinuousLinearMap.restrictScalarsₗ.{u3, u5, u4, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 S _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17)) (ContinuousLinearMap.restrictScalars.{u3, u5, u4, u2} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11)
+ forall {A : Type.{u3}} {M : Type.{u5}} {M₂ : Type.{u4}} [_inst_1 : Ring.{u3} A] [_inst_2 : AddCommGroup.{u5} M] [_inst_3 : AddCommGroup.{u4} M₂] [_inst_4 : Module.{u3, u5} A M (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2)] [_inst_5 : Module.{u3, u4} A M₂ (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u5} M] [_inst_7 : TopologicalSpace.{u4} M₂] {R : Type.{u2}} [_inst_8 : Ring.{u2} R] [_inst_9 : Module.{u2, u5} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2)] [_inst_10 : Module.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u5, u4, u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) R A (Ring.toSemiring.{u3} A _inst_1) (SMulZeroClass.toSMul.{u2, u5} R M (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u5} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u5} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (Module.toMulActionWithZero.{u2, u5} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u2, u4} R M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10)))) _inst_5] {S : Type.{u1}} [_inst_12 : Ring.{u1} S] [_inst_13 : Module.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_14 : ContinuousConstSMul.{u1, u4} S M₂ _inst_7 (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_15 : SMulCommClass.{u3, u1, u4} A S M₂ (SMulZeroClass.toSMul.{u3, u4} A M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u3, u4} A M₂ (MonoidWithZero.toZero.{u3} A (Semiring.toMonoidWithZero.{u3} A (Ring.toSemiring.{u3} A _inst_1))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A M₂ (Semiring.toMonoidWithZero.{u3} A (Ring.toSemiring.{u3} A _inst_1)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u3, u4} A M₂ (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_16 : SMulCommClass.{u2, u1, u4} R S M₂ (SMulZeroClass.toSMul.{u2, u4} R M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10)))) (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_17 : TopologicalAddGroup.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3)], Eq.{max (succ u5) (succ u4)} (forall (ᾰ : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) => ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10) ᾰ) (FunLike.coe.{max (succ u5) (succ u4), max (succ u5) (succ u4), max (succ u5) (succ u4)} (LinearMap.{u1, u1, max u4 u5, max u4 u5} S S (Ring.toSemiring.{u1} S _inst_12) (Ring.toSemiring.{u1} S _inst_12) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.addCommMonoid.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5 (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.addCommMonoid.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10 (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.module.{u3, u3, u1, u5, u4} A A S (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u1} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_4 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_5 _inst_13 _inst_15 _inst_14 (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.module.{u2, u2, u1, u5, u4} R R S (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_9 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10 _inst_13 _inst_16 _inst_14 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17))) (ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) (fun (_x : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) => ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u5 u4, max u5 u4} S S (ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10) (Ring.toSemiring.{u1} S _inst_12) (Ring.toSemiring.{u1} S _inst_12) (ContinuousLinearMap.addCommMonoid.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5 (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.addCommMonoid.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10 (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.module.{u3, u3, u1, u5, u4} A A S (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u1} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_4 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_5 _inst_13 _inst_15 _inst_14 (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.module.{u2, u2, u1, u5, u4} R R S (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_9 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10 _inst_13 _inst_16 _inst_14 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_12)))) (ContinuousLinearMap.restrictScalarsₗ.{u3, u5, u4, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 S _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17)) (ContinuousLinearMap.restrictScalars.{u3, u5, u4, u2} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11)
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_restrict_scalarsₗ ContinuousLinearMap.coe_restrictScalarsₗₓ'. -/
@[simp]
theorem coe_restrictScalarsₗ : ⇑(restrictScalarsₗ A M M₂ R S) = restrictScalars R :=
@@ -4392,7 +4392,7 @@ variable {R M : Type _} [Ring R] [AddCommGroup M] [Module R M] [TopologicalSpace
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : TopologicalSpace.{u2} M] (S : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : TopologicalAddGroup.{u2} M _inst_4 (AddCommGroup.toAddGroup.{u2} M _inst_2)], IsOpenMap.{u2, u2} M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) _inst_4 (Quotient.topologicalSpace.{u2} M (Submodule.quotientRel.{u1, u2} R M _inst_1 _inst_2 _inst_3 S) _inst_4) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) => M -> (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 S))
but is expected to have type
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : TopologicalSpace.{u2} M] (S : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : TopologicalAddGroup.{u2} M _inst_4 (AddCommGroup.toAddGroup.{u2} M _inst_2)], IsOpenMap.{u2, u2} M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) _inst_4 (QuotientModule.Quotient.topologicalSpace.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 S) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 S))
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : TopologicalSpace.{u2} M] (S : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : TopologicalAddGroup.{u2} M _inst_4 (AddCommGroup.toAddGroup.{u2} M _inst_2)], IsOpenMap.{u2, u2} M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) _inst_4 (QuotientModule.Quotient.topologicalSpace.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 S) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 S))
Case conversion may be inaccurate. Consider using '#align submodule.is_open_map_mkq Submodule.isOpenMap_mkQₓ'. -/
theorem isOpenMap_mkQ [TopologicalAddGroup M] : IsOpenMap S.mkQ :=
QuotientAddGroup.isOpenMap_coe S.toAddSubgroup
mathlib commit https://github.com/leanprover-community/mathlib/commit/f8c79b0a623404854a2902b836eac32156fd7712
@@ -1378,9 +1378,9 @@ instance : Mul (M₁ →L[R₁] M₁) :=
/- warning: continuous_linear_map.mul_def -> ContinuousLinearMap.mul_def is a dubious translation:
lean 3 declaration is
- forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] (f : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (g : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14), Eq.{succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (HMul.hMul.{u2, u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (instHMul.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.mul.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14)) f g) (ContinuousLinearMap.comp.{u1, u1, u1, u2, u2, u2} R₁ R₁ R₁ _inst_1 _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14 _inst_14 (RingHomCompTriple.right_ids.{u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) f g)
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] (f : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (g : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14), Eq.{succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (HMul.hMul.{u2, u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (instHMul.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.instMul.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14)) f g) (ContinuousLinearMap.comp.{u1, u1, u1, u2, u2, u2} R₁ R₁ R₁ _inst_1 _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14 _inst_14 (RingHomCompTriple.right_ids.{u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) f g)
but is expected to have type
- forall {R₁ : Type.{u2}} [_inst_1 : Semiring.{u2} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_14 : Module.{u2, u1} R₁ M₁ _inst_1 _inst_5] (f : ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (g : ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14), Eq.{succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (HMul.hMul.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (instHMul.{u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.mul.{u2, u1} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14)) f g) (ContinuousLinearMap.comp.{u2, u2, u2, u1, u1, u1} R₁ R₁ R₁ _inst_1 _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14 _inst_14 (RingHomCompTriple.ids.{u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) f g)
+ forall {R₁ : Type.{u2}} [_inst_1 : Semiring.{u2} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_14 : Module.{u2, u1} R₁ M₁ _inst_1 _inst_5] (f : ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (g : ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14), Eq.{succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (HMul.hMul.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (instHMul.{u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.instMul.{u2, u1} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14)) f g) (ContinuousLinearMap.comp.{u2, u2, u2, u1, u1, u1} R₁ R₁ R₁ _inst_1 _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14 _inst_14 (RingHomCompTriple.ids.{u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) f g)
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.mul_def ContinuousLinearMap.mul_defₓ'. -/
theorem mul_def (f g : M₁ →L[R₁] M₁) : f * g = f.comp g :=
rfl
@@ -1388,9 +1388,9 @@ theorem mul_def (f g : M₁ →L[R₁] M₁) : f * g = f.comp g :=
/- warning: continuous_linear_map.coe_mul -> ContinuousLinearMap.coe_mul is a dubious translation:
lean 3 declaration is
- forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] (f : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (g : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14), Eq.{succ u2} (M₁ -> M₁) (coeFn.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) => M₁ -> M₁) (ContinuousLinearMap.toFun.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (HMul.hMul.{u2, u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (instHMul.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.mul.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14)) f g)) (Function.comp.{succ u2, succ u2, succ u2} M₁ M₁ M₁ (coeFn.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) => M₁ -> M₁) (ContinuousLinearMap.toFun.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) f) (coeFn.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) => M₁ -> M₁) (ContinuousLinearMap.toFun.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) g))
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] (f : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (g : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14), Eq.{succ u2} (M₁ -> M₁) (coeFn.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) => M₁ -> M₁) (ContinuousLinearMap.toFun.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (HMul.hMul.{u2, u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (instHMul.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.instMul.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14)) f g)) (Function.comp.{succ u2, succ u2, succ u2} M₁ M₁ M₁ (coeFn.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) => M₁ -> M₁) (ContinuousLinearMap.toFun.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) f) (coeFn.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) => M₁ -> M₁) (ContinuousLinearMap.toFun.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) g))
but is expected to have type
- forall {R₁ : Type.{u2}} [_inst_1 : Semiring.{u2} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_14 : Module.{u2, u1} R₁ M₁ _inst_1 _inst_5] (f : ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (g : ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14), Eq.{succ u1} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₁) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₁) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ M₁ _inst_4 _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14))) (HMul.hMul.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (instHMul.{u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.mul.{u2, u1} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14)) f g)) (Function.comp.{succ u1, succ u1, succ u1} M₁ M₁ M₁ (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₁) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ M₁ _inst_4 _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14))) f) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₁) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ M₁ _inst_4 _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14))) g))
+ forall {R₁ : Type.{u2}} [_inst_1 : Semiring.{u2} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_14 : Module.{u2, u1} R₁ M₁ _inst_1 _inst_5] (f : ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (g : ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14), Eq.{succ u1} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₁) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₁) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ M₁ _inst_4 _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14))) (HMul.hMul.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (instHMul.{u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.instMul.{u2, u1} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14)) f g)) (Function.comp.{succ u1, succ u1, succ u1} M₁ M₁ M₁ (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₁) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ M₁ _inst_4 _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14))) f) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₁) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ M₁ _inst_4 _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14))) g))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_mul ContinuousLinearMap.coe_mulₓ'. -/
@[simp]
theorem coe_mul (f g : M₁ →L[R₁] M₁) : ⇑(f * g) = f ∘ g :=
@@ -1399,9 +1399,9 @@ theorem coe_mul (f g : M₁ →L[R₁] M₁) : ⇑(f * g) = f ∘ g :=
/- warning: continuous_linear_map.mul_apply -> ContinuousLinearMap.mul_apply is a dubious translation:
lean 3 declaration is
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but is expected to have type
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(Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (instHMul.{u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.mul.{u2, u1} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14)) f g) x) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₁) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ M₁ _inst_4 _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14))) f (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₁) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ M₁ _inst_4 _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14))) g x))
+ forall {R₁ : Type.{u2}} [_inst_1 : Semiring.{u2} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_14 : Module.{u2, u1} R₁ M₁ _inst_1 _inst_5] (f : ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (g : ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (x : M₁), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₁) x) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₁) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ M₁ _inst_4 _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14))) (HMul.hMul.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (instHMul.{u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.instMul.{u2, u1} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14)) f g) x) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₁) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ M₁ _inst_4 _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14))) f (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₁) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ M₁ _inst_4 _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14))) g x))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.mul_apply ContinuousLinearMap.mul_applyₓ'. -/
theorem mul_apply (f g : M₁ →L[R₁] M₁) (x : M₁) : (f * g) x = f (g x) :=
rfl
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -272,7 +272,7 @@ theorem Submodule.topologicalClosure_coe (s : Submodule R M) :
/- warning: submodule.le_topological_closure -> Submodule.le_topologicalClosure is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))] (s : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5), LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) s (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 s)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))] (s : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5), LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) s (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 s)
but is expected to have type
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] [_inst_5 : ContinuousConstSMul.{u1, u2} R M _inst_2 (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_3 _inst_4))))] [_inst_6 : ContinuousAdd.{u2} M _inst_2 (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))] (_inst_7 : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4), LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))))) _inst_7 (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7)
Case conversion may be inaccurate. Consider using '#align submodule.le_topological_closure Submodule.le_topologicalClosureₓ'. -/
@@ -292,7 +292,7 @@ theorem Submodule.isClosed_topologicalClosure (s : Submodule R M) :
/- warning: submodule.topological_closure_minimal -> Submodule.topologicalClosure_minimal is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))] (s : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) {t : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5}, (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) s t) -> (IsClosed.{u2} M _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) t)) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 s) t)
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))] (s : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) {t : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5}, (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) s t) -> (IsClosed.{u2} M _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) t)) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 s) t)
but is expected to have type
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] [_inst_5 : ContinuousConstSMul.{u1, u2} R M _inst_2 (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_3 _inst_4))))] [_inst_6 : ContinuousAdd.{u2} M _inst_2 (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))] (_inst_7 : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) {s : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))))) _inst_7 s) -> (IsClosed.{u2} M _inst_2 (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) s)) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))))) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) s)
Case conversion may be inaccurate. Consider using '#align submodule.topological_closure_minimal Submodule.topologicalClosure_minimalₓ'. -/
@@ -303,7 +303,7 @@ theorem Submodule.topologicalClosure_minimal (s : Submodule R M) {t : Submodule
/- warning: submodule.topological_closure_mono -> Submodule.topologicalClosure_mono is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))] {s : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5} {t : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5}, (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) s t) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 s) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 t))
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))] {s : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5} {t : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5}, (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) s t) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 s) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 t))
but is expected to have type
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] [_inst_5 : ContinuousConstSMul.{u1, u2} R M _inst_2 (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_3 _inst_4))))] [_inst_6 : ContinuousAdd.{u2} M _inst_2 (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))] {_inst_7 : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {s : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))))) _inst_7 s) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))))) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))
Case conversion may be inaccurate. Consider using '#align submodule.topological_closure_mono Submodule.topologicalClosure_monoₓ'. -/
@@ -898,7 +898,7 @@ theorem ext_on [T2Space M₂] {s : Set M₁} (hs : Dense (Submodule.span R₁ s
/- warning: submodule.topological_closure_map -> Submodule.topologicalClosure_map is a dubious translation:
lean 3 declaration is
- forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] [_inst_14 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_9] [_inst_18 : RingHomSurjective.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂] [_inst_19 : TopologicalSpace.{u1} R₁] [_inst_20 : TopologicalSpace.{u2} R₂] [_inst_21 : ContinuousSMul.{u1, u3} R₁ M₁ (SMulZeroClass.toHasSmul.{u1, u3} R₁ M₁ (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5))) (SMulWithZero.toSmulZeroClass.{u1, u3} R₁ M₁ (MulZeroClass.toHasZero.{u1} R₁ (MulZeroOneClass.toMulZeroClass.{u1} R₁ (MonoidWithZero.toMulZeroOneClass.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)))) (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5))) (MulActionWithZero.toSMulWithZero.{u1, u3} R₁ M₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5))) (Module.toMulActionWithZero.{u1, u3} R₁ M₁ _inst_1 _inst_5 _inst_14)))) _inst_19 _inst_4] [_inst_22 : ContinuousAdd.{u3} M₁ _inst_4 (AddZeroClass.toHasAdd.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5)))] [_inst_23 : ContinuousSMul.{u2, u4} R₂ M₂ (SMulZeroClass.toHasSmul.{u2, u4} R₂ M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (SMulWithZero.toSmulZeroClass.{u2, u4} R₂ M₂ (MulZeroClass.toHasZero.{u2} R₂ (MulZeroOneClass.toMulZeroClass.{u2} R₂ (MonoidWithZero.toMulZeroOneClass.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)))) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (MulActionWithZero.toSMulWithZero.{u2, u4} R₂ M₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (Module.toMulActionWithZero.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)))) _inst_20 _inst_8] [_inst_24 : ContinuousAdd.{u4} M₂ _inst_8 (AddZeroClass.toHasAdd.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9)))] (f : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (s : Submodule.{u1, u3} R₁ M₁ _inst_1 _inst_5 _inst_14), LE.le.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) (Preorder.toLE.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) (PartialOrder.toPreorder.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) (SetLike.partialOrder.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)))) (Submodule.map.{u1, u2, u3, u4, max u3 u4} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂ _inst_18 (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) ((fun (a : Sort.{max (succ u3) (succ u4)}) (b : Sort.{max (succ u3) (succ u4)}) [self : HasLiftT.{max (succ u3) (succ u4), max (succ u3) (succ u4)} a b] => self.0) (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (HasLiftT.mk.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 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_inst_16 _inst_23 _inst_24 (Submodule.map.{u1, u2, u3, u4, max u3 u4} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂ _inst_18 (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) ((fun (a : Sort.{max (succ u3) (succ u4)}) (b : Sort.{max (succ u3) (succ u4)}) [self : HasLiftT.{max (succ u3) (succ u4), max (succ u3) (succ u4)} a b] => self.0) (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (HasLiftT.mk.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 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+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] [_inst_14 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_9] [_inst_18 : RingHomSurjective.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂] [_inst_19 : TopologicalSpace.{u1} R₁] [_inst_20 : TopologicalSpace.{u2} R₂] [_inst_21 : ContinuousSMul.{u1, u3} R₁ M₁ (SMulZeroClass.toHasSmul.{u1, u3} R₁ M₁ (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5))) (SMulWithZero.toSmulZeroClass.{u1, u3} R₁ M₁ (MulZeroClass.toHasZero.{u1} R₁ (MulZeroOneClass.toMulZeroClass.{u1} R₁ (MonoidWithZero.toMulZeroOneClass.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)))) (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5))) (MulActionWithZero.toSMulWithZero.{u1, u3} R₁ M₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5))) (Module.toMulActionWithZero.{u1, u3} R₁ M₁ _inst_1 _inst_5 _inst_14)))) _inst_19 _inst_4] [_inst_22 : ContinuousAdd.{u3} M₁ _inst_4 (AddZeroClass.toHasAdd.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5)))] [_inst_23 : ContinuousSMul.{u2, u4} R₂ M₂ (SMulZeroClass.toHasSmul.{u2, u4} R₂ M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (SMulWithZero.toSmulZeroClass.{u2, u4} R₂ M₂ (MulZeroClass.toHasZero.{u2} R₂ (MulZeroOneClass.toMulZeroClass.{u2} R₂ (MonoidWithZero.toMulZeroOneClass.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)))) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (MulActionWithZero.toSMulWithZero.{u2, u4} R₂ M₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (Module.toMulActionWithZero.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)))) _inst_20 _inst_8] [_inst_24 : ContinuousAdd.{u4} M₂ _inst_8 (AddZeroClass.toHasAdd.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9)))] (f : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (s : Submodule.{u1, u3} R₁ M₁ _inst_1 _inst_5 _inst_14), LE.le.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) (Preorder.toHasLe.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) (PartialOrder.toPreorder.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) 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but is expected to have type
forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] [_inst_18 : RingHomSurjective.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂] [_inst_19 : TopologicalSpace.{u4} R₁] [_inst_20 : TopologicalSpace.{u3} R₂] [_inst_21 : ContinuousSMul.{u4, u2} R₁ M₁ (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)))) _inst_19 _inst_4] [_inst_22 : ContinuousAdd.{u2} M₁ _inst_4 (AddZeroClass.toAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)))] [_inst_23 : ContinuousSMul.{u3, u1} R₂ M₂ (SMulZeroClass.toSMul.{u3, u1} R₂ M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u3, u1} R₂ M₂ (MonoidWithZero.toZero.{u3} R₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u3, u1} R₂ M₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16)))) _inst_20 _inst_8] [_inst_24 : ContinuousAdd.{u1} M₂ _inst_8 (AddZeroClass.toAdd.{u1} M₂ (AddMonoid.toAddZeroClass.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)))] (f : ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (s : Submodule.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14), LE.le.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (Preorder.toLE.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (PartialOrder.toPreorder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (Submodule.completeLattice.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16))))) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂ _inst_18 (LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f) (Submodule.topologicalClosure.{u4, u2} R₁ M₁ _inst_1 _inst_4 _inst_5 _inst_14 (ContinuousSMul.continuousConstSMul.{u4, u2} R₁ M₁ _inst_19 _inst_4 (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)))) _inst_21) _inst_22 s)) (Submodule.topologicalClosure.{u3, u1} R₂ M₂ _inst_2 _inst_8 _inst_9 _inst_16 (ContinuousSMul.continuousConstSMul.{u3, u1} R₂ M₂ _inst_20 _inst_8 (SMulZeroClass.toSMul.{u3, u1} R₂ M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u3, u1} R₂ M₂ (MonoidWithZero.toZero.{u3} R₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u3, u1} R₂ M₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16)))) _inst_23) _inst_24 (Submodule.map.{u4, u3, u2, u1, max u2 u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂ _inst_18 (LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f) s))
Case conversion may be inaccurate. Consider using '#align submodule.topological_closure_map Submodule.topologicalClosure_mapₓ'. -/
@@ -2243,7 +2243,7 @@ theorem range_prod_eq {f : M →L[R] M₂} {g : M →L[R] M₃} (h : ker f ⊔ k
/- warning: continuous_linear_map.ker_prod_ker_le_ker_coprod -> ContinuousLinearMap.ker_prod_ker_le_ker_coprod is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] {M₃ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₃] [_inst_9 : AddCommGroup.{u4} M₃] [_inst_12 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_15 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_16 : Module.{u1, u4} R M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)] [_inst_18 : ContinuousAdd.{u4} M₃ _inst_8 (AddZeroClass.toHasAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (SubNegMonoid.toAddMonoid.{u4} M₃ (AddGroup.toSubNegMonoid.{u4} M₃ (AddCommGroup.toAddGroup.{u4} M₃ _inst_9)))))] (f : ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (g : ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16), LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M₂) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15)) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M₂) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15)) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M₂) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15)) (SetLike.partialOrder.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M₂) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15)) (Prod.{u2, u3} M M₂) (Submodule.setLike.{u1, max u2 u3} R (Prod.{u2, u3} M M₂) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15))))) (Submodule.prod.{u1, u2, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12 (LinearMap.ker.{u1, u1, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u1, u1, u2, u4} (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16)) f) M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_15 (LinearMap.ker.{u1, u1, u3, u4, max u3 u4} R R M₂ M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u4, u1, u1, u3, u4} (ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16)) g)) (LinearMap.ker.{u1, u1, max u2 u3, u4, max (max u2 u3) u4} R R (Prod.{u2, u3} M M₂) M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, max u2 u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max (max u2 u3) u4, u1, u1, max u2 u3, u4} (ContinuousLinearMap.{u1, u1, max u2 u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, max u2 u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16)) (ContinuousLinearMap.coprod.{u1, u2, u3, u4} R (Ring.toSemiring.{u1} R _inst_1) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_15 _inst_16 _inst_18 f g))
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] {M₃ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₃] [_inst_9 : AddCommGroup.{u4} M₃] [_inst_12 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_15 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_16 : Module.{u1, u4} R M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)] [_inst_18 : ContinuousAdd.{u4} M₃ _inst_8 (AddZeroClass.toHasAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (SubNegMonoid.toAddMonoid.{u4} M₃ (AddGroup.toSubNegMonoid.{u4} M₃ (AddCommGroup.toAddGroup.{u4} M₃ _inst_9)))))] (f : ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (g : ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16), LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M₂) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15)) (Preorder.toHasLe.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M₂) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15)) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M₂) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15)) (SetLike.partialOrder.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M₂) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15)) (Prod.{u2, u3} M M₂) (Submodule.setLike.{u1, max u2 u3} R (Prod.{u2, u3} M M₂) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15))))) (Submodule.prod.{u1, u2, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12 (LinearMap.ker.{u1, u1, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u1, u1, u2, u4} (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16)) f) M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_15 (LinearMap.ker.{u1, u1, u3, u4, max u3 u4} R R M₂ M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u4, u1, u1, u3, u4} (ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16)) g)) (LinearMap.ker.{u1, u1, max u2 u3, u4, max (max u2 u3) u4} R R (Prod.{u2, u3} M M₂) M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, max u2 u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max (max u2 u3) u4, u1, u1, max u2 u3, u4} (ContinuousLinearMap.{u1, u1, max u2 u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, max u2 u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16)) (ContinuousLinearMap.coprod.{u1, u2, u3, u4} R (Ring.toSemiring.{u1} R _inst_1) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_15 _inst_16 _inst_18 f g))
but is expected to have type
forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] {M₃ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₃] [_inst_9 : AddCommGroup.{u4} M₃] [_inst_12 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_15 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] [_inst_16 : Module.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)] [_inst_18 : ContinuousAdd.{u4} M₃ _inst_8 (AddZeroClass.toAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (SubNegMonoid.toAddMonoid.{u4} M₃ (AddGroup.toSubNegMonoid.{u4} M₃ (AddCommGroup.toAddGroup.{u4} M₃ _inst_9)))))] (f : ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (g : ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16), LE.le.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (Preorder.toLE.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (PartialOrder.toPreorder.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (Submodule.completeLattice.{u3, max u2 u1} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)))))) (Submodule.prod.{u3, u2, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12 (LinearMap.ker.{u3, u3, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u3, u3, u2, u4} (ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16)) f) M₂ (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_15 (LinearMap.ker.{u3, u3, u1, u4, max u1 u4} R R M₂ M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u1 u4, u3, u3, u1, u4} (ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16)) g)) (LinearMap.ker.{u3, u3, max u2 u1, u4, max (max u2 u4) u1} R R (Prod.{u2, u1} M M₂) M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, max u1 u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max (max u2 u1) u4, u3, u3, max u2 u1, u4} (ContinuousLinearMap.{u3, u3, max u1 u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, max u2 u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16)) (ContinuousLinearMap.coprod.{u3, u2, u1, u4} R (Ring.toSemiring.{u3} R _inst_1) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_15 _inst_16 _inst_18 f g))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ker_prod_ker_le_ker_coprod ContinuousLinearMap.ker_prod_ker_le_ker_coprodₓ'. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -2157,7 +2157,7 @@ variable (R φ)
lean 3 declaration is
forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {ι : Type.{u2}} (φ : ι -> Type.{u3}) [_inst_8 : forall (i : ι), TopologicalSpace.{u3} (φ i)] [_inst_9 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_10 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_9 i)] {I : Set.{u2} ι} {J : Set.{u2} ι} [_inst_11 : DecidablePred.{succ u2} ι (fun (i : ι) => Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i I)], (Disjoint.{u2} (Set.{u2} ι) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} ι) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.completeBooleanAlgebra.{u2} ι)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u2} (Set.{u2} ι) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u2} (Set.{u2} ι) (Set.booleanAlgebra.{u2} ι))) I J) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) (Set.univ.{u2} ι) (Union.union.{u2} (Set.{u2} ι) (Set.hasUnion.{u2} ι) I J)) -> (ContinuousLinearEquiv.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (coeSort.{succ (max u2 u3), succ (succ (max u2 u3))} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) Type.{max u2 u3} (SetLike.hasCoeToSort.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (forall (i : ι), φ i) 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i J) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i J) => LinearMap.ker.{u1, u1, max u2 u3, u3, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (ContinuousLinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i)) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u3, u1, u1, max u2 u3, u3} (ContinuousLinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i)) R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i) (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i))) (ContinuousLinearMap.proj.{u1, u2, u3} R _inst_1 ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a) (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i) i))))) (Pi.module.{u2, u3, u1} (Set.Elem.{u2} ι I) (fun (i : Set.Elem.{u2} ι I) => φ (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) i)) R _inst_1 (fun (i : Set.Elem.{u2} ι I) => _inst_9 (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) i)) (fun (i : Set.Elem.{u2} ι I) => _inst_10 (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) i))))
+ forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {ι : Type.{u2}} (φ : ι -> Type.{u3}) [_inst_8 : forall (i : ι), TopologicalSpace.{u3} (φ i)] [_inst_9 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_10 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_9 i)] {I : Set.{u2} ι} {J : Set.{u2} ι} [_inst_11 : DecidablePred.{succ u2} ι (fun (i : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i I)], (Disjoint.{u2} (Set.{u2} ι) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.instCompleteBooleanAlgebraSet.{u2} ι)))))) (BoundedOrder.toOrderBot.{u2} (Set.{u2} ι) (Preorder.toLE.{u2} (Set.{u2} ι) (PartialOrder.toPreorder.{u2} (Set.{u2} ι) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.instCompleteBooleanAlgebraSet.{u2} ι)))))))) (CompleteLattice.toBoundedOrder.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.instCompleteBooleanAlgebraSet.{u2} ι)))))) I J) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (Set.univ.{u2} ι) (Union.union.{u2} (Set.{u2} ι) (Set.instUnionSet.{u2} ι) I J)) -> (ContinuousLinearEquiv.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ (max u2 u3)} (forall (i : ι), φ i) (fun (x : forall (i : ι), φ i) => Membership.mem.{max u2 u3, max u2 u3} (forall (i : ι), φ i) (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (SetLike.instMembership.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (forall (i : ι), φ i) (Submodule.setLike.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)))) x (iInf.{max u2 u3, succ 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(fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i J) (fun (h._@.Mathlib.Topology.Algebra.Module.Basic._hyg.34403 : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i J) => LinearMap.ker.{u1, u1, max u2 u3, u3, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (ContinuousLinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) 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(Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i) (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i))) (ContinuousLinearMap.proj.{u1, u2, u3} R _inst_1 ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a) (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i) i)))))) (instTopologicalSpaceSubtype.{max u2 u3} (forall (i : ι), φ i) (fun (x : forall (i : ι), φ i) => Membership.mem.{max u2 u3, max u2 u3} (forall (i : ι), φ i) (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (SetLike.instMembership.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (forall (i : ι), φ i) (Submodule.setLike.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)))) x (iInf.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (Submodule.instInfSetSubmodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) ι (fun (i : ι) => iInf.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (Submodule.instInfSetSubmodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i J) (fun (H : 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i J) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i J) => LinearMap.ker.{u1, u1, max u2 u3, u3, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (ContinuousLinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i)) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 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_inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i))) (ContinuousLinearMap.proj.{u1, u2, u3} R _inst_1 ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a) (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i) i))))) (Pi.module.{u2, u3, u1} (Set.Elem.{u2} ι I) (fun (i : Set.Elem.{u2} ι I) => φ (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) i)) R _inst_1 (fun (i : Set.Elem.{u2} ι I) => _inst_9 (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) i)) (fun (i : Set.Elem.{u2} ι I) => _inst_10 (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) i))))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.infi_ker_proj_equiv ContinuousLinearMap.iInfKerProjEquivₓ'. -/
/-- If `I` and `J` are complementary index sets, the product of the kernels of the `J`th projections
of `φ` is linearly equivalent to the product over `I`. -/
@@ -4140,7 +4140,7 @@ variable {ι R M}
lean 3 declaration is
forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Unique.{succ u1} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u3} M], Eq.{max (succ (max u1 u3)) (succ u3)} ((ι -> M) -> M) (coeFn.{max (succ (max u1 u3)) (succ u3), max (succ (max u1 u3)) (succ u3)} (ContinuousLinearEquiv.{u2, u2, max u1 u3, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.Function.module.{u1, u2, u3} ι R M _inst_2 _inst_3 _inst_4) _inst_4) (fun (_x : ContinuousLinearEquiv.{u2, u2, max u1 u3, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.Function.module.{u1, u2, u3} ι R M _inst_2 _inst_3 _inst_4) _inst_4) => (ι -> M) -> M) (ContinuousLinearEquiv.hasCoeToFun.{u2, u2, max u1 u3, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.Function.module.{u1, u2, u3} ι R M _inst_2 _inst_3 _inst_4) _inst_4) (ContinuousLinearEquiv.funUnique.{u1, u2, u3} ι R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Function.eval.{succ u1, succ u3} ι (fun (x : ι) => M) (Inhabited.default.{succ u1} ι (Unique.inhabited.{succ u1} ι _inst_1)))
but is expected to have type
- forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Unique.{succ u3} ι] [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], Eq.{max (succ u3) (succ u2)} (forall (ᾰ : ι -> M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : ι -> M) => M) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), succ u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) (ι -> M) (fun (_x : ι -> M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : ι -> M) => M) _x) (ContinuousMapClass.toFunLike.{max u3 u2, max u3 u2, u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) (ι -> M) M (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) _inst_5 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u1, u1, max u3 u2, u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u3 u2, u1, u1, max u3 u2, u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4)))) (ContinuousLinearEquiv.funUnique.{u3, u1, u2} ι R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Function.eval.{succ u3, succ u2} ι (fun (x : ι) => M) (Inhabited.default.{succ u3} ι (Unique.instInhabited.{succ u3} ι _inst_1)))
+ forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Unique.{succ u3} ι] [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], Eq.{max (succ u3) (succ u2)} (forall (ᾰ : ι -> M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : ι -> M) => M) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), succ u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) (ι -> M) (fun (_x : ι -> M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : ι -> M) => M) _x) (ContinuousMapClass.toFunLike.{max u3 u2, max u3 u2, u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) (ι -> M) M (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (a : ι) => _inst_5)) _inst_5 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u1, u1, max u3 u2, u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u3 u2, u1, u1, max u3 u2, u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4)))) (ContinuousLinearEquiv.funUnique.{u3, u1, u2} ι R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Function.eval.{succ u3, succ u2} ι (fun (x : ι) => M) (Inhabited.default.{succ u3} ι (Unique.instInhabited.{succ u3} ι _inst_1)))
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_fun_unique ContinuousLinearEquiv.coe_funUniqueₓ'. -/
@[simp]
theorem coe_funUnique : ⇑(funUnique ι R M) = Function.eval default :=
@@ -4151,7 +4151,7 @@ theorem coe_funUnique : ⇑(funUnique ι R M) = Function.eval default :=
lean 3 declaration is
forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Unique.{succ u1} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u3} M], Eq.{max (succ u3) (succ (max u1 u3))} (M -> ι -> M) (coeFn.{max (succ u3) (succ (max u1 u3)), max (succ u3) (succ (max u1 u3))} (ContinuousLinearEquiv.{u2, u2, u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.Function.module.{u1, u2, u3} ι R M _inst_2 _inst_3 _inst_4)) (fun (_x : ContinuousLinearEquiv.{u2, u2, u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.Function.module.{u1, u2, u3} ι R M _inst_2 _inst_3 _inst_4)) => M -> ι -> M) (ContinuousLinearEquiv.hasCoeToFun.{u2, u2, u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.Function.module.{u1, u2, u3} ι R M _inst_2 _inst_3 _inst_4)) (ContinuousLinearEquiv.symm.{u2, u2, max u1 u3, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.Function.module.{u1, u2, u3} ι R M _inst_2 _inst_3 _inst_4) _inst_4 (ContinuousLinearEquiv.funUnique.{u1, u2, u3} ι R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Function.const.{succ u3, succ u1} M ι)
but is expected to have type
- forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Unique.{succ u3} ι] [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], Eq.{max (succ u3) (succ u2)} (forall (ᾰ : M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => ι -> M) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => ι -> M) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u2, max u3 u2} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) M (ι -> M) _inst_5 (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u1, u1, u2, max u3 u2} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u3 u2, u1, u1, u2, max u3 u2} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)))))) (ContinuousLinearEquiv.symm.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4 (ContinuousLinearEquiv.funUnique.{u3, u1, u2} ι R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Function.const.{succ u2, succ u3} M ι)
+ forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Unique.{succ u3} ι] [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], Eq.{max (succ u3) (succ u2)} (forall (ᾰ : M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => ι -> M) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => ι -> M) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u2, max u3 u2} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) M (ι -> M) _inst_5 (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (a : ι) => _inst_5)) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u1, u1, u2, max u3 u2} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u3 u2, u1, u1, u2, max u3 u2} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)))))) (ContinuousLinearEquiv.symm.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61164 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4 (ContinuousLinearEquiv.funUnique.{u3, u1, u2} ι R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Function.const.{succ u2, succ u3} M ι)
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_fun_unique_symm ContinuousLinearEquiv.coe_funUnique_symmₓ'. -/
@[simp]
theorem coe_funUnique_symm : ⇑(funUnique ι R M).symm = Function.const ι :=
@@ -4177,7 +4177,7 @@ def piFinTwo (M : Fin 2 → Type _) [∀ i, AddCommMonoid (M i)] [∀ i, Module
lean 3 declaration is
forall (R : Type.{u1}) (M : Type.{u2}) [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], ContinuousLinearEquiv.{u1, u1, u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) ((Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> M) (Pi.topologicalSpace.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => M) (fun (a : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => _inst_5)) (Pi.addCommMonoid.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => M) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => _inst_3)) (Prod.{u2, u2} M M) (Prod.topologicalSpace.{u2, u2} M M _inst_5 _inst_5) (Prod.addCommMonoid.{u2, u2} M M _inst_3 _inst_3) (Pi.Function.module.{0, u1, u2} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) R M _inst_2 _inst_3 _inst_4) (Prod.module.{u1, u2, u2} R M M _inst_2 _inst_3 _inst_3 _inst_4 _inst_4)
but is expected to have type
- forall (R : Type.{u1}) (M : Type.{u2}) [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], ContinuousLinearEquiv.{u1, u1, u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) ((Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> M) (Pi.topologicalSpace.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M) (fun (a : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_5)) (Pi.addCommMonoid.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_3)) (Prod.{u2, u2} M M) (instTopologicalSpaceProd.{u2, u2} M M _inst_5 _inst_5) (Prod.instAddCommMonoidSum.{u2, u2} M M _inst_3 _inst_3) (Pi.module.{0, u2, u1} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61743 : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M) R _inst_2 (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_3) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_4)) (Prod.module.{u1, u2, u2} R M M _inst_2 _inst_3 _inst_3 _inst_4 _inst_4)
+ forall (R : Type.{u1}) (M : Type.{u2}) [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], ContinuousLinearEquiv.{u1, u1, u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) ((Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> M) (Pi.topologicalSpace.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M) (fun (a : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_5)) (Pi.addCommMonoid.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_3)) (Prod.{u2, u2} M M) (instTopologicalSpaceProd.{u2, u2} M M _inst_5 _inst_5) (Prod.instAddCommMonoidSum.{u2, u2} M M _inst_3 _inst_3) (Pi.module.{0, u2, u1} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61449 : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M) R _inst_2 (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_3) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_4)) (Prod.module.{u1, u2, u2} R M M _inst_2 _inst_3 _inst_3 _inst_4 _inst_4)
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.fin_two_arrow ContinuousLinearEquiv.finTwoArrowₓ'. -/
/-- Continuous linear equivalence between vectors in `M² = fin 2 → M` and `M × M`. -/
@[simps (config := { fullyApplied := false })]
mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee
@@ -517,8 +517,8 @@ theorem isClosed_setOf_map_smul : IsClosed { f : M₁ → M₂ | ∀ c x, f (c
by
simp only [Set.setOf_forall]
exact
- isClosed_interᵢ fun c =>
- isClosed_interᵢ fun x => isClosed_eq (continuous_apply _) ((continuous_apply _).const_smul _)
+ isClosed_iInter fun c =>
+ isClosed_iInter fun x => isClosed_eq (continuous_apply _) ((continuous_apply _).const_smul _)
#align is_closed_set_of_map_smul isClosed_setOf_map_smulₓ
end
@@ -2141,31 +2141,31 @@ theorem proj_pi (f : ∀ i, M₂ →L[R] φ i) (i : ι) : (proj i).comp (pi f) =
ext fun c => rfl
#align continuous_linear_map.proj_pi ContinuousLinearMap.proj_pi
-/- warning: continuous_linear_map.infi_ker_proj -> ContinuousLinearMap.infᵢ_ker_proj is a dubious translation:
+/- warning: continuous_linear_map.infi_ker_proj -> ContinuousLinearMap.iInf_ker_proj is a dubious translation:
lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {ι : Type.{u2}} {φ : ι -> Type.{u3}} [_inst_8 : forall (i : ι), TopologicalSpace.{u3} (φ i)] [_inst_9 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_10 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_9 i)], Eq.{succ (max u2 u3)} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (infᵢ.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) ι (fun (i : ι) => LinearMap.ker.{u1, u1, max u2 u3, u3, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (ContinuousLinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i)) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u3, u1, u1, max u2 u3, u3} (ContinuousLinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i)) R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i) (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i))) (ContinuousLinearMap.proj.{u1, u2, u3} R _inst_1 ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a) (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i) i))) (Bot.bot.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (Submodule.hasBot.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))))
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {ι : Type.{u2}} {φ : ι -> Type.{u3}} [_inst_8 : forall (i : ι), TopologicalSpace.{u3} (φ i)] [_inst_9 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_10 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_9 i)], Eq.{succ (max u2 u3)} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (iInf.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) ι (fun (i : ι) => LinearMap.ker.{u1, u1, max u2 u3, u3, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (ContinuousLinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i)) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u3, u1, u1, max u2 u3, u3} (ContinuousLinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i)) R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i) (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i))) (ContinuousLinearMap.proj.{u1, u2, u3} R _inst_1 ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a) (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i) i))) (Bot.bot.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (Submodule.hasBot.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))))
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {ι : Type.{u3}} {φ : ι -> Type.{u2}} [_inst_8 : forall (i : ι), TopologicalSpace.{u2} (φ i)] [_inst_9 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_10 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_9 i)], Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (infᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) ι (fun (i : ι) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (_inst_9 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (ContinuousLinearMap.{u1, u1, max u3 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u3, u2} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i)) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u2, u1, u1, max u3 u2, u2} (ContinuousLinearMap.{u1, u1, max u3 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u3, u2} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i)) R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u3, u2} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i) (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, max u3 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u3, u2} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i))) (ContinuousLinearMap.proj.{u1, u3, u2} R _inst_1 ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a) (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i) i))) (Bot.bot.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (Submodule.instBotSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))))
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.infi_ker_proj ContinuousLinearMap.infᵢ_ker_projₓ'. -/
-theorem infᵢ_ker_proj : (⨅ i, ker (proj i : (∀ i, φ i) →L[R] φ i) : Submodule R (∀ i, φ i)) = ⊥ :=
- LinearMap.infᵢ_ker_proj
-#align continuous_linear_map.infi_ker_proj ContinuousLinearMap.infᵢ_ker_proj
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {ι : Type.{u3}} {φ : ι -> Type.{u2}} [_inst_8 : forall (i : ι), TopologicalSpace.{u2} (φ i)] [_inst_9 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_10 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_9 i)], Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (iInf.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) ι (fun (i : ι) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (_inst_9 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (ContinuousLinearMap.{u1, u1, max u3 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u3, u2} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i)) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u2, u1, u1, max u3 u2, u2} (ContinuousLinearMap.{u1, u1, max u3 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u3, u2} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i)) R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u3, u2} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i) (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, max u3 u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u3, u2} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i))) (ContinuousLinearMap.proj.{u1, u3, u2} R _inst_1 ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a) (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i) i))) (Bot.bot.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (Submodule.instBotSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.infi_ker_proj ContinuousLinearMap.iInf_ker_projₓ'. -/
+theorem iInf_ker_proj : (⨅ i, ker (proj i : (∀ i, φ i) →L[R] φ i) : Submodule R (∀ i, φ i)) = ⊥ :=
+ LinearMap.iInf_ker_proj
+#align continuous_linear_map.infi_ker_proj ContinuousLinearMap.iInf_ker_proj
variable (R φ)
-/- warning: continuous_linear_map.infi_ker_proj_equiv -> ContinuousLinearMap.infᵢKerProjEquiv is a dubious translation:
+/- warning: continuous_linear_map.infi_ker_proj_equiv -> ContinuousLinearMap.iInfKerProjEquiv is a dubious translation:
lean 3 declaration is
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(Set.univ.{u2} ι) (Union.union.{u2} (Set.{u2} ι) (Set.hasUnion.{u2} ι) I J)) -> (ContinuousLinearEquiv.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (coeSort.{succ (max u2 u3), succ (succ (max u2 u3))} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) Type.{max u2 u3} (SetLike.hasCoeToSort.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (forall (i : ι), φ i) 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u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (Submodule.instInfSetSubmodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) ι (fun (i : ι) => infᵢ.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (Submodule.instInfSetSubmodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i J) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i J) => LinearMap.ker.{u1, u1, max u2 u3, u3, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (ContinuousLinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i)) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u3, u1, u1, max u2 u3, u3} (ContinuousLinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i)) R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i) (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i))) (ContinuousLinearMap.proj.{u1, u2, u3} R _inst_1 ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a) (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i) i))))) (Pi.module.{u2, u3, u1} (Set.Elem.{u2} ι I) (fun (i : Set.Elem.{u2} ι I) => φ (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) i)) R _inst_1 (fun (i : Set.Elem.{u2} ι I) => _inst_9 (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) i)) (fun (i : Set.Elem.{u2} ι I) => _inst_10 (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) i))))
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.infi_ker_proj_equiv ContinuousLinearMap.infᵢKerProjEquivₓ'. -/
+ forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {ι : Type.{u2}} (φ : ι -> Type.{u3}) [_inst_8 : forall (i : ι), TopologicalSpace.{u3} (φ i)] [_inst_9 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_10 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_9 i)] {I : Set.{u2} ι} {J : Set.{u2} ι} [_inst_11 : DecidablePred.{succ u2} ι (fun (i : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i I)], (Disjoint.{u2} (Set.{u2} ι) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.instCompleteBooleanAlgebraSet.{u2} ι)))))) (BoundedOrder.toOrderBot.{u2} (Set.{u2} ι) (Preorder.toLE.{u2} (Set.{u2} ι) (PartialOrder.toPreorder.{u2} (Set.{u2} ι) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.instCompleteBooleanAlgebraSet.{u2} ι)))))))) (CompleteLattice.toBoundedOrder.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.instCompleteBooleanAlgebraSet.{u2} ι)))))) I J) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (Set.univ.{u2} ι) (Union.union.{u2} (Set.{u2} ι) (Set.instUnionSet.{u2} ι) I J)) -> (ContinuousLinearEquiv.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ (max u2 u3)} (forall (i : ι), φ i) (fun (x : forall (i : ι), φ i) => Membership.mem.{max u2 u3, max u2 u3} (forall (i : ι), φ i) (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (SetLike.instMembership.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (forall (i : ι), φ i) (Submodule.setLike.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)))) x (iInf.{max u2 u3, succ 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(fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i J) (fun (h._@.Mathlib.Topology.Algebra.Module.Basic._hyg.34409 : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i J) => LinearMap.ker.{u1, u1, max u2 u3, u3, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (ContinuousLinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) 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_inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (SetLike.instMembership.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (forall (i : ι), φ i) (Submodule.setLike.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)))) x (iInf.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R 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u2 u3, u3} (ContinuousLinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i)) R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i) (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 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ι) => _inst_10 i)) (_inst_10 i)) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u3, u1, u1, max u2 u3, u3} (ContinuousLinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i)) R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i) (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i))) (ContinuousLinearMap.proj.{u1, u2, u3} R _inst_1 ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a) (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i) i))))) (forall (i : Set.Elem.{u2} ι I), φ (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) i)) (Pi.topologicalSpace.{u2, u3} (Set.Elem.{u2} ι I) (fun (i : Set.Elem.{u2} ι I) => φ (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) i)) (fun (a : Set.Elem.{u2} ι I) => _inst_8 (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) a))) (Pi.addCommMonoid.{u2, u3} (Set.Elem.{u2} ι I) (fun (i : Set.Elem.{u2} ι I) => φ (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) i)) (fun (i : Set.Elem.{u2} ι I) => _inst_9 (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) i))) (Submodule.module.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (iInf.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (Submodule.instInfSetSubmodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) ι (fun (i : ι) => iInf.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (Submodule.instInfSetSubmodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i J) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i J) => LinearMap.ker.{u1, u1, max u2 u3, u3, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (ContinuousLinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i)) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 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_inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i))) (ContinuousLinearMap.proj.{u1, u2, u3} R _inst_1 ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a) (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i) i))))) (Pi.module.{u2, u3, u1} (Set.Elem.{u2} ι I) (fun (i : Set.Elem.{u2} ι I) => φ (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) i)) R _inst_1 (fun (i : Set.Elem.{u2} ι I) => _inst_9 (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) i)) (fun (i : Set.Elem.{u2} ι I) => _inst_10 (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) i))))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.infi_ker_proj_equiv ContinuousLinearMap.iInfKerProjEquivₓ'. -/
/-- If `I` and `J` are complementary index sets, the product of the kernels of the `J`th projections
of `φ` is linearly equivalent to the product over `I`. -/
-def infᵢKerProjEquiv {I J : Set ι} [DecidablePred fun i => i ∈ I] (hd : Disjoint I J)
+def iInfKerProjEquiv {I J : Set ι} [DecidablePred fun i => i ∈ I] (hd : Disjoint I J)
(hu : Set.univ ⊆ I ∪ J) :
(⨅ i ∈ J, ker (proj i : (∀ i, φ i) →L[R] φ i) : Submodule R (∀ i, φ i)) ≃L[R] ∀ i : I, φ i
where
- toLinearEquiv := LinearMap.infᵢKerProjEquiv R φ hd hu
+ toLinearEquiv := LinearMap.iInfKerProjEquiv R φ hd hu
continuous_toFun :=
continuous_pi fun i =>
by
@@ -2179,7 +2179,7 @@ def infᵢKerProjEquiv {I J : Set ι} [DecidablePred fun i => i ∈ I] (hd : Dis
(continuous_pi fun i => by dsimp;
split_ifs <;> [apply continuous_apply, exact continuous_zero])
_
-#align continuous_linear_map.infi_ker_proj_equiv ContinuousLinearMap.infᵢKerProjEquiv
+#align continuous_linear_map.infi_ker_proj_equiv ContinuousLinearMap.iInfKerProjEquiv
end Pi
mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1
@@ -2197,7 +2197,7 @@ section
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} (f : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (x : M), Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) => M -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) f (Neg.neg.{u3} M (SubNegMonoid.toHasNeg.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_5))) x)) (Neg.neg.{u4} M₂ (SubNegMonoid.toHasNeg.{u4} M₂ (AddGroup.toSubNegMonoid.{u4} M₂ (AddCommGroup.toAddGroup.{u4} M₂ _inst_7))) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) => M -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) f x))
but is expected to have type
- forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_13 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2))} (f : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) (Neg.neg.{u2} M (NegZeroClass.toNeg.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_5))))) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) f (Neg.neg.{u2} M (NegZeroClass.toNeg.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_5))))) x)) (Neg.neg.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (NegZeroClass.toNeg.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) _inst_7))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) f x))
+ forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_13 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))} (f : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) (Neg.neg.{u2} M (NegZeroClass.toNeg.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_5))))) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) f (Neg.neg.{u2} M (NegZeroClass.toNeg.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_5))))) x)) (Neg.neg.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (NegZeroClass.toNeg.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) _inst_7))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) f x))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_neg ContinuousLinearMap.map_negₓ'. -/
protected theorem map_neg (f : M →SL[σ₁₂] M₂) (x : M) : f (-x) = -f x :=
map_neg _ _
@@ -2207,7 +2207,7 @@ protected theorem map_neg (f : M →SL[σ₁₂] M₂) (x : M) : f (-x) = -f x :
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} (f : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (x : M) (y : M), Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) => M -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) f (HSub.hSub.{u3, u3, u3} M M M (instHSub.{u3} M (SubNegMonoid.toHasSub.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_5)))) x y)) (HSub.hSub.{u4, u4, u4} M₂ M₂ M₂ (instHSub.{u4} M₂ (SubNegMonoid.toHasSub.{u4} M₂ (AddGroup.toSubNegMonoid.{u4} M₂ (AddCommGroup.toAddGroup.{u4} M₂ _inst_7)))) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) => M -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) f x) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) => M -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) f y))
but is expected to have type
- forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_13 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2))} (f : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (x : M) (y : M), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) (HSub.hSub.{u2, u2, u2} M M M (instHSub.{u2} M (SubNegMonoid.toSub.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_5)))) x y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) f (HSub.hSub.{u2, u2, u2} M M M (instHSub.{u2} M (SubNegMonoid.toSub.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_5)))) x y)) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 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(ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) f x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) f y))
+ forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_13 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))} (f : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (x : M) (y : M), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) (HSub.hSub.{u2, u2, u2} M M M (instHSub.{u2} M (SubNegMonoid.toSub.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_5)))) x y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max 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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_sub ContinuousLinearMap.map_subₓ'. -/
protected theorem map_sub (f : M →SL[σ₁₂] M₂) (x y : M) : f (x - y) = f x - f y :=
map_sub _ _ _
@@ -2217,7 +2217,7 @@ protected theorem map_sub (f : M →SL[σ₁₂] M₂) (x y : M) : f (x - y) = f
lean 3 declaration is
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but is expected to have type
- forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_13 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2))} (f : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (g : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (instHSub.{max u2 u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (LinearMap.instSubLinearMapToAddCommMonoid.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_7 _inst_12 _inst_13 σ₁₂)) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 f) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 g)) x) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (instHSub.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubNegMonoid.toSub.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) _inst_7)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) f x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) g x))
+ forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_13 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))} (f : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (g : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (instHSub.{max u2 u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (LinearMap.instSubLinearMapToAddCommMonoid.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_7 _inst_12 _inst_13 σ₁₂)) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 f) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 g)) x) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (instHSub.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubNegMonoid.toSub.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) _inst_7)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) f x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) g x))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.sub_apply' ContinuousLinearMap.sub_apply'ₓ'. -/
@[simp]
theorem sub_apply' (f g : M →SL[σ₁₂] M₂) (x : M) : ((f : M →ₛₗ[σ₁₂] M₂) - g) x = f x - g x :=
@@ -2234,7 +2234,7 @@ variable [Module R M₂] [Module R M₃] [Module R M₄]
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] {M₃ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₃] [_inst_9 : AddCommGroup.{u4} M₃] [_inst_12 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_15 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_16 : Module.{u1, u4} R M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)] {f : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15} {g : ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16}, (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12))))) (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u3, u1, u1, u2, u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15)) f) (LinearMap.ker.{u1, u1, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u1, u1, u2, u4} (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16)) g)) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12))) -> (Eq.{succ (max u3 u4)} (Submodule.{u1, max u3 u4} R (Prod.{u3, u4} M₂ M₃) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u3, u4} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)) (Prod.module.{u1, u3, u4} R M₂ M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16)) (LinearMap.range.{u1, u1, u2, max u3 u4, max u2 u3 u4} R R M (Prod.{u3, u4} M₂ M₃) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (Prod.addCommMonoid.{u3, u4} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)) _inst_12 (Prod.module.{u1, u3, u4} R M₂ M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, max u3 u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (Prod.{u3, u4} M₂ M₃) (Prod.topologicalSpace.{u3, u4} M₂ M₃ _inst_6 _inst_8) (Prod.addCommMonoid.{u3, u4} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)) _inst_12 (Prod.module.{u1, u3, u4} R M₂ M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16)) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u3 u4, u1, u1, u2, max u3 u4} (ContinuousLinearMap.{u1, u1, u2, max u3 u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (Prod.{u3, u4} M₂ M₃) (Prod.topologicalSpace.{u3, u4} M₂ M₃ _inst_6 _inst_8) (Prod.addCommMonoid.{u3, u4} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)) _inst_12 (Prod.module.{u1, u3, u4} R M₂ M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16)) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (Prod.{u3, u4} M₂ M₃) (Prod.topologicalSpace.{u3, u4} M₂ M₃ _inst_6 _inst_8) (Prod.addCommMonoid.{u3, u4} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)) _inst_12 (Prod.module.{u1, u3, u4} R M₂ M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, max u3 u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (Prod.{u3, u4} M₂ M₃) (Prod.topologicalSpace.{u3, u4} M₂ M₃ _inst_6 _inst_8) (Prod.addCommMonoid.{u3, u4} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)) _inst_12 (Prod.module.{u1, u3, u4} R M₂ M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousLinearMap.prod.{u1, u2, u3, u4} R (Ring.toSemiring.{u1} R _inst_1) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_15 _inst_16 f g)) (Submodule.prod.{u1, u3, u4} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_15 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u3, u1, u1, u2, u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15)) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f) M₃ (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16 (LinearMap.range.{u1, u1, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u1, u1, u2, u4} (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16)) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) g)))
but is expected to have type
- forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u2}} [_inst_6 : TopologicalSpace.{u2} M₂] [_inst_7 : AddCommGroup.{u2} M₂] {M₃ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₃] [_inst_9 : AddCommGroup.{u1} M₃] [_inst_12 : Module.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_15 : Module.{u4, u2} R M₂ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7)] [_inst_16 : Module.{u4, u1} R M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)] {f : ContinuousLinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15} {g : ContinuousLinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16}, (Eq.{succ u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (Sup.sup.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (SemilatticeSup.toSup.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (Lattice.toSemilatticeSup.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (ConditionallyCompleteLattice.toLattice.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (Submodule.completeLattice.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12))))) (LinearMap.ker.{u4, u4, u3, u2, max u3 u2} R R M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15 (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) (ContinuousLinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u2, u4, u4, u3, u2} (ContinuousLinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15) R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15)) f) (LinearMap.ker.{u4, u4, u3, u1, max u3 u1} R R M M₃ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) (ContinuousLinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u1, u4, u4, u3, u1} (ContinuousLinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16)) g)) (Top.top.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (Submodule.instTopSubmodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12))) -> (Eq.{max (succ u2) (succ u1)} (Submodule.{u4, max u2 u1} R (Prod.{u2, u1} M₂ M₃) (Ring.toSemiring.{u4} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)) (Prod.module.{u4, u2, u1} R M₂ M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_15 _inst_16)) (LinearMap.range.{u4, u4, u3, max u2 u1, max (max u3 u2) u1} R R M (Prod.{u2, u1} M₂ M₃) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (Prod.instAddCommMonoidSum.{u2, u1} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)) _inst_12 (Prod.module.{u4, u2, u1} R M₂ M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_15 _inst_16) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (ContinuousLinearMap.{u4, u4, u3, max u1 u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (Prod.{u2, u1} M₂ M₃) (instTopologicalSpaceProd.{u2, u1} M₂ M₃ _inst_6 _inst_8) (Prod.instAddCommMonoidSum.{u2, u1} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)) _inst_12 (Prod.module.{u4, u2, u1} R M₂ M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_15 _inst_16)) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max (max u3 u2) u1, u4, u4, u3, max u2 u1} (ContinuousLinearMap.{u4, u4, u3, max u1 u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (Prod.{u2, u1} M₂ M₃) (instTopologicalSpaceProd.{u2, u1} M₂ M₃ _inst_6 _inst_8) (Prod.instAddCommMonoidSum.{u2, u1} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)) _inst_12 (Prod.module.{u4, u2, u1} R M₂ M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_15 _inst_16)) R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (Prod.{u2, u1} M₂ M₃) (instTopologicalSpaceProd.{u2, u1} M₂ M₃ _inst_6 _inst_8) (Prod.instAddCommMonoidSum.{u2, u1} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)) _inst_12 (Prod.module.{u4, u2, u1} R M₂ M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_15 _inst_16) (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, max u2 u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (Prod.{u2, u1} M₂ M₃) (instTopologicalSpaceProd.{u2, u1} M₂ M₃ _inst_6 _inst_8) (Prod.instAddCommMonoidSum.{u2, u1} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)) _inst_12 (Prod.module.{u4, u2, u1} R M₂ M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_15 _inst_16))) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (ContinuousLinearMap.prod.{u4, u3, u2, u1} R (Ring.toSemiring.{u4} R _inst_1) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_15 _inst_16 f g)) (Submodule.prod.{u4, u2, u1} R M₂ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_15 (LinearMap.range.{u4, u4, u3, u2, max u3 u2} R R M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15 (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) (ContinuousLinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u2, u4, u4, u3, u2} (ContinuousLinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15) R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15)) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) f) M₃ (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_16 (LinearMap.range.{u4, u4, u3, u1, max u3 u1} R R M M₃ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) (ContinuousLinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u1, u4, u4, u3, u1} (ContinuousLinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16)) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) g)))
+ forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u2}} [_inst_6 : TopologicalSpace.{u2} M₂] [_inst_7 : AddCommGroup.{u2} M₂] {M₃ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₃] [_inst_9 : AddCommGroup.{u1} M₃] [_inst_12 : Module.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_15 : Module.{u4, u2} R M₂ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7)] [_inst_16 : Module.{u4, u1} R M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)] {f : ContinuousLinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15} {g : ContinuousLinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16}, (Eq.{succ u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (Sup.sup.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (SemilatticeSup.toSup.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (Lattice.toSemilatticeSup.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (ConditionallyCompleteLattice.toLattice.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (Submodule.completeLattice.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12))))) (LinearMap.ker.{u4, u4, u3, u2, max u3 u2} R R M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (ContinuousLinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u2, u4, u4, u3, u2} (ContinuousLinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15) R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15)) f) (LinearMap.ker.{u4, u4, u3, u1, max u3 u1} R R M M₃ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (ContinuousLinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u1, u4, u4, u3, u1} (ContinuousLinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16)) g)) (Top.top.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (Submodule.instTopSubmodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12))) -> (Eq.{max (succ u2) (succ u1)} (Submodule.{u4, max u2 u1} R (Prod.{u2, u1} M₂ M₃) (Ring.toSemiring.{u4} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)) (Prod.module.{u4, u2, u1} R M₂ M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_15 _inst_16)) (LinearMap.range.{u4, u4, u3, max u2 u1, max (max u3 u2) u1} R R M (Prod.{u2, u1} M₂ M₃) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (Prod.instAddCommMonoidSum.{u2, u1} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)) _inst_12 (Prod.module.{u4, u2, u1} R M₂ M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_15 _inst_16) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (ContinuousLinearMap.{u4, u4, u3, max u1 u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (Prod.{u2, u1} M₂ M₃) (instTopologicalSpaceProd.{u2, u1} M₂ M₃ _inst_6 _inst_8) (Prod.instAddCommMonoidSum.{u2, u1} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)) _inst_12 (Prod.module.{u4, u2, u1} R M₂ M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_15 _inst_16)) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max (max u3 u2) u1, u4, u4, u3, max u2 u1} (ContinuousLinearMap.{u4, u4, u3, max u1 u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (Prod.{u2, u1} M₂ M₃) (instTopologicalSpaceProd.{u2, u1} M₂ M₃ _inst_6 _inst_8) (Prod.instAddCommMonoidSum.{u2, u1} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)) _inst_12 (Prod.module.{u4, u2, u1} R M₂ M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_15 _inst_16)) R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (Prod.{u2, u1} M₂ M₃) (instTopologicalSpaceProd.{u2, u1} M₂ M₃ _inst_6 _inst_8) (Prod.instAddCommMonoidSum.{u2, u1} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)) _inst_12 (Prod.module.{u4, u2, u1} R M₂ M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_15 _inst_16) (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, max u2 u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (Prod.{u2, u1} M₂ M₃) (instTopologicalSpaceProd.{u2, u1} M₂ M₃ _inst_6 _inst_8) (Prod.instAddCommMonoidSum.{u2, u1} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)) _inst_12 (Prod.module.{u4, u2, u1} R M₂ M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_15 _inst_16))) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (ContinuousLinearMap.prod.{u4, u3, u2, u1} R (Ring.toSemiring.{u4} R _inst_1) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_15 _inst_16 f g)) (Submodule.prod.{u4, u2, u1} R M₂ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_15 (LinearMap.range.{u4, u4, u3, u2, max u3 u2} R R M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (ContinuousLinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u2, u4, u4, u3, u2} (ContinuousLinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15) R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15)) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) f) M₃ (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_16 (LinearMap.range.{u4, u4, u3, u1, max u3 u1} R R M M₃ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (ContinuousLinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u1, u4, u4, u3, u1} (ContinuousLinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16)) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) g)))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.range_prod_eq ContinuousLinearMap.range_prod_eqₓ'. -/
theorem range_prod_eq {f : M →L[R] M₂} {g : M →L[R] M₃} (h : ker f ⊔ ker g = ⊤) :
range (f.Prod g) = (range f).Prod (range g) :=
@@ -2245,7 +2245,7 @@ theorem range_prod_eq {f : M →L[R] M₂} {g : M →L[R] M₃} (h : ker f ⊔ k
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] {M₃ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₃] [_inst_9 : AddCommGroup.{u4} M₃] [_inst_12 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_15 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_16 : Module.{u1, u4} R M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)] [_inst_18 : ContinuousAdd.{u4} M₃ _inst_8 (AddZeroClass.toHasAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (SubNegMonoid.toAddMonoid.{u4} M₃ (AddGroup.toSubNegMonoid.{u4} M₃ (AddCommGroup.toAddGroup.{u4} M₃ _inst_9)))))] (f : ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (g : ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16), LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M₂) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15)) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M₂) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15)) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M₂) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15)) (SetLike.partialOrder.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M₂) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15)) (Prod.{u2, u3} M M₂) (Submodule.setLike.{u1, max u2 u3} R (Prod.{u2, u3} M M₂) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15))))) (Submodule.prod.{u1, u2, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12 (LinearMap.ker.{u1, u1, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u1, u1, u2, u4} (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16)) f) M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_15 (LinearMap.ker.{u1, u1, u3, u4, max u3 u4} R R M₂ M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u4, u1, u1, u3, u4} (ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16)) g)) (LinearMap.ker.{u1, u1, max u2 u3, u4, max (max u2 u3) u4} R R (Prod.{u2, u3} M M₂) M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, max u2 u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max (max u2 u3) u4, u1, u1, max u2 u3, u4} (ContinuousLinearMap.{u1, u1, max u2 u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, max u2 u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16)) (ContinuousLinearMap.coprod.{u1, u2, u3, u4} R (Ring.toSemiring.{u1} R _inst_1) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_15 _inst_16 _inst_18 f g))
but is expected to have type
- forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] {M₃ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₃] [_inst_9 : AddCommGroup.{u4} M₃] [_inst_12 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_15 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] [_inst_16 : Module.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)] [_inst_18 : ContinuousAdd.{u4} M₃ _inst_8 (AddZeroClass.toAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (SubNegMonoid.toAddMonoid.{u4} M₃ (AddGroup.toSubNegMonoid.{u4} M₃ (AddCommGroup.toAddGroup.{u4} M₃ _inst_9)))))] (f : ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (g : ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16), LE.le.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (Preorder.toLE.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (PartialOrder.toPreorder.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (Submodule.completeLattice.{u3, max u2 u1} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)))))) (Submodule.prod.{u3, u2, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12 (LinearMap.ker.{u3, u3, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u3, u3, u2, u4} (ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16)) f) M₂ (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_15 (LinearMap.ker.{u3, u3, u1, u4, max u1 u4} R R M₂ M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u1 u4, u3, u3, u1, u4} (ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16)) g)) (LinearMap.ker.{u3, u3, max u2 u1, u4, max (max u2 u4) u1} R R (Prod.{u2, u1} M M₂) M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, max u1 u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max (max u2 u1) u4, u3, u3, max u2 u1, u4} (ContinuousLinearMap.{u3, u3, max u1 u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, max u2 u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16)) (ContinuousLinearMap.coprod.{u3, u2, u1, u4} R (Ring.toSemiring.{u3} R _inst_1) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_15 _inst_16 _inst_18 f g))
+ forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] {M₃ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₃] [_inst_9 : AddCommGroup.{u4} M₃] [_inst_12 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_15 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] [_inst_16 : Module.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)] [_inst_18 : ContinuousAdd.{u4} M₃ _inst_8 (AddZeroClass.toAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (SubNegMonoid.toAddMonoid.{u4} M₃ (AddGroup.toSubNegMonoid.{u4} M₃ (AddCommGroup.toAddGroup.{u4} M₃ _inst_9)))))] (f : ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (g : ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16), LE.le.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (Preorder.toLE.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (PartialOrder.toPreorder.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (Submodule.completeLattice.{u3, max u2 u1} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)))))) (Submodule.prod.{u3, u2, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12 (LinearMap.ker.{u3, u3, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u3, u3, u2, u4} (ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16)) f) M₂ (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_15 (LinearMap.ker.{u3, u3, u1, u4, max u1 u4} R R M₂ M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u1 u4, u3, u3, u1, u4} (ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16)) g)) (LinearMap.ker.{u3, u3, max u2 u1, u4, max (max u2 u4) u1} R R (Prod.{u2, u1} M M₂) M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, max u1 u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max (max u2 u1) u4, u3, u3, max u2 u1, u4} (ContinuousLinearMap.{u3, u3, max u1 u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, max u2 u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16)) (ContinuousLinearMap.coprod.{u3, u2, u1, u4} R (Ring.toSemiring.{u3} R _inst_1) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_15 _inst_16 _inst_18 f g))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ker_prod_ker_le_ker_coprod ContinuousLinearMap.ker_prod_ker_le_ker_coprodₓ'. -/
theorem ker_prod_ker_le_ker_coprod [ContinuousAdd M₃] (f : M →L[R] M₃) (g : M₂ →L[R] M₃) :
(LinearMap.ker f).Prod (LinearMap.ker g) ≤ LinearMap.ker (f.coprod g) :=
@@ -2256,7 +2256,7 @@ theorem ker_prod_ker_le_ker_coprod [ContinuousAdd M₃] (f : M →L[R] M₃) (g
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] {M₃ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₃] [_inst_9 : AddCommGroup.{u4} M₃] [_inst_12 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_15 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_16 : Module.{u1, u4} R M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)] [_inst_18 : ContinuousAdd.{u4} M₃ _inst_8 (AddZeroClass.toHasAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (SubNegMonoid.toAddMonoid.{u4} M₃ (AddGroup.toSubNegMonoid.{u4} M₃ (AddCommGroup.toAddGroup.{u4} M₃ _inst_9)))))] (f : ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (g : ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16), (Disjoint.{u4} (Submodule.{u1, u4} R M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16) (SetLike.partialOrder.{u4, u4} (Submodule.{u1, u4} R M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16) M₃ (Submodule.setLike.{u1, u4} R M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16)) (Submodule.orderBot.{u1, u4} R M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16) (LinearMap.range.{u1, u1, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u1, u1, u2, u4} (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16)) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f) (LinearMap.range.{u1, u1, u3, u4, max u3 u4} R R M₂ M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u4, u1, u1, u3, u4} (ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16)) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) g)) -> (Eq.{succ (max u2 u3)} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M₂) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15)) (LinearMap.ker.{u1, u1, max u2 u3, u4, max (max u2 u3) u4} R R (Prod.{u2, u3} M M₂) M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, max u2 u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max (max u2 u3) u4, u1, u1, max u2 u3, u4} (ContinuousLinearMap.{u1, u1, max u2 u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, max u2 u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16)) (ContinuousLinearMap.coprod.{u1, u2, u3, u4} R (Ring.toSemiring.{u1} R _inst_1) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_15 _inst_16 _inst_18 f g)) (Submodule.prod.{u1, u2, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12 (LinearMap.ker.{u1, u1, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u1, u1, u2, u4} (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16)) f) M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_15 (LinearMap.ker.{u1, u1, u3, u4, max u3 u4} R R M₂ M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u4, u1, u1, u3, u4} (ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16)) g)))
but is expected to have type
- forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] {M₃ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₃] [_inst_9 : AddCommGroup.{u4} M₃] [_inst_12 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_15 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] [_inst_16 : Module.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)] [_inst_18 : ContinuousAdd.{u4} M₃ _inst_8 (AddZeroClass.toAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (SubNegMonoid.toAddMonoid.{u4} M₃ (AddGroup.toSubNegMonoid.{u4} M₃ (AddCommGroup.toAddGroup.{u4} M₃ _inst_9)))))] (f : ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (g : ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16), (Disjoint.{u4} (Submodule.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submodule.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submodule.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16) (Submodule.completeLattice.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16) (LinearMap.range.{u3, u3, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u3, u3, u2, u4} (ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16)) (RingHomSurjective.ids.{u3} R (Ring.toSemiring.{u3} R _inst_1)) f) (LinearMap.range.{u3, u3, u1, u4, max u1 u4} R R M₂ M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u1 u4, u3, u3, u1, u4} (ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16)) (RingHomSurjective.ids.{u3} R (Ring.toSemiring.{u3} R _inst_1)) g)) -> (Eq.{max (succ u2) (succ u1)} (Submodule.{u3, max u2 u1} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (LinearMap.ker.{u3, u3, max u2 u1, u4, max (max u2 u4) u1} R R (Prod.{u2, u1} M M₂) M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, max u1 u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max (max u2 u1) u4, u3, u3, max u2 u1, u4} (ContinuousLinearMap.{u3, u3, max u1 u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, max u2 u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16)) (ContinuousLinearMap.coprod.{u3, u2, u1, u4} R (Ring.toSemiring.{u3} R _inst_1) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_15 _inst_16 _inst_18 f g)) (Submodule.prod.{u3, u2, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12 (LinearMap.ker.{u3, u3, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u3, u3, u2, u4} (ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16)) f) M₂ (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_15 (LinearMap.ker.{u3, u3, u1, u4, max u1 u4} R R M₂ M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u1 u4, u3, u3, u1, u4} (ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16)) g)))
+ forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] {M₃ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₃] [_inst_9 : AddCommGroup.{u4} M₃] [_inst_12 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_15 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] [_inst_16 : Module.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)] [_inst_18 : ContinuousAdd.{u4} M₃ _inst_8 (AddZeroClass.toAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (SubNegMonoid.toAddMonoid.{u4} M₃ (AddGroup.toSubNegMonoid.{u4} M₃ (AddCommGroup.toAddGroup.{u4} M₃ _inst_9)))))] (f : ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (g : ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16), (Disjoint.{u4} (Submodule.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submodule.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submodule.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16) (Submodule.completeLattice.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16) (LinearMap.range.{u3, u3, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u3, u3, u2, u4} (ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16)) (RingHomSurjective.ids.{u3} R (Ring.toSemiring.{u3} R _inst_1)) f) (LinearMap.range.{u3, u3, u1, u4, max u1 u4} R R M₂ M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u1 u4, u3, u3, u1, u4} (ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16)) (RingHomSurjective.ids.{u3} R (Ring.toSemiring.{u3} R _inst_1)) g)) -> (Eq.{max (succ u2) (succ u1)} (Submodule.{u3, max u2 u1} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (LinearMap.ker.{u3, u3, max u2 u1, u4, max (max u2 u4) u1} R R (Prod.{u2, u1} M M₂) M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, max u1 u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max (max u2 u1) u4, u3, u3, max u2 u1, u4} (ContinuousLinearMap.{u3, u3, max u1 u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, max u2 u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16)) (ContinuousLinearMap.coprod.{u3, u2, u1, u4} R (Ring.toSemiring.{u3} R _inst_1) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_15 _inst_16 _inst_18 f g)) (Submodule.prod.{u3, u2, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12 (LinearMap.ker.{u3, u3, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u3, u3, u2, u4} (ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16)) f) M₂ (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_15 (LinearMap.ker.{u3, u3, u1, u4, max u1 u4} R R M₂ M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u1 u4, u3, u3, u1, u4} (ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16)) g)))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ker_coprod_of_disjoint_range ContinuousLinearMap.ker_coprod_of_disjoint_rangeₓ'. -/
theorem ker_coprod_of_disjoint_range [ContinuousAdd M₃] (f : M →L[R] M₃) (g : M₂ →L[R] M₃)
(hd : Disjoint (range f) (range g)) :
@@ -2277,7 +2277,7 @@ instance : Neg (M →SL[σ₁₂] M₂) :=
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} [_inst_15 : TopologicalAddGroup.{u4} M₂ _inst_6 (AddCommGroup.toAddGroup.{u4} M₂ _inst_7)] (f : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (x : M), Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) => M -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (Neg.neg.{max u3 u4} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.neg.{u1, u2, u3, u4} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_15) f) x) (Neg.neg.{u4} M₂ (SubNegMonoid.toHasNeg.{u4} M₂ (AddGroup.toSubNegMonoid.{u4} M₂ (AddCommGroup.toAddGroup.{u4} M₂ _inst_7))) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) => M -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) f x))
but is expected to have type
- forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_13 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2))} [_inst_15 : TopologicalAddGroup.{u1} M₂ _inst_6 (AddCommGroup.toAddGroup.{u1} M₂ _inst_7)] (f : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.neg.{u4, u3, u2, u1} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_15) f) x) (Neg.neg.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (NegZeroClass.toNeg.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) _inst_7))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) f x))
+ forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_13 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))} [_inst_15 : TopologicalAddGroup.{u1} M₂ _inst_6 (AddCommGroup.toAddGroup.{u1} M₂ _inst_7)] (f : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.neg.{u4, u3, u2, u1} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_15) f) x) (Neg.neg.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (NegZeroClass.toNeg.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) _inst_7))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) f x))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.neg_apply ContinuousLinearMap.neg_applyₓ'. -/
@[simp]
theorem neg_apply (f : M →SL[σ₁₂] M₂) (x : M) : (-f) x = -f x :=
@@ -2288,7 +2288,7 @@ theorem neg_apply (f : M →SL[σ₁₂] M₂) (x : M) : (-f) x = -f x :=
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} [_inst_15 : TopologicalAddGroup.{u4} M₂ _inst_6 (AddCommGroup.toAddGroup.{u4} M₂ _inst_7)] (f : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) 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_inst_13) (ContinuousLinearMap.neg.{u1, u2, u3, u4} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_15) f)) (Neg.neg.{max u3 u4} (LinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (LinearMap.hasNeg.{u1, u2, u3, u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_7 _inst_12 _inst_13 σ₁₂) ((fun (a : Sort.{max (succ u3) (succ u4)}) (b : Sort.{max (succ u3) (succ u4)}) [self : HasLiftT.{max (succ u3) (succ u4), max (succ u3) (succ u4)} a b] => self.0) (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) 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M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13)))) f))
but is expected to have type
- forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_13 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2))} [_inst_15 : TopologicalAddGroup.{u1} M₂ _inst_6 (AddCommGroup.toAddGroup.{u1} M₂ _inst_7)] (f : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u2) (succ u1)} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.neg.{u4, u3, u2, u1} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_15) f)) (Neg.neg.{max u2 u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (LinearMap.instNegLinearMapToAddCommMonoid.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_7 _inst_12 _inst_13 σ₁₂) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 f))
+ forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_13 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))} [_inst_15 : TopologicalAddGroup.{u1} M₂ _inst_6 (AddCommGroup.toAddGroup.{u1} M₂ _inst_7)] (f : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u2) (succ u1)} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.neg.{u4, u3, u2, u1} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_15) f)) (Neg.neg.{max u2 u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (LinearMap.instNegLinearMapToAddCommMonoid.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_7 _inst_12 _inst_13 σ₁₂) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 f))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_neg ContinuousLinearMap.coe_negₓ'. -/
@[simp, norm_cast]
theorem coe_neg (f : M →SL[σ₁₂] M₂) : (↑(-f) : M →ₛₗ[σ₁₂] M₂) = -f :=
@@ -2299,7 +2299,7 @@ theorem coe_neg (f : M →SL[σ₁₂] M₂) : (↑(-f) : M →ₛₗ[σ₁₂]
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} [_inst_15 : TopologicalAddGroup.{u4} M₂ _inst_6 (AddCommGroup.toAddGroup.{u4} M₂ _inst_7)] (f : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13), Eq.{succ (max u3 u4)} (M -> M₂) (coeFn.{succ (max u3 u4), succ (max u3 u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) => M -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (Neg.neg.{max u3 u4} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.neg.{u1, u2, u3, u4} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_15) f)) (Neg.neg.{max u3 u4} (M -> M₂) (Pi.instNeg.{u3, u4} M (fun (ᾰ : M) => M₂) (fun (i : M) => SubNegMonoid.toHasNeg.{u4} M₂ (AddGroup.toSubNegMonoid.{u4} M₂ (AddCommGroup.toAddGroup.{u4} M₂ _inst_7)))) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) => M -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) f))
but is expected to have type
- forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_13 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2))} [_inst_15 : TopologicalAddGroup.{u1} M₂ _inst_6 (AddCommGroup.toAddGroup.{u1} M₂ _inst_7)] (f : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.neg.{u4, u3, u2, u1} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_15) f)) (Neg.neg.{max u2 u1} (forall (ᾰ : M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) ᾰ) (Pi.instNeg.{u2, u1} M (fun (ᾰ : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) ᾰ) (fun (i : M) => NegZeroClass.toNeg.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) i) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) i) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) i) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) i) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) i) _inst_7)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) f))
+ forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_13 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))} [_inst_15 : TopologicalAddGroup.{u1} M₂ _inst_6 (AddCommGroup.toAddGroup.{u1} M₂ _inst_7)] (f : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.neg.{u4, u3, u2, u1} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_15) f)) (Neg.neg.{max u2 u1} (forall (ᾰ : M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) ᾰ) (Pi.instNeg.{u2, u1} M (fun (ᾰ : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) ᾰ) (fun (i : M) => NegZeroClass.toNeg.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) i) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) i) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) i) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) i) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) i) _inst_7)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) f))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_neg' ContinuousLinearMap.coe_neg'ₓ'. -/
@[norm_cast]
theorem coe_neg' (f : M →SL[σ₁₂] M₂) : ⇑(-f) = -f :=
@@ -2336,7 +2336,7 @@ instance : AddCommGroup (M →SL[σ₁₂] M₂) := by
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} [_inst_15 : TopologicalAddGroup.{u4} M₂ _inst_6 (AddCommGroup.toAddGroup.{u4} M₂ _inst_7)] (f : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (g : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (x : M), Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) => M -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (HSub.hSub.{max u3 u4, max u3 u4, max u3 u4} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (instHSub.{max u3 u4} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.sub.{u1, u2, u3, u4} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_15)) f g) x) (HSub.hSub.{u4, u4, u4} M₂ M₂ M₂ (instHSub.{u4} M₂ (SubNegMonoid.toHasSub.{u4} M₂ (AddGroup.toSubNegMonoid.{u4} M₂ (AddCommGroup.toAddGroup.{u4} M₂ _inst_7)))) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) => M -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) f x) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) => M -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) g x))
but is expected to have type
- forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_13 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2))} [_inst_15 : TopologicalAddGroup.{u1} M₂ _inst_6 (AddCommGroup.toAddGroup.{u1} M₂ _inst_7)] (f : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) 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_inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ 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u2, u1} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_15)) f g) x) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (instHSub.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubNegMonoid.toSub.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) _inst_7)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) f x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) g x))
+ forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_13 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))} [_inst_15 : TopologicalAddGroup.{u1} M₂ _inst_6 (AddCommGroup.toAddGroup.{u1} M₂ _inst_7)] (f : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (g : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (instHSub.{max u2 u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.sub.{u4, u3, u2, u1} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_15)) f g) x) (HSub.hSub.{u1, u1, u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (instHSub.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubNegMonoid.toSub.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) _inst_7)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) f x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) g x))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.sub_apply ContinuousLinearMap.sub_applyₓ'. -/
theorem sub_apply (f g : M →SL[σ₁₂] M₂) (x : M) : (f - g) x = f x - g x :=
rfl
@@ -2346,7 +2346,7 @@ theorem sub_apply (f g : M →SL[σ₁₂] M₂) (x : M) : (f - g) x = f x - g x
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} [_inst_15 : TopologicalAddGroup.{u4} M₂ _inst_6 (AddCommGroup.toAddGroup.{u4} M₂ _inst_7)] (f : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) 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but is expected to have type
- forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_13 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2))} [_inst_15 : TopologicalAddGroup.{u1} M₂ _inst_6 (AddCommGroup.toAddGroup.{u1} M₂ _inst_7)] (f : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (g : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u2) (succ u1)} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (instHSub.{max u2 u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.sub.{u4, u3, u2, u1} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_15)) f g)) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (instHSub.{max u2 u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (LinearMap.instSubLinearMapToAddCommMonoid.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_7 _inst_12 _inst_13 σ₁₂)) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 f) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 g))
+ forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_13 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))} [_inst_15 : TopologicalAddGroup.{u1} M₂ _inst_6 (AddCommGroup.toAddGroup.{u1} M₂ _inst_7)] (f : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (g : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u2) (succ u1)} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (instHSub.{max u2 u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.sub.{u4, u3, u2, u1} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_15)) f g)) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (instHSub.{max u2 u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (LinearMap.instSubLinearMapToAddCommMonoid.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_7 _inst_12 _inst_13 σ₁₂)) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 f) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 g))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_sub ContinuousLinearMap.coe_subₓ'. -/
@[simp, norm_cast]
theorem coe_sub (f g : M →SL[σ₁₂] M₂) : (↑(f - g) : M →ₛₗ[σ₁₂] M₂) = f - g :=
@@ -2357,7 +2357,7 @@ theorem coe_sub (f g : M →SL[σ₁₂] M₂) : (↑(f - g) : M →ₛₗ[σ₁
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} [_inst_15 : TopologicalAddGroup.{u4} M₂ _inst_6 (AddCommGroup.toAddGroup.{u4} M₂ _inst_7)] (f : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (g : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13), Eq.{succ (max u3 u4)} (M -> M₂) (coeFn.{succ (max u3 u4), succ (max u3 u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) => M -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (HSub.hSub.{max u3 u4, max u3 u4, max u3 u4} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (instHSub.{max u3 u4} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.sub.{u1, u2, u3, u4} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_15)) f g)) (HSub.hSub.{max u3 u4, max u3 u4, max u3 u4} (M -> M₂) (M -> M₂) (M -> M₂) (instHSub.{max u3 u4} (M -> M₂) (Pi.instSub.{u3, u4} M (fun (ᾰ : M) => M₂) (fun (i : M) => SubNegMonoid.toHasSub.{u4} M₂ (AddGroup.toSubNegMonoid.{u4} M₂ (AddCommGroup.toAddGroup.{u4} M₂ _inst_7))))) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) => M -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) => M -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) g))
but is expected to have type
- forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_13 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2))} [_inst_15 : TopologicalAddGroup.{u1} M₂ _inst_6 (AddCommGroup.toAddGroup.{u1} M₂ _inst_7)] (f : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (g : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (instHSub.{max u2 u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.sub.{u4, u3, u2, u1} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_15)) f g)) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (forall (ᾰ : M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) ᾰ) (forall (ᾰ : M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) ᾰ) (forall (ᾰ : M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) ᾰ) (instHSub.{max u2 u1} (forall (ᾰ : M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) ᾰ) (Pi.instSub.{u2, u1} M (fun (ᾰ : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) ᾰ) (fun (i : M) => SubNegMonoid.toSub.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) i) (AddGroup.toSubNegMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) i) (AddCommGroup.toAddGroup.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) i) _inst_7))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) g))
+ forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_13 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))} [_inst_15 : TopologicalAddGroup.{u1} M₂ _inst_6 (AddCommGroup.toAddGroup.{u1} M₂ _inst_7)] (f : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (g : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M 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(x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) i) _inst_7))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) g))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_sub' ContinuousLinearMap.coe_sub'ₓ'. -/
@[simp, norm_cast]
theorem coe_sub' (f g : M →SL[σ₁₂] M₂) : ⇑(f - g) = f - g :=
@@ -2370,7 +2370,7 @@ end
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {R₃ : Type.{u3}} [_inst_3 : Ring.{u3} R₃] {M : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} M] [_inst_5 : AddCommGroup.{u4} M] {M₂ : Type.{u5}} [_inst_6 : TopologicalSpace.{u5} M₂] [_inst_7 : AddCommGroup.{u5} M₂] {M₃ : Type.{u6}} [_inst_8 : TopologicalSpace.{u6} M₃] [_inst_9 : AddCommGroup.{u6} M₃] [_inst_12 : Module.{u1, u4} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5)] [_inst_13 : Module.{u2, u5} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7)] [_inst_14 : Module.{u3, u6} R₃ M₃ (Ring.toSemiring.{u3} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₃ : RingHom.{u2, u3} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u3} R₃ (Ring.toNonAssocRing.{u3} R₃ _inst_3))} {σ₁₃ : RingHom.{u1, u3} R R₃ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₃ (Ring.toNonAssocRing.{u3} R₃ _inst_3))} [_inst_15 : RingHomCompTriple.{u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃] [_inst_16 : TopologicalAddGroup.{u5} M₂ _inst_6 (AddCommGroup.toAddGroup.{u5} M₂ _inst_7)] [_inst_17 : TopologicalAddGroup.{u6} M₃ _inst_8 (AddCommGroup.toAddGroup.{u6} M₃ _inst_9)] (g : ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_13 _inst_14) (f : ContinuousLinearMap.{u1, u2, u4, u5} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u4) (succ u6)} (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g (Neg.neg.{max u4 u5} (ContinuousLinearMap.{u1, u2, u4, u5} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.neg.{u1, u2, u4, u5} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_16) f)) (Neg.neg.{max u4 u6} (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.neg.{u1, u3, u4, u6} R _inst_1 R₃ _inst_3 M _inst_4 _inst_5 M₃ _inst_8 _inst_9 _inst_12 _inst_14 σ₁₃ _inst_17) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g f))
but is expected to have type
- forall {R : Type.{u6}} [_inst_1 : Ring.{u6} R] {R₂ : Type.{u5}} [_inst_2 : Ring.{u5} R₂] {R₃ : Type.{u4}} [_inst_3 : Ring.{u4} R₃] {M : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M] [_inst_5 : AddCommGroup.{u1} M] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] {M₃ : Type.{u2}} [_inst_8 : TopologicalSpace.{u2} M₃] [_inst_9 : AddCommGroup.{u2} M₃] [_inst_12 : Module.{u6, u1} R M (Ring.toSemiring.{u6} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_5)] [_inst_13 : Module.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_14 : Module.{u4, u2} R₃ M₃ (Ring.toSemiring.{u4} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9)] {σ₁₂ : RingHom.{u6, u5} R R₂ (NonAssocRing.toNonAssocSemiring.{u6} R (Ring.toNonAssocRing.{u6} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u5} R₂ (Ring.toNonAssocRing.{u5} R₂ _inst_2))} {σ₂₃ : RingHom.{u5, u4} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u5} R₂ (Ring.toNonAssocRing.{u5} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u4} R₃ (Ring.toNonAssocRing.{u4} R₃ _inst_3))} {σ₁₃ : RingHom.{u6, u4} R R₃ (NonAssocRing.toNonAssocSemiring.{u6} R (Ring.toNonAssocRing.{u6} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u4} R₃ (Ring.toNonAssocRing.{u4} R₃ _inst_3))} [_inst_15 : RingHomCompTriple.{u6, u5, u4} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃] [_inst_16 : TopologicalAddGroup.{u3} M₂ _inst_6 (AddCommGroup.toAddGroup.{u3} M₂ _inst_7)] [_inst_17 : TopologicalAddGroup.{u2} M₃ _inst_8 (AddCommGroup.toAddGroup.{u2} M₃ _inst_9)] (g : ContinuousLinearMap.{u5, u4, u3, u2} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_13 _inst_14) (f : ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u1) (succ u2)} (ContinuousLinearMap.{u6, u4, u1, u2} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u3, u2} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g (Neg.neg.{max u1 u3} (ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.neg.{u6, u5, u1, u3} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_16) f)) (Neg.neg.{max u1 u2} (ContinuousLinearMap.{u6, u4, u1, u2} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.neg.{u6, u4, u1, u2} R _inst_1 R₃ _inst_3 M _inst_4 _inst_5 M₃ _inst_8 _inst_9 _inst_12 _inst_14 σ₁₃ _inst_17) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u3, u2} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g f))
+ forall {R : Type.{u6}} [_inst_1 : Ring.{u6} R] {R₂ : Type.{u5}} [_inst_2 : Ring.{u5} R₂] {R₃ : Type.{u4}} [_inst_3 : Ring.{u4} R₃] {M : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M] [_inst_5 : AddCommGroup.{u1} M] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] {M₃ : Type.{u2}} [_inst_8 : TopologicalSpace.{u2} M₃] [_inst_9 : AddCommGroup.{u2} M₃] [_inst_12 : Module.{u6, u1} R M (Ring.toSemiring.{u6} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_5)] [_inst_13 : Module.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_14 : Module.{u4, u2} R₃ M₃ (Ring.toSemiring.{u4} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9)] {σ₁₂ : RingHom.{u6, u5} R R₂ (Semiring.toNonAssocSemiring.{u6} R (Ring.toSemiring.{u6} R _inst_1)) (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2))} {σ₂₃ : RingHom.{u5, u4} R₂ R₃ (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2)) (Semiring.toNonAssocSemiring.{u4} R₃ (Ring.toSemiring.{u4} R₃ _inst_3))} {σ₁₃ : RingHom.{u6, u4} R R₃ (Semiring.toNonAssocSemiring.{u6} R (Ring.toSemiring.{u6} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} R₃ (Ring.toSemiring.{u4} R₃ _inst_3))} [_inst_15 : RingHomCompTriple.{u6, u5, u4} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃] [_inst_16 : TopologicalAddGroup.{u3} M₂ _inst_6 (AddCommGroup.toAddGroup.{u3} M₂ _inst_7)] [_inst_17 : TopologicalAddGroup.{u2} M₃ _inst_8 (AddCommGroup.toAddGroup.{u2} M₃ _inst_9)] (g : ContinuousLinearMap.{u5, u4, u3, u2} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_13 _inst_14) (f : ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u1) (succ u2)} (ContinuousLinearMap.{u6, u4, u1, u2} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u3, u2} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g (Neg.neg.{max u1 u3} (ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.neg.{u6, u5, u1, u3} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_16) f)) (Neg.neg.{max u1 u2} (ContinuousLinearMap.{u6, u4, u1, u2} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.neg.{u6, u4, u1, u2} R _inst_1 R₃ _inst_3 M _inst_4 _inst_5 M₃ _inst_8 _inst_9 _inst_12 _inst_14 σ₁₃ _inst_17) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u3, u2} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g f))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_neg ContinuousLinearMap.comp_negₓ'. -/
@[simp]
theorem comp_neg [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₂] [TopologicalAddGroup M₃]
@@ -2384,7 +2384,7 @@ theorem comp_neg [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddG
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {R₃ : Type.{u3}} [_inst_3 : Ring.{u3} R₃] {M : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} M] [_inst_5 : AddCommGroup.{u4} M] {M₂ : Type.{u5}} [_inst_6 : TopologicalSpace.{u5} M₂] [_inst_7 : AddCommGroup.{u5} M₂] {M₃ : Type.{u6}} [_inst_8 : TopologicalSpace.{u6} M₃] [_inst_9 : AddCommGroup.{u6} M₃] [_inst_12 : Module.{u1, u4} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5)] [_inst_13 : Module.{u2, u5} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7)] [_inst_14 : Module.{u3, u6} R₃ M₃ (Ring.toSemiring.{u3} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₃ : RingHom.{u2, u3} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u3} R₃ (Ring.toNonAssocRing.{u3} R₃ _inst_3))} {σ₁₃ : RingHom.{u1, u3} R R₃ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₃ (Ring.toNonAssocRing.{u3} R₃ _inst_3))} [_inst_15 : RingHomCompTriple.{u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃] [_inst_16 : TopologicalAddGroup.{u6} M₃ _inst_8 (AddCommGroup.toAddGroup.{u6} M₃ _inst_9)] (g : ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_13 _inst_14) (f : ContinuousLinearMap.{u1, u2, u4, u5} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u4) (succ u6)} (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 (Neg.neg.{max u5 u6} (ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_13 _inst_14) (ContinuousLinearMap.neg.{u2, u3, u5, u6} R₂ _inst_2 R₃ _inst_3 M₂ _inst_6 _inst_7 M₃ _inst_8 _inst_9 _inst_13 _inst_14 σ₂₃ _inst_16) g) f) (Neg.neg.{max u4 u6} (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.neg.{u1, u3, u4, u6} R _inst_1 R₃ _inst_3 M _inst_4 _inst_5 M₃ _inst_8 _inst_9 _inst_12 _inst_14 σ₁₃ _inst_16) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g f))
but is expected to have type
- forall {R : Type.{u6}} [_inst_1 : Ring.{u6} R] {R₂ : Type.{u5}} [_inst_2 : Ring.{u5} R₂] {R₃ : Type.{u4}} [_inst_3 : Ring.{u4} R₃] {M : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M] [_inst_5 : AddCommGroup.{u1} M] {M₂ : Type.{u2}} [_inst_6 : TopologicalSpace.{u2} M₂] [_inst_7 : AddCommGroup.{u2} M₂] {M₃ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₃] [_inst_9 : AddCommGroup.{u3} M₃] [_inst_12 : Module.{u6, u1} R M (Ring.toSemiring.{u6} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_5)] [_inst_13 : Module.{u5, u2} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7)] [_inst_14 : Module.{u4, u3} R₃ M₃ (Ring.toSemiring.{u4} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9)] {σ₁₂ : RingHom.{u6, u5} R R₂ (NonAssocRing.toNonAssocSemiring.{u6} R (Ring.toNonAssocRing.{u6} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u5} R₂ (Ring.toNonAssocRing.{u5} R₂ _inst_2))} {σ₂₃ : RingHom.{u5, u4} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u5} R₂ (Ring.toNonAssocRing.{u5} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u4} R₃ (Ring.toNonAssocRing.{u4} R₃ _inst_3))} {σ₁₃ : RingHom.{u6, u4} R R₃ (NonAssocRing.toNonAssocSemiring.{u6} R (Ring.toNonAssocRing.{u6} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u4} R₃ (Ring.toNonAssocRing.{u4} R₃ _inst_3))} [_inst_15 : RingHomCompTriple.{u6, u5, u4} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃] [_inst_16 : TopologicalAddGroup.{u3} M₃ _inst_8 (AddCommGroup.toAddGroup.{u3} M₃ _inst_9)] (g : ContinuousLinearMap.{u5, u4, u2, u3} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_13 _inst_14) (f : ContinuousLinearMap.{u6, u5, u1, u2} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u1) (succ u3)} (ContinuousLinearMap.{u6, u4, u1, u3} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u5, u4, u2, u3} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_13 _inst_14) (ContinuousLinearMap.neg.{u5, u4, u2, u3} R₂ _inst_2 R₃ _inst_3 M₂ _inst_6 _inst_7 M₃ _inst_8 _inst_9 _inst_13 _inst_14 σ₂₃ _inst_16) g) f) (Neg.neg.{max u1 u3} (ContinuousLinearMap.{u6, u4, u1, u3} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.neg.{u6, u4, u1, u3} R _inst_1 R₃ _inst_3 M _inst_4 _inst_5 M₃ _inst_8 _inst_9 _inst_12 _inst_14 σ₁₃ _inst_16) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g f))
+ forall {R : Type.{u6}} [_inst_1 : Ring.{u6} R] {R₂ : Type.{u5}} [_inst_2 : Ring.{u5} R₂] {R₃ : Type.{u4}} [_inst_3 : Ring.{u4} R₃] {M : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M] [_inst_5 : AddCommGroup.{u1} M] {M₂ : Type.{u2}} [_inst_6 : TopologicalSpace.{u2} M₂] [_inst_7 : AddCommGroup.{u2} M₂] {M₃ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₃] [_inst_9 : AddCommGroup.{u3} M₃] [_inst_12 : Module.{u6, u1} R M (Ring.toSemiring.{u6} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_5)] [_inst_13 : Module.{u5, u2} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7)] [_inst_14 : Module.{u4, u3} R₃ M₃ (Ring.toSemiring.{u4} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9)] {σ₁₂ : RingHom.{u6, u5} R R₂ (Semiring.toNonAssocSemiring.{u6} R (Ring.toSemiring.{u6} R _inst_1)) (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2))} {σ₂₃ : RingHom.{u5, u4} R₂ R₃ (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2)) (Semiring.toNonAssocSemiring.{u4} R₃ (Ring.toSemiring.{u4} R₃ _inst_3))} {σ₁₃ : RingHom.{u6, u4} R R₃ (Semiring.toNonAssocSemiring.{u6} R (Ring.toSemiring.{u6} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} R₃ (Ring.toSemiring.{u4} R₃ _inst_3))} [_inst_15 : RingHomCompTriple.{u6, u5, u4} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃] [_inst_16 : TopologicalAddGroup.{u3} M₃ _inst_8 (AddCommGroup.toAddGroup.{u3} M₃ _inst_9)] (g : ContinuousLinearMap.{u5, u4, u2, u3} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_13 _inst_14) (f : ContinuousLinearMap.{u6, u5, u1, u2} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u1) (succ u3)} (ContinuousLinearMap.{u6, u4, u1, u3} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u5, u4, u2, u3} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_13 _inst_14) (ContinuousLinearMap.neg.{u5, u4, u2, u3} R₂ _inst_2 R₃ _inst_3 M₂ _inst_6 _inst_7 M₃ _inst_8 _inst_9 _inst_13 _inst_14 σ₂₃ _inst_16) g) f) (Neg.neg.{max u1 u3} (ContinuousLinearMap.{u6, u4, u1, u3} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.neg.{u6, u4, u1, u3} R _inst_1 R₃ _inst_3 M _inst_4 _inst_5 M₃ _inst_8 _inst_9 _inst_12 _inst_14 σ₁₃ _inst_16) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g f))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.neg_comp ContinuousLinearMap.neg_compₓ'. -/
@[simp]
theorem neg_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₃] (g : M₂ →SL[σ₂₃] M₃)
@@ -2398,7 +2398,7 @@ theorem neg_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddG
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {R₃ : Type.{u3}} [_inst_3 : Ring.{u3} R₃] {M : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} M] [_inst_5 : AddCommGroup.{u4} M] {M₂ : Type.{u5}} [_inst_6 : TopologicalSpace.{u5} M₂] [_inst_7 : AddCommGroup.{u5} M₂] {M₃ : Type.{u6}} [_inst_8 : TopologicalSpace.{u6} M₃] [_inst_9 : AddCommGroup.{u6} M₃] [_inst_12 : Module.{u1, u4} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5)] [_inst_13 : Module.{u2, u5} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7)] [_inst_14 : Module.{u3, u6} R₃ M₃ (Ring.toSemiring.{u3} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₃ : RingHom.{u2, u3} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u3} R₃ (Ring.toNonAssocRing.{u3} R₃ _inst_3))} {σ₁₃ : RingHom.{u1, u3} R R₃ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₃ (Ring.toNonAssocRing.{u3} R₃ _inst_3))} [_inst_15 : RingHomCompTriple.{u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃] [_inst_16 : TopologicalAddGroup.{u5} M₂ _inst_6 (AddCommGroup.toAddGroup.{u5} M₂ _inst_7)] [_inst_17 : TopologicalAddGroup.{u6} M₃ _inst_8 (AddCommGroup.toAddGroup.{u6} M₃ _inst_9)] (g : ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_13 _inst_14) (f₁ : ContinuousLinearMap.{u1, u2, u4, u5} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) _inst_12 _inst_13) (f₂ : ContinuousLinearMap.{u1, u2, u4, u5} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u4) (succ u6)} (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g (HSub.hSub.{max u4 u5, max u4 u5, max u4 u5} (ContinuousLinearMap.{u1, u2, u4, u5} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.{u1, u2, u4, u5} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.{u1, u2, u4, u5} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) _inst_12 _inst_13) (instHSub.{max u4 u5} (ContinuousLinearMap.{u1, u2, u4, u5} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.sub.{u1, u2, u4, u5} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_16)) f₁ f₂)) (HSub.hSub.{max u4 u6, max u4 u6, max u4 u6} (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_14) (instHSub.{max u4 u6} (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.sub.{u1, u3, u4, u6} R _inst_1 R₃ _inst_3 M _inst_4 _inst_5 M₃ _inst_8 _inst_9 _inst_12 _inst_14 σ₁₃ _inst_17)) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g f₁) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g f₂))
but is expected to have type
- forall {R : Type.{u6}} [_inst_1 : Ring.{u6} R] {R₂ : Type.{u5}} [_inst_2 : Ring.{u5} R₂] {R₃ : Type.{u4}} [_inst_3 : Ring.{u4} R₃] {M : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M] [_inst_5 : AddCommGroup.{u1} M] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] {M₃ : Type.{u2}} [_inst_8 : TopologicalSpace.{u2} M₃] [_inst_9 : AddCommGroup.{u2} M₃] [_inst_12 : Module.{u6, u1} R M (Ring.toSemiring.{u6} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_5)] [_inst_13 : Module.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_14 : Module.{u4, u2} R₃ M₃ (Ring.toSemiring.{u4} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9)] {σ₁₂ : RingHom.{u6, u5} R R₂ (NonAssocRing.toNonAssocSemiring.{u6} R (Ring.toNonAssocRing.{u6} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u5} R₂ (Ring.toNonAssocRing.{u5} R₂ _inst_2))} {σ₂₃ : RingHom.{u5, u4} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u5} R₂ (Ring.toNonAssocRing.{u5} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u4} R₃ (Ring.toNonAssocRing.{u4} R₃ _inst_3))} {σ₁₃ : RingHom.{u6, u4} R R₃ (NonAssocRing.toNonAssocSemiring.{u6} R (Ring.toNonAssocRing.{u6} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u4} R₃ (Ring.toNonAssocRing.{u4} R₃ _inst_3))} [_inst_15 : RingHomCompTriple.{u6, u5, u4} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃] [_inst_16 : TopologicalAddGroup.{u3} M₂ _inst_6 (AddCommGroup.toAddGroup.{u3} M₂ _inst_7)] [_inst_17 : TopologicalAddGroup.{u2} M₃ _inst_8 (AddCommGroup.toAddGroup.{u2} M₃ _inst_9)] (g : ContinuousLinearMap.{u5, u4, u3, u2} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_13 _inst_14) (f₁ : ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13) (f₂ : ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u1) (succ u2)} (ContinuousLinearMap.{u6, u4, u1, u2} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u3, u2} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g (HSub.hSub.{max u1 u3, max u1 u3, max u1 u3} (ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13) (instHSub.{max u1 u3} (ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.sub.{u6, u5, u1, u3} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_16)) f₁ f₂)) (HSub.hSub.{max u1 u2, max u1 u2, max u1 u2} (ContinuousLinearMap.{u6, u4, u1, u2} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.{u6, u4, u1, u2} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.{u6, u4, u1, u2} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_14) (instHSub.{max u1 u2} (ContinuousLinearMap.{u6, u4, u1, u2} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.sub.{u6, u4, u1, u2} R _inst_1 R₃ _inst_3 M _inst_4 _inst_5 M₃ _inst_8 _inst_9 _inst_12 _inst_14 σ₁₃ _inst_17)) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u3, u2} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g f₁) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u3, u2} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g f₂))
+ forall {R : Type.{u6}} [_inst_1 : Ring.{u6} R] {R₂ : Type.{u5}} [_inst_2 : Ring.{u5} R₂] {R₃ : Type.{u4}} [_inst_3 : Ring.{u4} R₃] {M : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M] [_inst_5 : AddCommGroup.{u1} M] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] {M₃ : Type.{u2}} [_inst_8 : TopologicalSpace.{u2} M₃] [_inst_9 : AddCommGroup.{u2} M₃] [_inst_12 : Module.{u6, u1} R M (Ring.toSemiring.{u6} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_5)] [_inst_13 : Module.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_14 : Module.{u4, u2} R₃ M₃ (Ring.toSemiring.{u4} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9)] {σ₁₂ : RingHom.{u6, u5} R R₂ (Semiring.toNonAssocSemiring.{u6} R (Ring.toSemiring.{u6} R _inst_1)) (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2))} {σ₂₃ : RingHom.{u5, u4} R₂ R₃ (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2)) (Semiring.toNonAssocSemiring.{u4} R₃ (Ring.toSemiring.{u4} R₃ _inst_3))} {σ₁₃ : RingHom.{u6, u4} R R₃ (Semiring.toNonAssocSemiring.{u6} R (Ring.toSemiring.{u6} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} R₃ (Ring.toSemiring.{u4} R₃ _inst_3))} [_inst_15 : RingHomCompTriple.{u6, u5, u4} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃] [_inst_16 : TopologicalAddGroup.{u3} M₂ _inst_6 (AddCommGroup.toAddGroup.{u3} M₂ _inst_7)] [_inst_17 : TopologicalAddGroup.{u2} M₃ _inst_8 (AddCommGroup.toAddGroup.{u2} M₃ _inst_9)] (g : ContinuousLinearMap.{u5, u4, u3, u2} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_13 _inst_14) (f₁ : ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13) (f₂ : ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u1) (succ u2)} (ContinuousLinearMap.{u6, u4, u1, u2} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u3, u2} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g (HSub.hSub.{max u1 u3, max u1 u3, max u1 u3} (ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13) (instHSub.{max u1 u3} (ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.sub.{u6, u5, u1, u3} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_16)) f₁ f₂)) (HSub.hSub.{max u1 u2, max u1 u2, max u1 u2} (ContinuousLinearMap.{u6, u4, u1, u2} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.{u6, u4, u1, u2} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.{u6, u4, u1, u2} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_14) (instHSub.{max u1 u2} (ContinuousLinearMap.{u6, u4, u1, u2} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.sub.{u6, u4, u1, u2} R _inst_1 R₃ _inst_3 M _inst_4 _inst_5 M₃ _inst_8 _inst_9 _inst_12 _inst_14 σ₁₃ _inst_17)) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u3, u2} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g f₁) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u3, u2} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g f₂))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_sub ContinuousLinearMap.comp_subₓ'. -/
@[simp]
theorem comp_sub [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₂] [TopologicalAddGroup M₃]
@@ -2412,7 +2412,7 @@ theorem comp_sub [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddG
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {R₃ : Type.{u3}} [_inst_3 : Ring.{u3} R₃] {M : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} M] [_inst_5 : AddCommGroup.{u4} M] {M₂ : Type.{u5}} [_inst_6 : TopologicalSpace.{u5} M₂] [_inst_7 : AddCommGroup.{u5} M₂] {M₃ : Type.{u6}} [_inst_8 : TopologicalSpace.{u6} M₃] [_inst_9 : AddCommGroup.{u6} M₃] [_inst_12 : Module.{u1, u4} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5)] [_inst_13 : Module.{u2, u5} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7)] [_inst_14 : Module.{u3, u6} R₃ M₃ (Ring.toSemiring.{u3} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₃ : RingHom.{u2, u3} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u3} R₃ (Ring.toNonAssocRing.{u3} R₃ _inst_3))} {σ₁₃ : RingHom.{u1, u3} R R₃ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₃ (Ring.toNonAssocRing.{u3} R₃ _inst_3))} [_inst_15 : RingHomCompTriple.{u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃] [_inst_16 : TopologicalAddGroup.{u6} M₃ _inst_8 (AddCommGroup.toAddGroup.{u6} M₃ _inst_9)] (g₁ : ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_13 _inst_14) (g₂ : ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_13 _inst_14) (f : ContinuousLinearMap.{u1, u2, u4, u5} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u4) (succ u6)} (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 (HSub.hSub.{max u5 u6, max u5 u6, max u5 u6} (ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_13 _inst_14) (ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_13 _inst_14) (ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_13 _inst_14) (instHSub.{max u5 u6} (ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_13 _inst_14) (ContinuousLinearMap.sub.{u2, u3, u5, u6} R₂ _inst_2 R₃ _inst_3 M₂ _inst_6 _inst_7 M₃ _inst_8 _inst_9 _inst_13 _inst_14 σ₂₃ _inst_16)) g₁ g₂) f) (HSub.hSub.{max u4 u6, max u4 u6, max u4 u6} (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_14) (instHSub.{max u4 u6} (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.sub.{u1, u3, u4, u6} R _inst_1 R₃ _inst_3 M _inst_4 _inst_5 M₃ _inst_8 _inst_9 _inst_12 _inst_14 σ₁₃ _inst_16)) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g₁ f) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g₂ f))
but is expected to have type
- forall {R : Type.{u6}} [_inst_1 : Ring.{u6} R] {R₂ : Type.{u5}} [_inst_2 : Ring.{u5} R₂] {R₃ : Type.{u4}} [_inst_3 : Ring.{u4} R₃] {M : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M] [_inst_5 : AddCommGroup.{u1} M] {M₂ : Type.{u2}} [_inst_6 : TopologicalSpace.{u2} M₂] [_inst_7 : AddCommGroup.{u2} M₂] {M₃ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₃] [_inst_9 : AddCommGroup.{u3} M₃] [_inst_12 : Module.{u6, u1} R M (Ring.toSemiring.{u6} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_5)] [_inst_13 : Module.{u5, u2} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7)] [_inst_14 : Module.{u4, u3} R₃ M₃ (Ring.toSemiring.{u4} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9)] {σ₁₂ : RingHom.{u6, u5} R R₂ (NonAssocRing.toNonAssocSemiring.{u6} R (Ring.toNonAssocRing.{u6} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u5} R₂ (Ring.toNonAssocRing.{u5} R₂ _inst_2))} {σ₂₃ : RingHom.{u5, u4} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u5} R₂ (Ring.toNonAssocRing.{u5} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u4} R₃ (Ring.toNonAssocRing.{u4} R₃ _inst_3))} {σ₁₃ : RingHom.{u6, u4} R R₃ (NonAssocRing.toNonAssocSemiring.{u6} R (Ring.toNonAssocRing.{u6} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u4} R₃ (Ring.toNonAssocRing.{u4} R₃ _inst_3))} [_inst_15 : RingHomCompTriple.{u6, u5, u4} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃] [_inst_16 : TopologicalAddGroup.{u3} M₃ _inst_8 (AddCommGroup.toAddGroup.{u3} M₃ _inst_9)] (g₁ : ContinuousLinearMap.{u5, u4, u2, u3} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_13 _inst_14) (g₂ : ContinuousLinearMap.{u5, u4, u2, u3} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_13 _inst_14) (f : ContinuousLinearMap.{u6, u5, u1, u2} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u1) (succ u3)} (ContinuousLinearMap.{u6, u4, u1, u3} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 (HSub.hSub.{max 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(AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_13 _inst_14) (ContinuousLinearMap.sub.{u5, u4, u2, u3} R₂ _inst_2 R₃ _inst_3 M₂ _inst_6 _inst_7 M₃ _inst_8 _inst_9 _inst_13 _inst_14 σ₂₃ _inst_16)) g₁ g₂) f) (HSub.hSub.{max u1 u3, max u1 u3, max u1 u3} (ContinuousLinearMap.{u6, u4, u1, u3} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.{u6, u4, u1, u3} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.{u6, u4, u1, u3} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_14) (instHSub.{max u1 u3} (ContinuousLinearMap.{u6, u4, u1, u3} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.sub.{u6, u4, u1, u3} R _inst_1 R₃ _inst_3 M _inst_4 _inst_5 M₃ _inst_8 _inst_9 _inst_12 _inst_14 σ₁₃ _inst_16)) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g₁ f) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g₂ f))
+ forall {R : Type.{u6}} [_inst_1 : Ring.{u6} R] {R₂ : Type.{u5}} [_inst_2 : Ring.{u5} R₂] {R₃ : Type.{u4}} [_inst_3 : Ring.{u4} R₃] {M : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M] [_inst_5 : AddCommGroup.{u1} M] {M₂ : Type.{u2}} [_inst_6 : TopologicalSpace.{u2} M₂] [_inst_7 : AddCommGroup.{u2} M₂] {M₃ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₃] [_inst_9 : AddCommGroup.{u3} M₃] [_inst_12 : Module.{u6, u1} R M (Ring.toSemiring.{u6} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_5)] [_inst_13 : Module.{u5, u2} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7)] [_inst_14 : Module.{u4, u3} R₃ M₃ (Ring.toSemiring.{u4} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9)] {σ₁₂ : RingHom.{u6, u5} R R₂ (Semiring.toNonAssocSemiring.{u6} R (Ring.toSemiring.{u6} R _inst_1)) (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2))} {σ₂₃ : RingHom.{u5, u4} R₂ R₃ (Semiring.toNonAssocSemiring.{u5} R₂ (Ring.toSemiring.{u5} R₂ _inst_2)) (Semiring.toNonAssocSemiring.{u4} R₃ (Ring.toSemiring.{u4} R₃ _inst_3))} {σ₁₃ : RingHom.{u6, u4} R R₃ (Semiring.toNonAssocSemiring.{u6} R (Ring.toSemiring.{u6} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} R₃ (Ring.toSemiring.{u4} R₃ _inst_3))} [_inst_15 : RingHomCompTriple.{u6, u5, u4} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃] [_inst_16 : TopologicalAddGroup.{u3} M₃ _inst_8 (AddCommGroup.toAddGroup.{u3} M₃ _inst_9)] (g₁ : ContinuousLinearMap.{u5, u4, u2, u3} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_13 _inst_14) (g₂ : ContinuousLinearMap.{u5, u4, u2, u3} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_13 _inst_14) (f : ContinuousLinearMap.{u6, u5, u1, u2} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u1) (succ u3)} (ContinuousLinearMap.{u6, u4, u1, u3} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u5, u4, u2, u3} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_13 _inst_14) (ContinuousLinearMap.{u5, u4, u2, u3} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_13 _inst_14) (ContinuousLinearMap.{u5, u4, u2, u3} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_13 _inst_14) (instHSub.{max u2 u3} (ContinuousLinearMap.{u5, u4, u2, u3} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_13 _inst_14) (ContinuousLinearMap.sub.{u5, u4, u2, u3} R₂ _inst_2 R₃ _inst_3 M₂ _inst_6 _inst_7 M₃ _inst_8 _inst_9 _inst_13 _inst_14 σ₂₃ _inst_16)) g₁ g₂) f) (HSub.hSub.{max u1 u3, max u1 u3, max u1 u3} (ContinuousLinearMap.{u6, u4, u1, u3} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.{u6, u4, u1, u3} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.{u6, u4, u1, u3} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_14) (instHSub.{max u1 u3} (ContinuousLinearMap.{u6, u4, u1, u3} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.sub.{u6, u4, u1, u3} R _inst_1 R₃ _inst_3 M _inst_4 _inst_5 M₃ _inst_8 _inst_9 _inst_12 _inst_14 σ₁₃ _inst_16)) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g₁ f) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g₂ f))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.sub_comp ContinuousLinearMap.sub_compₓ'. -/
@[simp]
theorem sub_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₃] (g₁ g₂ : M₂ →SL[σ₂₃] M₃)
@@ -2432,7 +2432,7 @@ instance [TopologicalAddGroup M] : Ring (M →L[R] M) :=
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_15 : TopologicalSpace.{u1} R] [_inst_16 : TopologicalRing.{u1} R _inst_15 (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))] (c : R) (n : Nat), Eq.{succ u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) Nat (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Ring.toMonoid.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.ring.{u1, u1} R _inst_1 R _inst_15 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (TopologicalRing.to_topologicalAddGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) _inst_15 _inst_16))))) (ContinuousLinearMap.smulRight.{u1, u1, u1, u1} R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (IsScalarTower.left.{u1, u1} R R (Ring.toMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (Ring.toMonoid.{u1} R _inst_1))) _inst_15 (ContinuousMul.to_continuousSMul.{u1} R _inst_15 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1)) (TopologicalSemiring.to_continuousMul.{u1} R _inst_15 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (TopologicalRing.to_topologicalSemiring.{u1} R _inst_15 (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) _inst_16))) (OfNat.ofNat.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) 1 (One.one.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.one.{u1, u1} R (Ring.toSemiring.{u1} R _inst_1) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) c) n) (ContinuousLinearMap.smulRight.{u1, u1, u1, u1} R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (IsScalarTower.left.{u1, u1} R R (Ring.toMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (Ring.toMonoid.{u1} R _inst_1))) _inst_15 (ContinuousMul.to_continuousSMul.{u1} R _inst_15 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1)) (TopologicalSemiring.to_continuousMul.{u1} R _inst_15 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (TopologicalRing.to_topologicalSemiring.{u1} R _inst_15 (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) _inst_16))) (OfNat.ofNat.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) 1 (One.one.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.one.{u1, u1} R (Ring.toSemiring.{u1} R _inst_1) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R _inst_1))) c n))
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_15 : TopologicalSpace.{u1} R] [_inst_16 : TopologicalRing.{u1} R _inst_15 (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))] (c : R) (n : Nat), Eq.{succ u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) Nat (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.monoidWithZero.{u1, u1} R (Ring.toSemiring.{u1} R _inst_1) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (ContinuousLinearMap.smulRight.{u1, u1, u1, u1} R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (IsScalarTower.left.{u1, u1} R R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_15 (ContinuousMul.to_continuousSMul.{u1} R _inst_15 (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (TopologicalSemiring.toContinuousMul.{u1} R _inst_15 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (TopologicalRing.toTopologicalSemiring.{u1} R _inst_15 (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) _inst_16))) (OfNat.ofNat.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.one.{u1, u1} R (Ring.toSemiring.{u1} R _inst_1) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) c) n) (ContinuousLinearMap.smulRight.{u1, u1, u1, u1} R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (IsScalarTower.left.{u1, u1} R R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_15 (ContinuousMul.to_continuousSMul.{u1} R _inst_15 (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (TopologicalSemiring.toContinuousMul.{u1} R _inst_15 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (TopologicalRing.toTopologicalSemiring.{u1} R _inst_15 (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) _inst_16))) (OfNat.ofNat.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.one.{u1, u1} R (Ring.toSemiring.{u1} R _inst_1) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) c n))
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_15 : TopologicalSpace.{u1} R] [_inst_16 : TopologicalRing.{u1} R _inst_15 (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))] (c : R) (n : Nat), Eq.{succ u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) Nat (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.monoidWithZero.{u1, u1} R (Ring.toSemiring.{u1} R _inst_1) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (ContinuousLinearMap.smulRight.{u1, u1, u1, u1} R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (IsScalarTower.left.{u1, u1} R R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_15 (ContinuousMul.to_continuousSMul.{u1} R _inst_15 (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (TopologicalSemiring.toContinuousMul.{u1} R _inst_15 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (TopologicalRing.toTopologicalSemiring.{u1} R _inst_15 (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) _inst_16))) (OfNat.ofNat.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.one.{u1, u1} R (Ring.toSemiring.{u1} R _inst_1) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) c) n) (ContinuousLinearMap.smulRight.{u1, u1, u1, u1} R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (IsScalarTower.left.{u1, u1} R R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_15 (ContinuousMul.to_continuousSMul.{u1} R _inst_15 (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (TopologicalSemiring.toContinuousMul.{u1} R _inst_15 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (TopologicalRing.toTopologicalSemiring.{u1} R _inst_15 (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) _inst_16))) (OfNat.ofNat.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.one.{u1, u1} R (Ring.toSemiring.{u1} R _inst_1) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) c n))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_right_one_pow ContinuousLinearMap.smulRight_one_powₓ'. -/
theorem smulRight_one_pow [TopologicalSpace R] [TopologicalRing R] (c : R) (n : ℕ) :
smulRight (1 : R →L[R] R) c ^ n = smulRight (1 : R →L[R] R) (c ^ n) :=
@@ -2451,7 +2451,7 @@ variable {σ₂₁ : R₂ →+* R} [RingHomInvPair σ₁₂ σ₂₁]
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u1} R₂ R (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))} [_inst_15 : RingHomInvPair.{u1, u2} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : TopologicalAddGroup.{u3} M _inst_4 (AddCommGroup.toAddGroup.{u3} M _inst_5)] (f₁ : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (f₂ : ContinuousLinearMap.{u2, u1, u4, u3} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_13 _inst_12), (Function.RightInverse.{succ u3, succ u4} M M₂ (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (ContinuousLinearMap.{u2, u1, u4, u3} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_13 _inst_12) (fun (_x : ContinuousLinearMap.{u2, u1, u4, u3} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_13 _inst_12) => M₂ -> M) (ContinuousLinearMap.toFun.{u2, u1, u4, u3} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_13 _inst_12) f₂) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) => M -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) f₁)) -> (ContinuousLinearMap.{u1, u1, u3, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) M (Submodule.setLike.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12)) (LinearMap.ker.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u4, u1, u2, u3, u4} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13)) f₁)) (Subtype.topologicalSpace.{u3} M (fun (x : M) => Membership.Mem.{u3, u3} M (Submodule.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) M (Submodule.setLike.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12)) x (LinearMap.ker.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u4, u1, u2, u3, u4} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (Submodule.addCommMonoid.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12 (LinearMap.ker.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u4, u1, u2, u3, u4} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_12 (Submodule.module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12 (LinearMap.ker.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u4, u1, u2, u3, u4} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13)) f₁)))
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u1} R₂ R (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))} [_inst_15 : RingHomInvPair.{u1, u2} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : TopologicalAddGroup.{u3} M _inst_4 (AddCommGroup.toAddGroup.{u3} M _inst_5)] (f₁ : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (f₂ : ContinuousLinearMap.{u2, u1, u4, u3} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_13 _inst_12), (Function.RightInverse.{succ u3, succ u4} M M₂ (FunLike.coe.{max (succ u3) (succ u4), succ u4, succ u3} (ContinuousLinearMap.{u2, u1, u4, u3} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_13 _inst_12) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M) _x) (ContinuousMapClass.toFunLike.{max u3 u4, u4, u3} (ContinuousLinearMap.{u2, u1, u4, u3} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_13 _inst_12) M₂ M _inst_6 _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u4, u2, u1, u4, u3} (ContinuousLinearMap.{u2, u1, u4, u3} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_13 _inst_12) R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_13 _inst_12 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u1, u4, u3} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_13 _inst_12))) f₂) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u3 u4, u3, u4} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u4, u1, u2, u3, u4} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13))) f₁)) -> (ContinuousLinearMap.{u1, u1, u3, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submodule.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) M (Submodule.setLike.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12)) x (LinearMap.ker.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u4, u1, u2, u3, u4} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13)) f₁))) (instTopologicalSpaceSubtype.{u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submodule.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) M (Submodule.setLike.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12)) x (LinearMap.ker.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u4, u1, u2, u3, u4} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (Submodule.addCommMonoid.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12 (LinearMap.ker.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u4, u1, u2, u3, u4} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_12 (Submodule.module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12 (LinearMap.ker.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u4, u1, u2, u3, u4} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13)) f₁)))
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R₂ (Ring.toSemiring.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u1} R₂ R (Semiring.toNonAssocSemiring.{u2} R₂ (Ring.toSemiring.{u2} R₂ _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))} [_inst_15 : RingHomInvPair.{u1, u2} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : TopologicalAddGroup.{u3} M _inst_4 (AddCommGroup.toAddGroup.{u3} M _inst_5)] (f₁ : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (f₂ : ContinuousLinearMap.{u2, u1, u4, u3} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_13 _inst_12), (Function.RightInverse.{succ u3, succ u4} M M₂ (FunLike.coe.{max (succ u3) (succ u4), succ u4, succ u3} (ContinuousLinearMap.{u2, u1, u4, u3} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_13 _inst_12) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M) _x) 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_inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_13 _inst_12))) f₂) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u3 u4, u3, u4} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u4, u1, u2, u3, u4} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R 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_inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13)) f₁)))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.proj_ker_of_right_inverse ContinuousLinearMap.projKerOfRightInverseₓ'. -/
/-- Given a right inverse `f₂ : M₂ →L[R] M` to `f₁ : M →L[R] M₂`,
`proj_ker_of_right_inverse f₁ f₂ h` is the projection `M →L[R] f₁.ker` along `f₂.range`. -/
@@ -2464,7 +2464,7 @@ def projKerOfRightInverse [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u1} R₂ R (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))} [_inst_15 : RingHomInvPair.{u1, u2} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : TopologicalAddGroup.{u3} M _inst_4 (AddCommGroup.toAddGroup.{u3} M _inst_5)] (f₁ : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (f₂ : ContinuousLinearMap.{u2, u1, u4, u3} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_13 _inst_12) (h : Function.RightInverse.{succ u3, succ u4} M M₂ (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (ContinuousLinearMap.{u2, u1, u4, u3} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_13 _inst_12) (fun (_x : ContinuousLinearMap.{u2, u1, u4, u3} R₂ R 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but is expected to have type
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(Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ 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_inst_12 _inst_13)) f₁))) _x) (ContinuousMapClass.toFunLike.{u4, u4, u4} (ContinuousLinearMap.{u3, u3, u4, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M 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_inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) _inst_4 (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) 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(AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (Submodule.addCommMonoid.{u3, u4} R M 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M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))))) (ContinuousLinearMap.projKerOfRightInverse.{u3, u2, u4, u1} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ σ₂₁ _inst_15 _inst_16 f₁ f₂ h) x)) (HSub.hSub.{u4, u4, u4} M ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (a : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) a) (ContinuousMapClass.toFunLike.{max u4 u1, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) f₁ x)) M (instHSub.{u4} M (SubNegMonoid.toSub.{u4} M (AddGroup.toSubNegMonoid.{u4} M (AddCommGroup.toAddGroup.{u4} M _inst_5)))) x (FunLike.coe.{max (succ u4) (succ u1), succ u1, succ u4} (ContinuousLinearMap.{u2, u3, u1, u4} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_13 _inst_12) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M) _x) (ContinuousMapClass.toFunLike.{max u4 u1, u1, u4} (ContinuousLinearMap.{u2, u3, u1, u4} R₂ R (Ring.toSemiring.{u2} 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_inst_13 _inst_12))) f₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u4 u1, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) M M₂ _inst_4 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) f₁ x)))
+ forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} M] [_inst_5 : AddCommGroup.{u4} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5)] [_inst_13 : Module.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R₂ (Ring.toSemiring.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u3} R₂ R (Semiring.toNonAssocSemiring.{u2} R₂ (Ring.toSemiring.{u2} R₂ _inst_2)) (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))} [_inst_15 : RingHomInvPair.{u3, u2} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : TopologicalAddGroup.{u4} M _inst_4 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_inst_12 _inst_13)) f₁))) (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (Submodule.addCommMonoid.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_12 (Submodule.module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) M (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) _inst_4 (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (ContinuousSemilinearMapClass.toContinuousMapClass.{u4, u3, u3, u4, u4} (ContinuousLinearMap.{u3, u3, u4, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (Submodule.addCommMonoid.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M 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_inst_12 _inst_13)) f₁))) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) 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_inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (Submodule.addCommMonoid.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ 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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_proj_ker_of_right_inverse_apply ContinuousLinearMap.coe_projKerOfRightInverse_applyₓ'. -/
@[simp]
theorem coe_projKerOfRightInverse_apply [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂)
@@ -2477,7 +2477,7 @@ theorem coe_projKerOfRightInverse_apply [TopologicalAddGroup M] (f₁ : M →SL[
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u1} R₂ R (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))} [_inst_15 : RingHomInvPair.{u1, u2} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : 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but is expected to have type
- forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} M] [_inst_5 : AddCommGroup.{u4} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5)] [_inst_13 : Module.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u3, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u3} R₂ R (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))} [_inst_15 : RingHomInvPair.{u3, u2} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : 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(AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) M (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) _inst_4 (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (ContinuousSemilinearMapClass.toContinuousMapClass.{u4, u3, u3, u4, u4} (ContinuousLinearMap.{u3, u3, u4, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (Submodule.addCommMonoid.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_12 (Submodule.module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (Submodule.addCommMonoid.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ 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(AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_12 (Submodule.module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u4, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (Submodule.addCommMonoid.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_12 (Submodule.module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))))) (ContinuousLinearMap.projKerOfRightInverse.{u3, u2, u4, u1} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ σ₂₁ _inst_15 _inst_16 f₁ f₂ h) (Subtype.val.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Set.{u4} M) (Set.instMembershipSet.{u4} M) x (SetLike.coe.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) x)) x
+ forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} M] [_inst_5 : AddCommGroup.{u4} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5)] [_inst_13 : Module.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R₂ (Ring.toSemiring.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u3} R₂ R (Semiring.toNonAssocSemiring.{u2} R₂ (Ring.toSemiring.{u2} R₂ _inst_2)) (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))} [_inst_15 : RingHomInvPair.{u3, u2} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : TopologicalAddGroup.{u4} M _inst_4 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(AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) _x) (ContinuousMapClass.toFunLike.{u4, u4, u4} (ContinuousLinearMap.{u3, u3, u4, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) 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σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 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_inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_12 (Submodule.module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, 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(ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) M (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) _inst_4 (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (ContinuousSemilinearMapClass.toContinuousMapClass.{u4, u3, u3, u4, u4} (ContinuousLinearMap.{u3, u3, u4, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M 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_inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} 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(AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 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(ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_12 (Submodule.module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ 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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.proj_ker_of_right_inverse_apply_idem ContinuousLinearMap.projKerOfRightInverse_apply_idemₓ'. -/
@[simp]
theorem projKerOfRightInverse_apply_idem [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂)
@@ -2490,7 +2490,7 @@ theorem projKerOfRightInverse_apply_idem [TopologicalAddGroup M] (f₁ : M →SL
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u1} R₂ R (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))} [_inst_15 : RingHomInvPair.{u1, u2} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : TopologicalAddGroup.{u3} M _inst_4 (AddCommGroup.toAddGroup.{u3} M _inst_5)] (f₁ : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (f₂ : ContinuousLinearMap.{u2, u1, u4, u3} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_13 _inst_12) (h : Function.RightInverse.{succ u3, succ u4} M M₂ (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (ContinuousLinearMap.{u2, u1, u4, u3} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_13 _inst_12) (fun (_x : ContinuousLinearMap.{u2, u1, u4, u3} R₂ R 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but is expected to have type
- forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} M] [_inst_5 : AddCommGroup.{u4} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5)] [_inst_13 : Module.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u3, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u3} R₂ R (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))} [_inst_15 : RingHomInvPair.{u3, u2} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : TopologicalAddGroup.{u4} M _inst_4 (AddCommGroup.toAddGroup.{u4} M _inst_5)] (f₁ : ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (f₂ : ContinuousLinearMap.{u2, u3, u1, u4} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_13 _inst_12) (h : Function.RightInverse.{succ u4, succ u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u1, succ u4} (ContinuousLinearMap.{u2, u3, u1, u4} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_13 _inst_12) M₂ (fun (_x : M₂) => (fun 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_inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) M (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) _inst_4 (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ 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(AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (ContinuousSemilinearMapClass.toContinuousMapClass.{u4, u3, u3, u4, u4} (ContinuousLinearMap.{u3, u3, u4, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) 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_inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R 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(AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (Submodule.addCommMonoid.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ 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(AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_12 (Submodule.module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u4, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} 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(ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))))
+ forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} M] [_inst_5 : AddCommGroup.{u4} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5)] [_inst_13 : Module.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R₂ (Ring.toSemiring.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u3} R₂ R (Semiring.toNonAssocSemiring.{u2} R₂ (Ring.toSemiring.{u2} R₂ _inst_2)) (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))} [_inst_15 : RingHomInvPair.{u3, u2} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : TopologicalAddGroup.{u4} M _inst_4 (AddCommGroup.toAddGroup.{u4} M _inst_5)] (f₁ : ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (f₂ : ContinuousLinearMap.{u2, u3, u1, u4} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_13 _inst_12) (h : Function.RightInverse.{succ u4, succ u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u1, succ u4} (ContinuousLinearMap.{u2, u3, u1, u4} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_13 _inst_12) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M) _x) 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_inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) M (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) _inst_4 (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) 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_inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (Submodule.addCommMonoid.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, 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(ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_12 (Submodule.module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (Submodule.addCommMonoid.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_12 (Submodule.module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u4, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, 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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.proj_ker_of_right_inverse_comp_inv ContinuousLinearMap.projKerOfRightInverse_comp_invₓ'. -/
@[simp]
theorem projKerOfRightInverse_comp_inv [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂)
@@ -2511,7 +2511,7 @@ variable {R M : Type _}
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : DivisionRing.{u1} R] [_inst_3 : ContinuousSub.{u1} R _inst_1 (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_2))))))] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : TopologicalSpace.{u2} M] [_inst_6 : ContinuousAdd.{u2} M _inst_5 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_4)))))] [_inst_7 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_8 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_7)))) _inst_1 _inst_5] (f : ContinuousLinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) R _inst_1 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_2))))) _inst_7 (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))), (Ne.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) R _inst_1 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_2))))) _inst_7 (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) f (OfNat.ofNat.{max u2 u1} (ContinuousLinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) R _inst_1 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_2))))) _inst_7 (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) 0 (OfNat.mk.{max u2 u1} (ContinuousLinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) R _inst_1 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_2))))) _inst_7 (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) 0 (Zero.zero.{max u2 u1} (ContinuousLinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) R _inst_1 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_2))))) _inst_7 (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) (ContinuousLinearMap.zero.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) R _inst_1 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_2))))) _inst_7 (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))))))) -> (IsOpenMap.{u2, u1} M R _inst_5 _inst_1 (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (ContinuousLinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) R _inst_1 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_2))))) _inst_7 (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) R _inst_1 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_2))))) _inst_7 (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) => M -> R) (ContinuousLinearMap.toFun.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) R _inst_1 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_2))))) _inst_7 (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) f))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} R] [_inst_2 : DivisionRing.{u2} R] [_inst_3 : ContinuousSub.{u2} R _inst_1 (Ring.toSub.{u2} R (DivisionRing.toRing.{u2} R _inst_2))] [_inst_4 : AddCommGroup.{u1} M] [_inst_5 : TopologicalSpace.{u1} M] [_inst_6 : ContinuousAdd.{u1} M _inst_5 (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_4)))))] [_inst_7 : Module.{u2, u1} R M (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4)] [_inst_8 : ContinuousSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (Module.toMulActionWithZero.{u2, u1} R M (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_7)))) _inst_1 _inst_5] (f : ContinuousLinearMap.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))), (Ne.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) f (OfNat.ofNat.{max u2 u1} (ContinuousLinearMap.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) 0 (Zero.toOfNat0.{max u2 u1} (ContinuousLinearMap.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) (ContinuousLinearMap.zero.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2))))))) -> (IsOpenMap.{u1, u2} M R _inst_5 _inst_1 (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousLinearMap.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => R) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousLinearMap.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) M R _inst_5 _inst_1 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u2, u2, u1, u2} (ContinuousLinearMap.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2))) (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))))) f))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} R] [_inst_2 : DivisionRing.{u2} R] [_inst_3 : ContinuousSub.{u2} R _inst_1 (Ring.toSub.{u2} R (DivisionRing.toRing.{u2} R _inst_2))] [_inst_4 : AddCommGroup.{u1} M] [_inst_5 : TopologicalSpace.{u1} M] [_inst_6 : ContinuousAdd.{u1} M _inst_5 (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_4)))))] [_inst_7 : Module.{u2, u1} R M (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4)] [_inst_8 : ContinuousSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (Module.toMulActionWithZero.{u2, u1} R M (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_7)))) _inst_1 _inst_5] (f : ContinuousLinearMap.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))), (Ne.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) f (OfNat.ofNat.{max u2 u1} (ContinuousLinearMap.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) 0 (Zero.toOfNat0.{max u2 u1} (ContinuousLinearMap.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) (ContinuousLinearMap.zero.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2))))))) -> (IsOpenMap.{u1, u2} M R _inst_5 _inst_1 (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousLinearMap.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => R) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousLinearMap.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) M R _inst_5 _inst_1 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u2, u2, u1, u2} (ContinuousLinearMap.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2))) (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))))) f))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.is_open_map_of_ne_zero ContinuousLinearMap.isOpenMap_of_ne_zeroₓ'. -/
/-- A nonzero continuous linear functional is open. -/
protected theorem isOpenMap_of_ne_zero [TopologicalSpace R] [DivisionRing R] [ContinuousSub R]
@@ -2788,7 +2788,7 @@ variable {R}
lean 3 declaration is
forall {A : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u4}} [_inst_8 : Ring.{u4} R] [_inst_9 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_10 : Module.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u2, u3, u4, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toHasSmul.{u4, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u4, u2} R M (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u4, u2} R M (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5] (f : ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u2) (succ u3)} (LinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) ((fun (a : Sort.{max (succ u2) (succ u3)}) (b : Sort.{max (succ u2) (succ u3)}) [self : HasLiftT.{max (succ u2) (succ u3), max (succ u2) (succ u3)} a b] => self.0) (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} 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but is expected to have type
- forall {A : Type.{u4}} {M : Type.{u3}} {M₂ : Type.{u2}} [_inst_1 : Ring.{u4} A] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u2} M₂] [_inst_4 : Module.{u4, u3} A M (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_5 : Module.{u4, u2} A M₂ (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : TopologicalSpace.{u2} M₂] {R : Type.{u1}} [_inst_8 : Ring.{u1} R] [_inst_9 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_10 : Module.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u3, u2, u1, u4} M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) R A (Ring.toSemiring.{u4} A _inst_1) (SMulZeroClass.toSMul.{u1, u3} R M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (Module.toMulActionWithZero.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u1, u2} R M₂ (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_10)))) _inst_5] (f : ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u3) (succ u2)} (LinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.toLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10 (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f)) (LinearMap.restrictScalars.{u1, u4, u3, u2} R A M M₂ (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10 _inst_4 _inst_5 _inst_11 (ContinuousLinearMap.toLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5 f))
+ forall {A : Type.{u4}} {M : Type.{u3}} {M₂ : Type.{u2}} [_inst_1 : Ring.{u4} A] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u2} M₂] [_inst_4 : Module.{u4, u3} A M (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_5 : Module.{u4, u2} A M₂ (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : TopologicalSpace.{u2} M₂] {R : Type.{u1}} [_inst_8 : Ring.{u1} R] [_inst_9 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_10 : Module.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u3, u2, u1, u4} M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) R A (Ring.toSemiring.{u4} A _inst_1) (SMulZeroClass.toSMul.{u1, u3} R M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (Module.toMulActionWithZero.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u1, u2} R M₂ (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_10)))) _inst_5] (f : ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u3) (succ u2)} (LinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.toLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10 (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f)) (LinearMap.restrictScalars.{u1, u4, u3, u2} R A M M₂ (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10 _inst_4 _inst_5 _inst_11 (ContinuousLinearMap.toLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5 f))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_restrict_scalars ContinuousLinearMap.coe_restrictScalarsₓ'. -/
@[simp, norm_cast]
theorem coe_restrictScalars (f : M →L[A] M₂) :
@@ -2800,7 +2800,7 @@ theorem coe_restrictScalars (f : M →L[A] M₂) :
lean 3 declaration is
forall {A : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u4}} [_inst_8 : Ring.{u4} R] [_inst_9 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_10 : Module.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u2, u3, u4, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toHasSmul.{u4, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u4, u2} R M (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u4, u2} R M (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5] (f : ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u2) (succ u3)} (M -> M₂) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (fun (_x : ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) => M -> M₂) (ContinuousLinearMap.toFun.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) => M -> M₂) (ContinuousLinearMap.toFun.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) f)
but is expected to have type
- forall {A : Type.{u4}} {M : Type.{u3}} {M₂ : Type.{u2}} [_inst_1 : Ring.{u4} A] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u2} M₂] [_inst_4 : Module.{u4, u3} A M (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_5 : Module.{u4, u2} A M₂ (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : TopologicalSpace.{u2} M₂] {R : Type.{u1}} [_inst_8 : Ring.{u1} R] [_inst_9 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_10 : Module.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u3, u2, u1, u4} M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) R A (Ring.toSemiring.{u4} A _inst_1) (SMulZeroClass.toSMul.{u1, u3} R M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (Module.toMulActionWithZero.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u1, u2} R M₂ (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_10)))) _inst_5] (f : ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u3) (succ u2)} (forall (ᾰ : M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u3, u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) M M₂ _inst_6 _inst_7 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u1, u1, u3, u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10))) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u3, u2} (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) M M₂ _inst_6 _inst_7 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u4, u4, u3, u2} (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5))) f)
+ forall {A : Type.{u4}} {M : Type.{u3}} {M₂ : Type.{u2}} [_inst_1 : Ring.{u4} A] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u2} M₂] [_inst_4 : Module.{u4, u3} A M (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_5 : Module.{u4, u2} A M₂ (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : TopologicalSpace.{u2} M₂] {R : Type.{u1}} [_inst_8 : Ring.{u1} R] [_inst_9 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_10 : Module.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u3, u2, u1, u4} M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) R A (Ring.toSemiring.{u4} A _inst_1) (SMulZeroClass.toSMul.{u1, u3} R M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (Module.toMulActionWithZero.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u1, u2} R M₂ (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_10)))) _inst_5] (f : ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u3) (succ u2)} (forall (ᾰ : M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u3, u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) M M₂ _inst_6 _inst_7 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u1, u1, u3, u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10))) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u3, u2} (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) M M₂ _inst_6 _inst_7 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u4, u4, u3, u2} (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5))) f)
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_restrict_scalars' ContinuousLinearMap.coe_restrictScalars'ₓ'. -/
@[simp]
theorem coe_restrictScalars' (f : M →L[A] M₂) : ⇑(f.restrictScalars R) = f :=
@@ -2811,7 +2811,7 @@ theorem coe_restrictScalars' (f : M →L[A] M₂) : ⇑(f.restrictScalars R) = f
lean 3 declaration is
forall {A : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u4}} [_inst_8 : Ring.{u4} R] [_inst_9 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_10 : Module.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u2, u3, u4, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toHasSmul.{u4, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u4, u2} R M (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u4, u2} R M (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5], Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (OfNat.ofNat.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) 0 (OfNat.mk.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) 0 (Zero.zero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.zero.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5))))) (OfNat.ofNat.{max u2 u3} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) 0 (OfNat.mk.{max u2 u3} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) 0 (Zero.zero.{max u2 u3} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.zero.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10))))
but is expected to have type
- forall {A : Type.{u1}} {M : Type.{u4}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u4} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u4} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u4} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u2}} [_inst_8 : Ring.{u2} R] [_inst_9 : Module.{u2, u4} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] [_inst_10 : Module.{u2, u3} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u4, u3, u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toSMul.{u2, u4} R M (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (Module.toMulActionWithZero.{u2, u4} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u2, u3} R M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u3} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u3} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5], Eq.{max (succ u4) (succ u3)} (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u1, u4, u3, u2} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (OfNat.ofNat.{max u4 u3} (ContinuousLinearMap.{u1, u1, u4, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) 0 (Zero.toOfNat0.{max u4 u3} (ContinuousLinearMap.{u1, u1, u4, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.zero.{u1, u1, u4, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5)))) (OfNat.ofNat.{max u4 u3} (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) 0 (Zero.toOfNat0.{max u4 u3} (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.zero.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10)))
+ forall {A : Type.{u1}} {M : Type.{u4}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u4} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u4} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u4} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u2}} [_inst_8 : Ring.{u2} R] [_inst_9 : Module.{u2, u4} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] [_inst_10 : Module.{u2, u3} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u4, u3, u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toSMul.{u2, u4} R M (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (Module.toMulActionWithZero.{u2, u4} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u2, u3} R M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u3} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u3} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5], Eq.{max (succ u4) (succ u3)} (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u1, u4, u3, u2} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (OfNat.ofNat.{max u4 u3} (ContinuousLinearMap.{u1, u1, u4, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) 0 (Zero.toOfNat0.{max u4 u3} (ContinuousLinearMap.{u1, u1, u4, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.zero.{u1, u1, u4, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5)))) (OfNat.ofNat.{max u4 u3} (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) 0 (Zero.toOfNat0.{max u4 u3} (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.zero.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10)))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.restrict_scalars_zero ContinuousLinearMap.restrictScalars_zeroₓ'. -/
@[simp]
theorem restrictScalars_zero : (0 : M →L[A] M₂).restrictScalars R = 0 :=
@@ -2826,7 +2826,7 @@ variable [TopologicalAddGroup M₂]
lean 3 declaration is
forall {A : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u4}} [_inst_8 : Ring.{u4} R] [_inst_9 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_10 : Module.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u2, u3, u4, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toHasSmul.{u4, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u4, u2} R M (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u4, u2} R M (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5] [_inst_12 : TopologicalAddGroup.{u3} M₂ _inst_7 (AddCommGroup.toAddGroup.{u3} M₂ _inst_3)] (f : ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (g : ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.add.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5 (TopologicalAddGroup.to_continuousAdd.{u3} M₂ _inst_7 (AddCommGroup.toAddGroup.{u3} M₂ _inst_3) _inst_12))) f g)) (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.add.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10 (TopologicalAddGroup.to_continuousAdd.{u3} M₂ _inst_7 (AddCommGroup.toAddGroup.{u3} M₂ _inst_3) _inst_12))) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 g))
but is expected to have type
- forall {A : Type.{u4}} {M : Type.{u3}} {M₂ : Type.{u2}} [_inst_1 : Ring.{u4} A] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u2} M₂] [_inst_4 : Module.{u4, u3} A M (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_5 : Module.{u4, u2} A M₂ (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : TopologicalSpace.{u2} M₂] {R : Type.{u1}} [_inst_8 : Ring.{u1} R] [_inst_9 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_10 : Module.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u3, u2, u1, u4} M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) R A (Ring.toSemiring.{u4} A _inst_1) (SMulZeroClass.toSMul.{u1, u3} R M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (Module.toMulActionWithZero.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u1, u2} R M₂ (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_10)))) _inst_5] [_inst_12 : TopologicalAddGroup.{u2} M₂ _inst_7 (AddCommGroup.toAddGroup.{u2} M₂ _inst_3)] (f : ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) (g : ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (HAdd.hAdd.{max u3 u2, max u3 u2, max u3 u2} (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) (instHAdd.{max u3 u2} (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.add.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5 (TopologicalAddGroup.toContinuousAdd.{u2} M₂ _inst_7 (AddCommGroup.toAddGroup.{u2} M₂ _inst_3) _inst_12))) f g)) (HAdd.hAdd.{max u3 u2, max u3 u2, max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (instHAdd.{max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.add.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10 (TopologicalAddGroup.toContinuousAdd.{u2} M₂ _inst_7 (AddCommGroup.toAddGroup.{u2} M₂ _inst_3) _inst_12))) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 g))
+ forall {A : Type.{u4}} {M : Type.{u3}} {M₂ : Type.{u2}} [_inst_1 : Ring.{u4} A] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u2} M₂] [_inst_4 : Module.{u4, u3} A M (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_5 : Module.{u4, u2} A M₂ (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : TopologicalSpace.{u2} M₂] {R : Type.{u1}} [_inst_8 : Ring.{u1} R] [_inst_9 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_10 : Module.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u3, u2, u1, u4} M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) R A (Ring.toSemiring.{u4} A _inst_1) (SMulZeroClass.toSMul.{u1, u3} R M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (Module.toMulActionWithZero.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u1, u2} R M₂ (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_10)))) _inst_5] [_inst_12 : TopologicalAddGroup.{u2} M₂ _inst_7 (AddCommGroup.toAddGroup.{u2} M₂ _inst_3)] (f : ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) (g : ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (HAdd.hAdd.{max u3 u2, max u3 u2, max u3 u2} (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) (instHAdd.{max u3 u2} (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.add.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5 (TopologicalAddGroup.toContinuousAdd.{u2} M₂ _inst_7 (AddCommGroup.toAddGroup.{u2} M₂ _inst_3) _inst_12))) f g)) (HAdd.hAdd.{max u3 u2, max u3 u2, max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (instHAdd.{max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.add.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10 (TopologicalAddGroup.toContinuousAdd.{u2} M₂ _inst_7 (AddCommGroup.toAddGroup.{u2} M₂ _inst_3) _inst_12))) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 g))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.restrict_scalars_add ContinuousLinearMap.restrictScalars_addₓ'. -/
@[simp]
theorem restrictScalars_add (f g : M →L[A] M₂) :
@@ -2838,7 +2838,7 @@ theorem restrictScalars_add (f g : M →L[A] M₂) :
lean 3 declaration is
forall {A : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u4}} [_inst_8 : Ring.{u4} R] [_inst_9 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_10 : Module.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u2, u3, u4, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toHasSmul.{u4, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u4, u2} R M (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u4, u2} R M (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5] [_inst_12 : TopologicalAddGroup.{u3} M₂ _inst_7 (AddCommGroup.toAddGroup.{u3} M₂ _inst_3)] (f : ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.neg.{u1, u1, u2, u3} A _inst_1 A _inst_1 M _inst_6 _inst_2 M₂ _inst_7 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) _inst_12) f)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.neg.{u4, u4, u2, u3} R _inst_8 R _inst_8 M _inst_6 _inst_2 M₂ _inst_7 _inst_3 _inst_9 _inst_10 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) _inst_12) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f))
but is expected to have type
- forall {A : Type.{u4}} {M : Type.{u3}} {M₂ : Type.{u2}} [_inst_1 : Ring.{u4} A] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u2} M₂] [_inst_4 : Module.{u4, u3} A M (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_5 : Module.{u4, u2} A M₂ (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : TopologicalSpace.{u2} M₂] {R : Type.{u1}} [_inst_8 : Ring.{u1} R] [_inst_9 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_10 : Module.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u3, u2, u1, u4} M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) R A (Ring.toSemiring.{u4} A _inst_1) (SMulZeroClass.toSMul.{u1, u3} R M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (Module.toMulActionWithZero.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u1, u2} R M₂ (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_10)))) _inst_5] [_inst_12 : TopologicalAddGroup.{u2} M₂ _inst_7 (AddCommGroup.toAddGroup.{u2} M₂ _inst_3)] (f : ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (Neg.neg.{max u3 u2} (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.neg.{u4, u4, u3, u2} A _inst_1 A _inst_1 M _inst_6 _inst_2 M₂ _inst_7 _inst_3 _inst_4 _inst_5 (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) _inst_12) f)) (Neg.neg.{max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.neg.{u1, u1, u3, u2} R _inst_8 R _inst_8 M _inst_6 _inst_2 M₂ _inst_7 _inst_3 _inst_9 _inst_10 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) _inst_12) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f))
+ forall {A : Type.{u4}} {M : Type.{u3}} {M₂ : Type.{u2}} [_inst_1 : Ring.{u4} A] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u2} M₂] [_inst_4 : Module.{u4, u3} A M (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_5 : Module.{u4, u2} A M₂ (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : TopologicalSpace.{u2} M₂] {R : Type.{u1}} [_inst_8 : Ring.{u1} R] [_inst_9 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_10 : Module.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u3, u2, u1, u4} M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) R A (Ring.toSemiring.{u4} A _inst_1) (SMulZeroClass.toSMul.{u1, u3} R M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (Module.toMulActionWithZero.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u1, u2} R M₂ (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_10)))) _inst_5] [_inst_12 : TopologicalAddGroup.{u2} M₂ _inst_7 (AddCommGroup.toAddGroup.{u2} M₂ _inst_3)] (f : ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (Neg.neg.{max u3 u2} (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.neg.{u4, u4, u3, u2} A _inst_1 A _inst_1 M _inst_6 _inst_2 M₂ _inst_7 _inst_3 _inst_4 _inst_5 (RingHom.id.{u4} A (Semiring.toNonAssocSemiring.{u4} A (Ring.toSemiring.{u4} A _inst_1))) _inst_12) f)) (Neg.neg.{max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.neg.{u1, u1, u3, u2} R _inst_8 R _inst_8 M _inst_6 _inst_2 M₂ _inst_7 _inst_3 _inst_9 _inst_10 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_8))) _inst_12) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.restrict_scalars_neg ContinuousLinearMap.restrictScalars_negₓ'. -/
@[simp]
theorem restrictScalars_neg (f : M →L[A] M₂) : (-f).restrictScalars R = -f.restrictScalars R :=
@@ -2854,7 +2854,7 @@ variable {S : Type _} [Ring S] [Module S M₂] [ContinuousConstSMul S M₂] [SMu
lean 3 declaration is
forall {A : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u4}} [_inst_8 : Ring.{u4} R] [_inst_9 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_10 : Module.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u2, u3, u4, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toHasSmul.{u4, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u4, u2} R M (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u4, u2} R M (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5] {S : Type.{u5}} [_inst_12 : Ring.{u5} S] [_inst_13 : Module.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_14 : ContinuousConstSMul.{u5, u3} S M₂ _inst_7 (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_15 : SMulCommClass.{u1, u5, u3} A S M₂ (SMulZeroClass.toHasSmul.{u1, u3} A M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u1, u3} A M₂ (MulZeroClass.toHasZero.{u1} A (MulZeroOneClass.toMulZeroClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A _inst_1))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u1, u3} A M₂ (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A _inst_1)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_16 : SMulCommClass.{u4, u5, u3} R S M₂ (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] (c : S) (f : ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (SMul.smul.{u5, max u2 u3} S (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (MulAction.toHasSmul.{u5, max u2 u3} S (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (Ring.toMonoid.{u5} S _inst_12) (ContinuousLinearMap.mulAction.{u1, u1, u2, u3, u5} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5 S (Ring.toMonoid.{u5} S _inst_12) (Module.toDistribMulAction.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13) _inst_15 _inst_14)) c f)) (SMul.smul.{u5, max u2 u3} S (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (MulAction.toHasSmul.{u5, max u2 u3} S (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (Ring.toMonoid.{u5} S _inst_12) (ContinuousLinearMap.mulAction.{u4, u4, u2, u3, u5} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10 S (Ring.toMonoid.{u5} S _inst_12) (Module.toDistribMulAction.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13) _inst_16 _inst_14)) c (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f))
but is expected to have type
- forall {A : Type.{u5}} {M : Type.{u4}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u5} A] [_inst_2 : AddCommGroup.{u4} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u5, u4} A M (Ring.toSemiring.{u5} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] [_inst_5 : Module.{u5, u3} A M₂ (Ring.toSemiring.{u5} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u4} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u2}} [_inst_8 : Ring.{u2} R] [_inst_9 : Module.{u2, u4} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] [_inst_10 : Module.{u2, u3} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u4, u3, u2, u5} M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u5} A _inst_1) (SMulZeroClass.toSMul.{u2, u4} R M (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (Module.toMulActionWithZero.{u2, u4} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u2, u3} R M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u3} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u3} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5] {S : Type.{u1}} [_inst_12 : Ring.{u1} S] [_inst_13 : Module.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_14 : ContinuousConstSMul.{u1, u3} S M₂ _inst_7 (SMulZeroClass.toSMul.{u1, u3} S M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u3} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_15 : SMulCommClass.{u5, u1, u3} A S M₂ (SMulZeroClass.toSMul.{u5, u3} A M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u5, u3} A M₂ (MonoidWithZero.toZero.{u5} A (Semiring.toMonoidWithZero.{u5} A (Ring.toSemiring.{u5} A _inst_1))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u5, u3} A M₂ (Semiring.toMonoidWithZero.{u5} A (Ring.toSemiring.{u5} A _inst_1)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u5, u3} A M₂ (Ring.toSemiring.{u5} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} S M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u3} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_16 : SMulCommClass.{u2, u1, u3} R S M₂ (SMulZeroClass.toSMul.{u2, u3} R M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u3} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u3} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) (SMulZeroClass.toSMul.{u1, u3} S M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u3} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] (c : S) (f : ContinuousLinearMap.{u5, u5, u4, u3} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (NonAssocRing.toNonAssocSemiring.{u5} A (Ring.toNonAssocRing.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u4) (succ u3)} (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u5, u4, u3, u2} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (HSMul.hSMul.{u1, max u3 u4, max u3 u4} S (ContinuousLinearMap.{u5, u5, u4, u3} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (NonAssocRing.toNonAssocSemiring.{u5} A (Ring.toNonAssocRing.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u5, u5, u4, u3} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (NonAssocRing.toNonAssocSemiring.{u5} A (Ring.toNonAssocRing.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (instHSMul.{u1, max u3 u4} S (ContinuousLinearMap.{u5, u5, u4, u3} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (NonAssocRing.toNonAssocSemiring.{u5} A (Ring.toNonAssocRing.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (MulAction.toSMul.{u1, max u3 u4} S (ContinuousLinearMap.{u5, u5, u4, u3} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (NonAssocRing.toNonAssocSemiring.{u5} A (Ring.toNonAssocRing.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (ContinuousLinearMap.mulAction.{u5, u5, u4, u3, u1} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (NonAssocRing.toNonAssocSemiring.{u5} A (Ring.toNonAssocRing.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5 S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (Module.toDistribMulAction.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13) _inst_15 _inst_14))) c f)) (HSMul.hSMul.{u1, max u3 u4, max u3 u4} S (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (instHSMul.{u1, max u3 u4} S (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (MulAction.toSMul.{u1, max u3 u4} S (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (ContinuousLinearMap.mulAction.{u2, u2, u4, u3, u1} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10 S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (Module.toDistribMulAction.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13) _inst_16 _inst_14))) c (ContinuousLinearMap.restrictScalars.{u5, u4, u3, u2} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f))
+ forall {A : Type.{u5}} {M : Type.{u4}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u5} A] [_inst_2 : AddCommGroup.{u4} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u5, u4} A M (Ring.toSemiring.{u5} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] [_inst_5 : Module.{u5, u3} A M₂ (Ring.toSemiring.{u5} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u4} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u2}} [_inst_8 : Ring.{u2} R] [_inst_9 : Module.{u2, u4} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] [_inst_10 : Module.{u2, u3} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u4, u3, u2, u5} M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u5} A _inst_1) (SMulZeroClass.toSMul.{u2, u4} R M (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (Module.toMulActionWithZero.{u2, u4} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u2, u3} R M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u3} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u3} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5] {S : Type.{u1}} [_inst_12 : Ring.{u1} S] [_inst_13 : Module.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_14 : ContinuousConstSMul.{u1, u3} S M₂ _inst_7 (SMulZeroClass.toSMul.{u1, u3} S M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u3} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_15 : SMulCommClass.{u5, u1, u3} A S M₂ (SMulZeroClass.toSMul.{u5, u3} A M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u5, u3} A M₂ (MonoidWithZero.toZero.{u5} A (Semiring.toMonoidWithZero.{u5} A (Ring.toSemiring.{u5} A _inst_1))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u5, u3} A M₂ (Semiring.toMonoidWithZero.{u5} A (Ring.toSemiring.{u5} A _inst_1)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u5, u3} A M₂ (Ring.toSemiring.{u5} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} S M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u3} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_16 : SMulCommClass.{u2, u1, u3} R S M₂ (SMulZeroClass.toSMul.{u2, u3} R M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u3} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u3} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) (SMulZeroClass.toSMul.{u1, u3} S M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u3} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] (c : S) (f : ContinuousLinearMap.{u5, u5, u4, u3} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A (Ring.toSemiring.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u4) (succ u3)} (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u5, u4, u3, u2} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (HSMul.hSMul.{u1, max u3 u4, max u3 u4} S (ContinuousLinearMap.{u5, u5, u4, u3} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A (Ring.toSemiring.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u5, u5, u4, u3} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A (Ring.toSemiring.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (instHSMul.{u1, max u3 u4} S (ContinuousLinearMap.{u5, u5, u4, u3} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A (Ring.toSemiring.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (MulAction.toSMul.{u1, max u3 u4} S (ContinuousLinearMap.{u5, u5, u4, u3} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A (Ring.toSemiring.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (ContinuousLinearMap.mulAction.{u5, u5, u4, u3, u1} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (Semiring.toNonAssocSemiring.{u5} A (Ring.toSemiring.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5 S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (Module.toDistribMulAction.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13) _inst_15 _inst_14))) c f)) (HSMul.hSMul.{u1, max u3 u4, max u3 u4} S (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (instHSMul.{u1, max u3 u4} S (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (MulAction.toSMul.{u1, max u3 u4} S (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (ContinuousLinearMap.mulAction.{u2, u2, u4, u3, u1} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10 S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (Module.toDistribMulAction.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13) _inst_16 _inst_14))) c (ContinuousLinearMap.restrictScalars.{u5, u4, u3, u2} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.restrict_scalars_smul ContinuousLinearMap.restrictScalars_smulₓ'. -/
@[simp]
theorem restrictScalars_smul (c : S) (f : M →L[A] M₂) :
@@ -2881,7 +2881,7 @@ variable {A M M₂ R S}
lean 3 declaration is
forall {A : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u4}} [_inst_8 : Ring.{u4} R] [_inst_9 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_10 : Module.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u2, u3, u4, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toHasSmul.{u4, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u4, u2} R M (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u4, u2} R M (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5] {S : Type.{u5}} [_inst_12 : Ring.{u5} S] [_inst_13 : Module.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_14 : ContinuousConstSMul.{u5, u3} S M₂ _inst_7 (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_15 : SMulCommClass.{u1, u5, u3} A S M₂ (SMulZeroClass.toHasSmul.{u1, u3} A M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u1, u3} A M₂ (MulZeroClass.toHasZero.{u1} A (MulZeroOneClass.toMulZeroClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A _inst_1))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u1, u3} A M₂ (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A _inst_1)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_16 : SMulCommClass.{u4, u5, u3} R S M₂ (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_17 : TopologicalAddGroup.{u3} M₂ _inst_7 (AddCommGroup.toAddGroup.{u3} M₂ _inst_3)], Eq.{succ (max u2 u3)} ((ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) -> (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10)) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (LinearMap.{u5, u5, max u2 u3, max u2 u3} S S (Ring.toSemiring.{u5} S _inst_12) (Ring.toSemiring.{u5} S _inst_12) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S (Ring.toSemiring.{u5} S _inst_12))) (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5 (ContinuousLinearMap.restrictScalarsₗ._proof_1.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.addCommMonoid.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10 (ContinuousLinearMap.restrictScalarsₗ._proof_2.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.module.{u1, u1, u5, u2, u3} A A S (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u5} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5 _inst_13 _inst_15 _inst_14 (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) (ContinuousLinearMap.restrictScalarsₗ._proof_3.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.module.{u4, u4, u5, u2, u3} R R S (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u5} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10 _inst_13 _inst_16 _inst_14 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) (ContinuousLinearMap.restrictScalarsₗ._proof_4.{u3} M₂ _inst_3 _inst_7 _inst_17))) (fun (_x : LinearMap.{u5, u5, max u2 u3, max u2 u3} S S (Ring.toSemiring.{u5} S _inst_12) (Ring.toSemiring.{u5} S _inst_12) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S (Ring.toSemiring.{u5} S _inst_12))) (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5 (ContinuousLinearMap.restrictScalarsₗ._proof_1.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.addCommMonoid.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10 _inst_13 _inst_16 _inst_14 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) (ContinuousLinearMap.restrictScalarsₗ._proof_4.{u3} M₂ _inst_3 _inst_7 _inst_17))) => (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) -> (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10)) (LinearMap.hasCoeToFun.{u5, u5, max u2 u3, max u2 u3} S S (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (Ring.toSemiring.{u5} S _inst_12) (Ring.toSemiring.{u5} S _inst_12) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5 (ContinuousLinearMap.restrictScalarsₗ._proof_1.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.addCommMonoid.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10 (ContinuousLinearMap.restrictScalarsₗ._proof_2.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.module.{u1, u1, u5, u2, u3} A A S (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u5} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5 _inst_13 _inst_15 _inst_14 (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) (ContinuousLinearMap.restrictScalarsₗ._proof_3.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.module.{u4, u4, u5, u2, u3} R R S (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u5} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10 _inst_13 _inst_16 _inst_14 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) (ContinuousLinearMap.restrictScalarsₗ._proof_4.{u3} M₂ _inst_3 _inst_7 _inst_17)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S (Ring.toSemiring.{u5} S _inst_12)))) (ContinuousLinearMap.restrictScalarsₗ.{u1, u2, u3, u4, u5} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 S _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17)) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11)
but is expected to have type
- forall {A : Type.{u3}} {M : Type.{u5}} {M₂ : Type.{u4}} [_inst_1 : Ring.{u3} A] [_inst_2 : AddCommGroup.{u5} M] [_inst_3 : AddCommGroup.{u4} M₂] [_inst_4 : Module.{u3, u5} A M (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2)] [_inst_5 : Module.{u3, u4} A M₂ (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u5} M] [_inst_7 : TopologicalSpace.{u4} M₂] {R : Type.{u2}} [_inst_8 : Ring.{u2} R] [_inst_9 : Module.{u2, u5} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2)] [_inst_10 : Module.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u5, u4, u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) R A (Ring.toSemiring.{u3} A _inst_1) (SMulZeroClass.toSMul.{u2, u5} R M (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u5} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u5} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (Module.toMulActionWithZero.{u2, u5} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u2, u4} R M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10)))) _inst_5] {S : Type.{u1}} [_inst_12 : Ring.{u1} S] [_inst_13 : Module.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_14 : ContinuousConstSMul.{u1, u4} S M₂ _inst_7 (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_15 : SMulCommClass.{u3, u1, u4} A S M₂ (SMulZeroClass.toSMul.{u3, u4} A M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u3, u4} A M₂ (MonoidWithZero.toZero.{u3} A (Semiring.toMonoidWithZero.{u3} A (Ring.toSemiring.{u3} A _inst_1))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A M₂ (Semiring.toMonoidWithZero.{u3} A (Ring.toSemiring.{u3} A _inst_1)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u3, u4} A M₂ (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_16 : SMulCommClass.{u2, u1, u4} R S M₂ (SMulZeroClass.toSMul.{u2, u4} R M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10)))) (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_17 : TopologicalAddGroup.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3)], Eq.{max (succ u5) (succ u4)} (forall (ᾰ : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) => ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10) ᾰ) (FunLike.coe.{max (succ u5) (succ u4), max (succ u5) (succ u4), max (succ u5) (succ u4)} (LinearMap.{u1, u1, max u4 u5, max u4 u5} S S (Ring.toSemiring.{u1} S _inst_12) (Ring.toSemiring.{u1} S _inst_12) (RingHom.id.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_12))) (ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) 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_inst_14 (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17))) (ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) (fun (_x : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ContinuousLinearMap.{u3, u3, u5, u4} A A 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(AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10) (Ring.toSemiring.{u1} S _inst_12) (Ring.toSemiring.{u1} S _inst_12) (ContinuousLinearMap.addCommMonoid.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5 (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.addCommMonoid.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10 (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.module.{u3, u3, u1, u5, u4} A A S (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u1} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_4 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_5 _inst_13 _inst_15 _inst_14 (RingHom.id.{u3} A (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A _inst_1))) (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.module.{u2, u2, u1, u5, u4} R R S (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_9 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10 _inst_13 _inst_16 _inst_14 (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (RingHom.id.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_12)))) (ContinuousLinearMap.restrictScalarsₗ.{u3, u5, u4, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 S _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17)) (ContinuousLinearMap.restrictScalars.{u3, u5, u4, u2} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11)
+ forall {A : Type.{u3}} {M : Type.{u5}} {M₂ : Type.{u4}} [_inst_1 : Ring.{u3} A] [_inst_2 : AddCommGroup.{u5} M] [_inst_3 : AddCommGroup.{u4} M₂] [_inst_4 : Module.{u3, u5} A M (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2)] [_inst_5 : Module.{u3, u4} A M₂ (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u5} M] [_inst_7 : TopologicalSpace.{u4} M₂] {R : Type.{u2}} [_inst_8 : Ring.{u2} R] [_inst_9 : Module.{u2, u5} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2)] [_inst_10 : Module.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u5, u4, u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) R A (Ring.toSemiring.{u3} A _inst_1) (SMulZeroClass.toSMul.{u2, u5} R M (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u5} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u5} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (Module.toMulActionWithZero.{u2, u5} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u2, u4} R M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10)))) _inst_5] {S : Type.{u1}} [_inst_12 : Ring.{u1} S] [_inst_13 : Module.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_14 : ContinuousConstSMul.{u1, u4} S M₂ _inst_7 (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_15 : SMulCommClass.{u3, u1, u4} A S M₂ (SMulZeroClass.toSMul.{u3, u4} A M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u3, u4} A M₂ (MonoidWithZero.toZero.{u3} A (Semiring.toMonoidWithZero.{u3} A (Ring.toSemiring.{u3} A _inst_1))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A M₂ (Semiring.toMonoidWithZero.{u3} A (Ring.toSemiring.{u3} A _inst_1)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u3, u4} A M₂ (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_16 : SMulCommClass.{u2, u1, u4} R S M₂ (SMulZeroClass.toSMul.{u2, u4} R M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10)))) (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_17 : TopologicalAddGroup.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3)], Eq.{max (succ u5) (succ u4)} (forall (ᾰ : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) => ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10) ᾰ) (FunLike.coe.{max (succ u5) (succ u4), max (succ u5) (succ u4), max (succ u5) (succ u4)} (LinearMap.{u1, u1, max u4 u5, max u4 u5} S S (Ring.toSemiring.{u1} S _inst_12) (Ring.toSemiring.{u1} S _inst_12) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.addCommMonoid.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5 (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.addCommMonoid.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_9 _inst_10 (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.module.{u3, u3, u1, u5, u4} A A S (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u1} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_4 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_5 _inst_13 _inst_15 _inst_14 (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (ContinuousLinearMap.module.{u2, u2, u1, u5, u4} R R S (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_9 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10 _inst_13 _inst_16 _inst_14 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17))) (ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) (fun (_x : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A 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(AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10 _inst_13 _inst_16 _inst_14 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (TopologicalAddGroup.toContinuousAdd.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3) _inst_17)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_12)))) (ContinuousLinearMap.restrictScalarsₗ.{u3, u5, u4, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 S _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17)) (ContinuousLinearMap.restrictScalars.{u3, u5, u4, u2} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11)
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_restrict_scalarsₗ ContinuousLinearMap.coe_restrictScalarsₗₓ'. -/
@[simp]
theorem coe_restrictScalarsₗ : ⇑(restrictScalarsₗ A M M₂ R S) = restrictScalars R :=
@@ -3890,7 +3890,7 @@ include σ₂₁
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_3 : TopologicalSpace.{u3} M] [_inst_4 : AddCommGroup.{u3} M] [_inst_5 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_8 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u1} R₂ R (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))} [_inst_9 : RingHomInvPair.{u1, u2} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_10 : RingHomInvPair.{u2, u1} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ σ₁₂] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) (x : M) (y : M), Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) => M -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) e (HSub.hSub.{u3, u3, u3} M M M (instHSub.{u3} M (SubNegMonoid.toHasSub.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_4)))) x y)) (HSub.hSub.{u4, u4, u4} M₂ M₂ M₂ (instHSub.{u4} M₂ (SubNegMonoid.toHasSub.{u4} M₂ (AddGroup.toSubNegMonoid.{u4} M₂ (AddCommGroup.toAddGroup.{u4} M₂ _inst_7)))) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) => M -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) e x) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) => M -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) e y))
but is expected to have type
- forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_8 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2))} {σ₂₁ : RingHom.{u3, u4} R₂ R (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))} [_inst_9 : RingHomInvPair.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_10 : RingHomInvPair.{u3, u4} R₂ R (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u4} R _inst_1) σ₂₁ σ₁₂] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) (x : M) (y : M), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) (HSub.hSub.{u2, u2, u2} M M M (instHSub.{u2} M (SubNegMonoid.toSub.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_4)))) x y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) M (fun (_x : M) => (fun 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σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8)))) e y))
+ forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_8 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))} {σ₂₁ : RingHom.{u3, u4} R₂ R (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2)) (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))} [_inst_9 : RingHomInvPair.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_10 : RingHomInvPair.{u3, u4} R₂ R 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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_sub ContinuousLinearEquiv.map_subₓ'. -/
@[simp]
theorem map_sub (e : M ≃SL[σ₁₂] M₂) (x y : M) : e (x - y) = e x - e y :=
@@ -3901,7 +3901,7 @@ theorem map_sub (e : M ≃SL[σ₁₂] M₂) (x y : M) : e (x - y) = e x - e y :
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_3 : TopologicalSpace.{u3} M] [_inst_4 : AddCommGroup.{u3} M] [_inst_5 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_8 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u1} R₂ R (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))} [_inst_9 : RingHomInvPair.{u1, u2} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_10 : RingHomInvPair.{u2, u1} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ σ₁₂] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) (x : M), Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) => M -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) e (Neg.neg.{u3} M (SubNegMonoid.toHasNeg.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_4))) x)) (Neg.neg.{u4} M₂ (SubNegMonoid.toHasNeg.{u4} M₂ (AddGroup.toSubNegMonoid.{u4} M₂ (AddCommGroup.toAddGroup.{u4} M₂ _inst_7))) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) => M -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) e x))
but is expected to have type
- forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_8 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2))} {σ₂₁ : RingHom.{u3, u4} R₂ R (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))} [_inst_9 : RingHomInvPair.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_10 : RingHomInvPair.{u3, u4} R₂ R (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u4} R _inst_1) σ₂₁ σ₁₂] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) (Neg.neg.{u2} M (NegZeroClass.toNeg.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_4))))) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) M M₂ _inst_3 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8)))) e (Neg.neg.{u2} M (NegZeroClass.toNeg.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_4))))) x)) (Neg.neg.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (NegZeroClass.toNeg.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) _inst_7))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) M M₂ _inst_3 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8)))) e x))
+ forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_8 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2))} {σ₂₁ : RingHom.{u3, u4} R₂ R (Semiring.toNonAssocSemiring.{u3} R₂ (Ring.toSemiring.{u3} R₂ _inst_2)) (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))} [_inst_9 : RingHomInvPair.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_10 : RingHomInvPair.{u3, u4} R₂ R (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u4} R _inst_1) σ₂₁ σ₁₂] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) (Neg.neg.{u2} M (NegZeroClass.toNeg.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_4))))) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) M M₂ _inst_3 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8)))) e (Neg.neg.{u2} M (NegZeroClass.toNeg.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_4))))) x)) (Neg.neg.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (NegZeroClass.toNeg.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) _inst_7))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) M M₂ _inst_3 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8)))) e x))
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_neg ContinuousLinearEquiv.map_negₓ'. -/
@[simp]
theorem map_neg (e : M ≃SL[σ₁₂] M₂) (x : M) : e (-x) = -e x :=
@@ -3922,7 +3922,7 @@ variable [TopologicalAddGroup M]
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_11 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)], (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) -> (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.ofUnit._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.ofUnit._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5)
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)], (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))) -> (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5)
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)], (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))) -> (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5)
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.of_unit ContinuousLinearEquiv.ofUnitₓ'. -/
/-- An invertible continuous linear map `f` determines a continuous equivalence from `M` to itself.
-/
@@ -3949,7 +3949,7 @@ def ofUnit (f : (M →L[R] M)ˣ) : M ≃L[R] M
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_11 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)], (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.toUnit._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.toUnit._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) -> (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11)))
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)], (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) -> (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)], (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) -> (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.to_unit ContinuousLinearEquiv.toUnitₓ'. -/
/-- A continuous equivalence from `M` to itself determines an invertible continuous linear map. -/
def toUnit (f : M ≃L[R] M) : (M →L[R] M)ˣ where
@@ -3969,7 +3969,7 @@ variable (R M)
lean 3 declaration is
forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (M : Type.{u2}) [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_11 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)], MulEquiv.{u2, u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MulOneClass.toHasMul.{u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (Units.mulOneClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11)))) (MulOneClass.toHasMul.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Monoid.toMulOneClass.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (DivInvMonoid.toMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Group.toDivInvMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearEquiv.automorphismGroup.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))))
but is expected to have type
- forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (M : Type.{u2}) [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)], MulEquiv.{u2, u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))) (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MulOneClass.toMul.{u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))) (Units.instMulOneClassUnits.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))) (MulOneClass.toMul.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Monoid.toMulOneClass.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (DivInvMonoid.toMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Group.toDivInvMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearEquiv.automorphismGroup.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))))
+ forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (M : Type.{u2}) [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)], MulEquiv.{u2, u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))) (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MulOneClass.toMul.{u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))) (Units.instMulOneClassUnits.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))) (MulOneClass.toMul.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Monoid.toMulOneClass.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (DivInvMonoid.toMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Group.toDivInvMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearEquiv.automorphismGroup.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))))
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv ContinuousLinearEquiv.unitsEquivₓ'. -/
/-- The units of the algebra of continuous `R`-linear endomorphisms of `M` is multiplicatively
equivalent to the type of continuous linear equivalences between `M` and itself. -/
@@ -3992,7 +3992,7 @@ def unitsEquiv : (M →L[R] M)ˣ ≃* M ≃L[R] M
lean 3 declaration is
forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (M : Type.{u2}) [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_11 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)] (f : Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (x : M), Eq.{succ u2} M (coeFn.{succ u2, succ u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (fun (_x : ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) => M -> M) (ContinuousLinearEquiv.hasCoeToFun.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (coeFn.{succ u2, succ u2} (MulEquiv.{u2, u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MulOneClass.toHasMul.{u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (Units.mulOneClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11)))) (MulOneClass.toHasMul.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Monoid.toMulOneClass.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (DivInvMonoid.toMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Group.toDivInvMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearEquiv.automorphismGroup.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))))) (fun (_x : MulEquiv.{u2, u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MulOneClass.toHasMul.{u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (Units.mulOneClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11)))) (MulOneClass.toHasMul.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Monoid.toMulOneClass.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (DivInvMonoid.toMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Group.toDivInvMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearEquiv.automorphismGroup.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))))) => (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) -> (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5)) (MulEquiv.hasCoeToFun.{u2, u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R 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(ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MulOneClass.toHasMul.{u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (Units.mulOneClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11)))) (MulOneClass.toHasMul.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Monoid.toMulOneClass.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (DivInvMonoid.toMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Group.toDivInvMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearEquiv.automorphismGroup.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))))) (ContinuousLinearEquiv.unitsEquiv.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11) f) x) (coeFn.{succ u2, succ u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (fun (x : Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) => M -> M) (coeFnTrans.{succ u2, succ u2, succ u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) => M -> M) (ContinuousLinearMap.toFun.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (coeBaseAux.{succ u2, succ u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Units.hasCoe.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))))) f x)
but is expected to have type
- forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (M : Type.{u2}) [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] (_inst_11 : Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))) (f : M), Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M) f) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))) => ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) _inst_11) M (fun (a : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M) a) (ContinuousMapClass.toFunLike.{u2, u2, u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Units.{u2} (ContinuousLinearMap.{u1, 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_inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{u2, u1, u1, u2, u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))) => ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) _inst_11) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5)))) (FunLike.coe.{succ u2, succ u2, succ u2} (MulEquiv.{u2, u2} (Units.{u2} 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(Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))) (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MulEquivClass.toEquivLike.{u2, u2, u2} (MulEquiv.{u2, u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))) (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MulOneClass.toMul.{u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))) (MulOneClass.toMul.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R 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(ContinuousLinearEquiv.automorphismGroup.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))))) (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))) (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MulOneClass.toMul.{u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, 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(NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))) (MulOneClass.toMul.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Monoid.toMulOneClass.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (DivInvMonoid.toMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Group.toDivInvMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearEquiv.automorphismGroup.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))))) (MulEquiv.instMulEquivClassMulEquiv.{u2, u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))) (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MulOneClass.toMul.{u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))) (Units.instMulOneClassUnits.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))) (MulOneClass.toMul.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Monoid.toMulOneClass.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (DivInvMonoid.toMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Group.toDivInvMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearEquiv.automorphismGroup.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))))))))) (ContinuousLinearEquiv.unitsEquiv.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5) _inst_11) f) (FunLike.coe.{succ u2, succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) M (fun (a : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M) a) (ContinuousMapClass.toFunLike.{u2, u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) M M _inst_3 _inst_3 (ContinuousSemilinearMapClass.toContinuousMapClass.{u2, u1, u1, u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5))) (Units.val.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) _inst_11) f)
+ forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (M : Type.{u2}) [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] (_inst_11 : Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))) (f : M), Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M) f) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))) => ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) _inst_11) M (fun (a : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M) a) (ContinuousMapClass.toFunLike.{u2, u2, u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))) => ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) _inst_11) M M _inst_3 _inst_3 (ContinuousSemilinearMapClass.toContinuousMapClass.{u2, u1, u1, u2, u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))) => ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) _inst_11) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{u2, u1, u1, u2, u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, 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(Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (DivInvMonoid.toMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Group.toDivInvMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearEquiv.automorphismGroup.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))))))))) (ContinuousLinearEquiv.unitsEquiv.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5) _inst_11) f) (FunLike.coe.{succ u2, succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) M (fun (a : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M) a) (ContinuousMapClass.toFunLike.{u2, u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) M M _inst_3 _inst_3 (ContinuousSemilinearMapClass.toContinuousMapClass.{u2, u1, u1, u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5))) (Units.val.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) _inst_11) f)
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv_apply ContinuousLinearEquiv.unitsEquiv_applyₓ'. -/
@[simp]
theorem unitsEquiv_apply (f : (M →L[R] M)ˣ) (x : M) : unitsEquiv R M f x = f x :=
@@ -4009,7 +4009,7 @@ variable (R) [TopologicalSpace R] [ContinuousMul R]
lean 3 declaration is
forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))], Equiv.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))
but is expected to have type
- forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))], Equiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))
+ forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))], Equiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv_aut ContinuousLinearEquiv.unitsEquivAutₓ'. -/
/-- Continuous linear equivalences `R ≃L[R] R` are enumerated by `Rˣ`. -/
def unitsEquivAut : Rˣ ≃ R ≃L[R] R
@@ -4030,7 +4030,7 @@ variable {R}
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))] (u : Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (x : R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (_x : ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => R -> R) (ContinuousLinearEquiv.hasCoeToFun.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : Equiv.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) -> (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Equiv.hasCoeToFun.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.unitsEquivAut.{u1} R _inst_1 _inst_11 _inst_12) u) x) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))) x ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (coeBase.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (Units.hasCoe.{u1} R (Ring.toMonoid.{u1} R _inst_1))))) u))
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))] (u : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) x) (FunLike.coe.{succ u1, succ u1, succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u) R (fun (_x : R) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u) R R _inst_11 _inst_11 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u1, u1, u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{u1, u1, u1, u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.unitsEquivAut.{u1} R _inst_1 _inst_11 _inst_12) u) x) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) x (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u))
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))] (u : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) x) (FunLike.coe.{succ u1, succ u1, succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u) R (fun (_x : R) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u) R R _inst_11 _inst_11 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u1, u1, u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{u1, u1, u1, u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R 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R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv_aut_apply ContinuousLinearEquiv.unitsEquivAut_applyₓ'. -/
@[simp]
theorem unitsEquivAut_apply (u : Rˣ) (x : R) : unitsEquivAut R u x = x * u :=
@@ -4041,7 +4041,7 @@ theorem unitsEquivAut_apply (u : Rˣ) (x : R) : unitsEquivAut R u x = x * u :=
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))] (u : Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (x : R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R 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(Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.symm.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : Equiv.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R 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(Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Equiv.hasCoeToFun.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.unitsEquivAut.{u1} R _inst_1 _inst_11 _inst_12) u)) x) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))) x ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (coeBase.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (Units.hasCoe.{u1} R (Ring.toMonoid.{u1} R _inst_1))))) (Inv.inv.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (Units.hasInv.{u1} R (Ring.toMonoid.{u1} R _inst_1)) u)))
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))] (u : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) x) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R _inst_11 _inst_11 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u1, u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{u1, u1, u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (ContinuousLinearEquiv.symm.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.unitsEquivAut.{u1} R _inst_1 _inst_11 _inst_12) u)) x) (HMul.hMul.{u1, u1, u1} R ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) x) R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) x (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Inv.inv.{u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Units.instInv.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) u)))
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))] (u : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) x) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R _inst_11 _inst_11 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u1, u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{u1, u1, u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (ContinuousLinearEquiv.symm.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.unitsEquivAut.{u1} R _inst_1 _inst_11 _inst_12) u)) x) (HMul.hMul.{u1, u1, u1} R ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) x) R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) x (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Inv.inv.{u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Units.instInv.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) u)))
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv_aut_apply_symm ContinuousLinearEquiv.unitsEquivAut_apply_symmₓ'. -/
@[simp]
theorem unitsEquivAut_apply_symm (u : Rˣ) (x : R) : (unitsEquivAut R u).symm x = x * ↑u⁻¹ :=
@@ -4052,7 +4052,7 @@ theorem unitsEquivAut_apply_symm (u : Rˣ) (x : R) : (unitsEquivAut R u).symm x
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))] (e : ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))), Eq.{succ u1} R ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (coeBase.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (Units.hasCoe.{u1} R (Ring.toMonoid.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1))) (fun (_x : Equiv.{succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1))) => (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) -> (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1))) (Equiv.hasCoeToFun.{succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1))) (Equiv.symm.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut.{u1} R _inst_1 _inst_11 _inst_12)) e)) (coeFn.{succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (_x : ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => R -> R) (ContinuousLinearEquiv.hasCoeToFun.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) e (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))))))
but is expected to have type
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(NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (_x : ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 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(RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Equiv.symm.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) 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_inst_11 _inst_12)) e)) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R _inst_11 _inst_11 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u1, u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{u1, u1, u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) e (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))] (e : ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (_x : ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Equiv.symm.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut.{u1} R _inst_1 _inst_11 _inst_12)) e)) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv_aut_symm_apply ContinuousLinearEquiv.unitsEquivAut_symm_applyₓ'. -/
@[simp]
theorem unitsEquivAut_symm_apply (e : R ≃L[R] R) : ↑((unitsEquivAut R).symm e) = e 1 :=
@@ -4071,7 +4071,7 @@ open _Root_.LinearMap (mem_ker)
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] [_inst_11 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_12 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)] (f₁ : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11) (f₂ : ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_11 _inst_5), (Function.RightInverse.{succ u2, succ u3} M M₂ (coeFn.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_11 _inst_5) (fun (_x : ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_11 _inst_5) => M₂ -> M) 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(Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11)) f₁))))
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] [_inst_11 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_12 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)] (f₁ : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11) (f₂ : ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_11 _inst_5), (Function.RightInverse.{succ u2, succ u3} M M₂ (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_11 _inst_5) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M) _x) (ContinuousMapClass.toFunLike.{max u2 u3, u3, u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R 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u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11)) f₁))) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u3, u1, u1, u2, u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11)) f₁)) _inst_11 (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u3, u1, u1, u2, u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11)) f₁))))
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] [_inst_11 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_12 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)] (f₁ : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11) (f₂ : ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_11 _inst_5), (Function.RightInverse.{succ u2, succ u3} M M₂ (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_11 _inst_5) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M) _x) (ContinuousMapClass.toFunLike.{max u2 u3, u3, u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_11 _inst_5) M₂ M _inst_6 _inst_3 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u3, u1, u1, u3, u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_11 _inst_5) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_11 _inst_5 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_11 _inst_5))) f₂) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u3, u2, u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11) M M₂ _inst_3 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u3, u1, u1, u2, u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11))) f₁)) -> (ContinuousLinearEquiv.{u1, u1, u2, max u2 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (Prod.{u3, u2} M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u3, u1, u1, u2, u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R 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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.equiv_of_right_inverse ContinuousLinearEquiv.equivOfRightInverseₓ'. -/
/-- A pair of continuous linear maps such that `f₁ ∘ f₂ = id` generates a continuous
linear equivalence `e` between `M` and `M₂ × f₁.ker` such that `(e x).2 = x` for `x ∈ f₁.ker`,
@@ -4086,7 +4086,7 @@ def equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M) (h : Fun
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] [_inst_11 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_12 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)] (f₁ : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11) (f₂ : ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_11 _inst_5) (h : Function.RightInverse.{succ u2, succ u3} M M₂ (coeFn.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_11 _inst_5) (fun (_x : ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_11 _inst_5) => M₂ -> M) 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but is expected to have type
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_inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (Submodule.addCommMonoid.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) 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(Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁)))) M (Prod.{u1, u2} M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R 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_inst_5 _inst_11)) f₁)) _inst_3)) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u3, u2, max u2 u1} (ContinuousLinearEquiv.{u3, u3, u2, max u2 u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (Prod.{u1, u2} M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R 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(Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁)))) (instTopologicalSpaceProd.{u1, u2} M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R 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(ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))) _inst_6 (instTopologicalSpaceSubtype.{u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁)) _inst_3)) (Prod.instAddCommMonoidSum.{u1, u2} M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (Submodule.addCommMonoid.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))) _inst_5 (Prod.module.{u3, u1, u2} R M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (Submodule.addCommMonoid.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) 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_inst_5 _inst_11)) f₁)))) (instTopologicalSpaceProd.{u1, u2} M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} 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_inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))))))) (ContinuousLinearEquiv.equivOfRightInverse.{u3, u2, u1} R _inst_1 M _inst_3 _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_11 _inst_12 f₁ f₂ h) x)) (FunLike.coe.{max (succ u2) (succ u1), 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+ forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_11 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] [_inst_12 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)] (f₁ : ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (f₂ : ContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁)))) _inst_3 (instTopologicalSpaceProd.{u1, u2} M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁)) _inst_3)) (Prod.instAddCommMonoidSum.{u1, u2} M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁)) _inst_3)) (Prod.instAddCommMonoidSum.{u1, u2} M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R 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(AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))))))) (ContinuousLinearEquiv.equivOfRightInverse.{u3, u2, u1} R _inst_1 M _inst_3 _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_11 _inst_12 f₁ f₂ h) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M 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(Ring.toSemiring.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11))) f₁ x)
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.fst_equiv_of_right_inverse ContinuousLinearEquiv.fst_equivOfRightInverseₓ'. -/
@[simp]
theorem fst_equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
@@ -4098,7 +4098,7 @@ theorem fst_equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] [_inst_11 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_12 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)] (f₁ : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11) (f₂ : ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R 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but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R 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u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁)))) 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(Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))) _inst_6 (instTopologicalSpaceSubtype.{u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R 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_inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 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_inst_5 _inst_11)) f₁))) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (Submodule.addCommMonoid.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R 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+ forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_11 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] [_inst_12 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)] (f₁ : ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (f₂ : ContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_11 _inst_5) (h : Function.RightInverse.{succ u2, succ u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_11 _inst_5) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (Submodule.addCommMonoid.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) 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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.snd_equiv_of_right_inverse ContinuousLinearEquiv.snd_equivOfRightInverseₓ'. -/
@[simp]
theorem snd_equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
@@ -4111,7 +4111,7 @@ theorem snd_equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] [_inst_11 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_12 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)] (f₁ : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11) (f₂ : ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R 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but is expected to have type
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(NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_1)) (Prod.{u1, u2} M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁)))) (instTopologicalSpaceProd.{u1, u2} M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))) _inst_6 (instTopologicalSpaceSubtype.{u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁)) _inst_3)) (Prod.instAddCommMonoidSum.{u1, u2} M₂ (Subtype.{succ 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (Submodule.addCommMonoid.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (Prod.module.{u3, u1, u2} R M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R 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(Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (Submodule.addCommMonoid.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 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_inst_5 _inst_11)) f₁))) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (Submodule.addCommMonoid.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R 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+ forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_11 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] [_inst_12 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)] (f₁ : ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (f₂ : ContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_11 _inst_5) (h : Function.RightInverse.{succ u2, succ u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_11 _inst_5) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_6 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R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁)))) (instTopologicalSpaceProd.{u1, u2} M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) 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_inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (Submodule.addCommMonoid.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) 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(AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (Submodule.addCommMonoid.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (Prod.module.{u3, u1, u2} R M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) 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_inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁)) _inst_3)) (Prod.instAddCommMonoidSum.{u1, u2} M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, 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(Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (Submodule.addCommMonoid.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) 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Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.equiv_of_right_inverse_symm_apply ContinuousLinearEquiv.equivOfRightInverse_symm_applyₓ'. -/
@[simp]
theorem equivOfRightInverse_symm_apply (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
@@ -4255,7 +4255,7 @@ variable [AddCommGroup M₂] [Module R M₂]
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} M] [_inst_3 : Ring.{u1} R] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : TopologicalAddGroup.{u2} M _inst_1 (AddCommGroup.toAddGroup.{u2} M _inst_4)] [_inst_6 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] (e : ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6), Eq.{succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (Ring.inverse.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_3) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (HasLiftT.mk.{succ u2, succ u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (CoeTCₓ.coe.{succ u2, succ u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (coeBase.{succ u2, succ u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6)))) e)) (ContinuousLinearMap.inverse.{u1, u2, u2} R M M _inst_1 _inst_1 (Ring.toSemiring.{u1} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (HasLiftT.mk.{succ u2, succ u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (CoeTCₓ.coe.{succ u2, succ u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (coeBase.{succ u2, succ u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6)))) e))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} M] [_inst_3 : Ring.{u2} R] [_inst_4 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4)] (_inst_6 : ContinuousLinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5 _inst_5), Eq.{succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5 _inst_5) (Ring.inverse.{u1} (ContinuousLinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u2, u1} R (Ring.toSemiring.{u2} R _inst_3) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5) (ContinuousLinearEquiv.toContinuousLinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5 _inst_5 _inst_6)) (ContinuousLinearMap.inverse.{u2, u1, u1} R M M _inst_1 _inst_1 (Ring.toSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5 (ContinuousLinearEquiv.toContinuousLinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5 _inst_5 _inst_6))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} M] [_inst_3 : Ring.{u2} R] [_inst_4 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4)] (_inst_6 : ContinuousLinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5 _inst_5), Eq.{succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5 _inst_5) (Ring.inverse.{u1} (ContinuousLinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u2, u1} R (Ring.toSemiring.{u2} R _inst_3) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5) (ContinuousLinearEquiv.toContinuousLinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5 _inst_5 _inst_6)) (ContinuousLinearMap.inverse.{u2, u1, u1} R M M _inst_1 _inst_1 (Ring.toSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5 (ContinuousLinearEquiv.toContinuousLinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5 _inst_5 _inst_6))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ring_inverse_equiv ContinuousLinearMap.ring_inverse_equivₓ'. -/
@[simp]
theorem ring_inverse_equiv (e : M ≃L[R] M) : Ring.inverse ↑e = inverse (e : M →L[R] M) :=
@@ -4270,7 +4270,7 @@ theorem ring_inverse_equiv (e : M ≃L[R] M) : Ring.inverse ↑e = inverse (e :
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} M] [_inst_2 : TopologicalSpace.{u3} M₂] [_inst_3 : Ring.{u1} R] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : TopologicalAddGroup.{u2} M _inst_1 (AddCommGroup.toAddGroup.{u2} M _inst_4)] [_inst_6 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_7 : AddCommGroup.{u3} M₂] [_inst_8 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] (e : ContinuousLinearEquiv.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M 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but is expected to have type
- forall {R : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} M] [_inst_2 : TopologicalSpace.{u1} M₂] [_inst_3 : Ring.{u3} R] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_6 : AddCommGroup.{u1} M₂] [_inst_7 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6)] (_inst_8 : ContinuousLinearEquiv.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_3))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) _inst_5 _inst_7) (e : ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) _inst_5 _inst_7), Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_7 _inst_5) (ContinuousLinearMap.inverse.{u3, u2, u1} R M M₂ _inst_1 _inst_2 (Ring.toSemiring.{u3} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 e) (ContinuousLinearMap.comp.{u3, u3, u3, u1, u2, u2} R R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_7 _inst_5 _inst_5 (RingHomCompTriple.ids.{u3, u3} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3)))) (Ring.inverse.{u2} (ContinuousLinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u3, u2} R (Ring.toSemiring.{u3} R _inst_3) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (ContinuousLinearMap.comp.{u3, u3, u3, u2, u1, u2} R R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_3))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_7 _inst_5 (RingHomCompTriple.ids.{u3, u3} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3)))) (ContinuousLinearEquiv.toContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_3))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_7 _inst_5 (ContinuousLinearEquiv.symm.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_3))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) _inst_5 _inst_7 _inst_8)) e)) (ContinuousLinearEquiv.toContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_3))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_7 _inst_5 (ContinuousLinearEquiv.symm.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_3))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) _inst_5 _inst_7 _inst_8)))
+ forall {R : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} M] [_inst_2 : TopologicalSpace.{u1} M₂] [_inst_3 : Ring.{u3} R] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_6 : AddCommGroup.{u1} M₂] [_inst_7 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6)] (_inst_8 : ContinuousLinearEquiv.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) _inst_5 _inst_7) (e : ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) _inst_5 _inst_7), Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_7 _inst_5) (ContinuousLinearMap.inverse.{u3, u2, u1} R M M₂ _inst_1 _inst_2 (Ring.toSemiring.{u3} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 e) (ContinuousLinearMap.comp.{u3, u3, u3, u1, u2, u2} R R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_7 _inst_5 _inst_5 (RingHomCompTriple.ids.{u3, u3} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3)))) (Ring.inverse.{u2} (ContinuousLinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u3, u2} R (Ring.toSemiring.{u3} R _inst_3) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (ContinuousLinearMap.comp.{u3, u3, u3, u2, u1, u2} R R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_7 _inst_5 (RingHomCompTriple.ids.{u3, u3} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3)))) (ContinuousLinearEquiv.toContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_7 _inst_5 (ContinuousLinearEquiv.symm.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) _inst_5 _inst_7 _inst_8)) e)) (ContinuousLinearEquiv.toContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_7 _inst_5 (ContinuousLinearEquiv.symm.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) _inst_5 _inst_7 _inst_8)))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.to_ring_inverse ContinuousLinearMap.to_ring_inverseₓ'. -/
/-- The function `continuous_linear_equiv.inverse` can be written in terms of `ring.inverse` for the
ring of self-maps of the domain. -/
@@ -4372,7 +4372,7 @@ end Submodule
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommGroup.{u2} M] {M₂ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₂] [_inst_5 : AddCommGroup.{u3} M₂] [_inst_6 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] [_inst_7 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5)] [_inst_8 : TopologicalAddGroup.{u2} M _inst_2 (AddCommGroup.toAddGroup.{u2} M _inst_3)] (f₁ : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_7) (f₂ : ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6), (Function.RightInverse.{succ u2, succ u3} M M₂ (coeFn.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6) (fun (_x : ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6) => M₂ -> M) (ContinuousLinearMap.toFun.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6) f₂) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_7) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_7) => M -> M₂) (ContinuousLinearMap.toFun.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_7) f₁)) -> (Submodule.ClosedComplemented.{u1, u2} R _inst_1 M _inst_2 _inst_3 _inst_6 (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_7) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u3, u1, u1, u2, u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_7) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_7 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_7)) f₁))
but is expected to have type
- forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {M : Type.{u2}} [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] [_inst_7 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] [_inst_8 : TopologicalAddGroup.{u2} M _inst_2 (AddCommGroup.toAddGroup.{u2} M _inst_3)] (f₁ : ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7) (f₂ : ContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6), (Function.RightInverse.{succ u2, succ u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6) M₂ M _inst_4 _inst_2 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u3, u1, u2} (ContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6))) f₂) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7) M M₂ _inst_2 _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7))) f₁)) -> (Submodule.ClosedComplemented.{u3, u2} R _inst_1 M _inst_2 _inst_3 _inst_6 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7)) f₁))
+ forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {M : Type.{u2}} [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] [_inst_7 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] [_inst_8 : TopologicalAddGroup.{u2} M _inst_2 (AddCommGroup.toAddGroup.{u2} M _inst_3)] (f₁ : ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7) (f₂ : ContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6), (Function.RightInverse.{succ u2, succ u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6) M₂ M _inst_4 _inst_2 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u3, u1, u2} (ContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6))) f₂) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7) M M₂ _inst_2 _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.closed_complemented_ker_of_right_inverse ContinuousLinearMap.closedComplemented_ker_of_rightInverseₓ'. -/
theorem ContinuousLinearMap.closedComplemented_ker_of_rightInverse {R : Type _} [Ring R]
{M : Type _} [TopologicalSpace M] [AddCommGroup M] {M₂ : Type _} [TopologicalSpace M₂]
mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1
@@ -1906,17 +1906,17 @@ theorem coe_prodMap [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (f
rfl
#align continuous_linear_map.coe_prod_map ContinuousLinearMap.coe_prodMap
-/- warning: continuous_linear_map.coe_prod_map' -> ContinuousLinearMap.coe_prod_map is a dubious translation:
+/- warning: continuous_linear_map.coe_prod_map' -> ContinuousLinearMap.coe_prodMap' is a dubious translation:
lean 3 declaration is
forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u4}} [_inst_10 : TopologicalSpace.{u4} M₃] [_inst_11 : AddCommMonoid.{u4} M₃] {M₄ : Type.{u5}} [_inst_12 : TopologicalSpace.{u5} M₄] [_inst_13 : AddCommMonoid.{u5} M₄] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u1, u4} R₁ M₃ _inst_1 _inst_11] [_inst_21 : Module.{u1, u5} R₁ M₄ _inst_1 _inst_13] (f₁ : ContinuousLinearMap.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) (f₂ : ContinuousLinearMap.{u1, u1, u4, u5} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_20 _inst_21), Eq.{max (succ (max u2 u4)) (succ (max u3 u5))} ((Prod.{u2, u4} M₁ M₃) -> (Prod.{u3, u5} M₂ M₄)) (coeFn.{max (succ (max u2 u4)) (succ (max u3 u5)), max (succ (max u2 u4)) (succ (max u3 u5))} (ContinuousLinearMap.{u1, u1, max u2 u4, max u3 u5} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u4} M₁ M₃) (Prod.topologicalSpace.{u2, u4} M₁ M₃ _inst_4 _inst_10) (Prod.addCommMonoid.{u2, u4} M₁ M₃ _inst_5 _inst_11) (Prod.{u3, u5} M₂ M₄) (Prod.topologicalSpace.{u3, u5} M₂ M₄ _inst_8 _inst_12) (Prod.addCommMonoid.{u3, u5} M₂ M₄ _inst_9 _inst_13) (Prod.module.{u1, u2, u4} R₁ M₁ M₃ _inst_1 _inst_5 _inst_11 _inst_14 _inst_20) (Prod.module.{u1, u3, u5} R₁ M₂ M₄ _inst_1 _inst_9 _inst_13 _inst_19 _inst_21)) (fun (_x : ContinuousLinearMap.{u1, u1, max u2 u4, max u3 u5} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u4} M₁ M₃) (Prod.topologicalSpace.{u2, u4} M₁ M₃ _inst_4 _inst_10) (Prod.addCommMonoid.{u2, u4} M₁ M₃ _inst_5 _inst_11) (Prod.{u3, u5} M₂ M₄) (Prod.topologicalSpace.{u3, u5} M₂ M₄ _inst_8 _inst_12) (Prod.addCommMonoid.{u3, u5} M₂ M₄ _inst_9 _inst_13) (Prod.module.{u1, u2, u4} R₁ M₁ M₃ _inst_1 _inst_5 _inst_11 _inst_14 _inst_20) (Prod.module.{u1, u3, u5} R₁ M₂ M₄ _inst_1 _inst_9 _inst_13 _inst_19 _inst_21)) => (Prod.{u2, u4} M₁ M₃) -> (Prod.{u3, u5} M₂ M₄)) (ContinuousLinearMap.toFun.{u1, u1, max u2 u4, max u3 u5} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u4} M₁ M₃) (Prod.topologicalSpace.{u2, u4} M₁ M₃ _inst_4 _inst_10) (Prod.addCommMonoid.{u2, u4} M₁ M₃ _inst_5 _inst_11) (Prod.{u3, u5} M₂ M₄) (Prod.topologicalSpace.{u3, u5} M₂ M₄ _inst_8 _inst_12) (Prod.addCommMonoid.{u3, u5} M₂ M₄ _inst_9 _inst_13) (Prod.module.{u1, u2, u4} R₁ M₁ M₃ _inst_1 _inst_5 _inst_11 _inst_14 _inst_20) (Prod.module.{u1, u3, u5} R₁ M₂ M₄ _inst_1 _inst_9 _inst_13 _inst_19 _inst_21)) (ContinuousLinearMap.prodMap.{u1, u2, u3, u4, u5} R₁ _inst_1 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_14 _inst_19 _inst_20 _inst_21 f₁ f₂)) (Prod.map.{u2, u3, u4, u5} M₁ M₂ M₃ M₄ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) => M₁ -> M₂) (ContinuousLinearMap.toFun.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) f₁) (coeFn.{max (succ u4) (succ u5), max (succ u4) (succ u5)} (ContinuousLinearMap.{u1, u1, u4, u5} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_20 _inst_21) (fun (_x : ContinuousLinearMap.{u1, u1, u4, u5} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_20 _inst_21) => M₃ -> M₄) (ContinuousLinearMap.toFun.{u1, u1, u4, u5} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_20 _inst_21) f₂))
but is expected to have type
forall {R₁ : Type.{u5}} [_inst_1 : Semiring.{u5} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] {M₃ : Type.{u3}} [_inst_10 : TopologicalSpace.{u3} M₃] [_inst_11 : AddCommMonoid.{u3} M₃] {M₄ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₄] [_inst_13 : AddCommMonoid.{u2} M₄] [_inst_14 : Module.{u5, u1} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u5, u4} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u5, u3} R₁ M₃ _inst_1 _inst_11] [_inst_21 : Module.{u5, u2} R₁ M₄ _inst_1 _inst_13] (f₁ : ContinuousLinearMap.{u5, u5, u1, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) (f₂ : ContinuousLinearMap.{u5, u5, u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_20 _inst_21), 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(Prod.module.{u5, u1, u3} R₁ M₁ M₃ _inst_1 _inst_5 _inst_11 _inst_14 _inst_20) (Prod.module.{u5, u4, u2} R₁ M₂ M₄ _inst_1 _inst_9 _inst_13 _inst_19 _inst_21) (ContinuousLinearMap.continuousSemilinearMapClass.{u5, u5, max u1 u3, max u4 u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (Prod.{u1, u3} M₁ M₃) (instTopologicalSpaceProd.{u1, u3} M₁ M₃ _inst_4 _inst_10) (Prod.instAddCommMonoidSum.{u1, u3} M₁ M₃ _inst_5 _inst_11) (Prod.{u4, u2} M₂ M₄) (instTopologicalSpaceProd.{u4, u2} M₂ M₄ _inst_8 _inst_12) (Prod.instAddCommMonoidSum.{u4, u2} M₂ M₄ _inst_9 _inst_13) (Prod.module.{u5, u1, u3} R₁ M₁ M₃ _inst_1 _inst_5 _inst_11 _inst_14 _inst_20) (Prod.module.{u5, u4, u2} R₁ M₂ M₄ _inst_1 _inst_9 _inst_13 _inst_19 _inst_21)))) (ContinuousLinearMap.prodMap.{u5, u1, u4, u3, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_14 _inst_19 _inst_20 _inst_21 f₁ f₂)) (Prod.map.{u1, u4, u3, u2} M₁ M₂ M₃ M₄ (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (ContinuousLinearMap.{u5, u5, u1, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u1 u4, u1, u4} (ContinuousLinearMap.{u5, u5, u1, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u1 u4, u5, u5, u1, u4} (ContinuousLinearMap.{u5, u5, u1, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19 (ContinuousLinearMap.continuousSemilinearMapClass.{u5, u5, u1, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19))) f₁) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (ContinuousLinearMap.{u5, u5, u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_20 _inst_21) M₃ (fun (_x : M₃) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₃) => M₄) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u3, u2} (ContinuousLinearMap.{u5, u5, u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_20 _inst_21) M₃ M₄ _inst_10 _inst_12 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u5, u5, u3, u2} (ContinuousLinearMap.{u5, u5, u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_20 _inst_21) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_20 _inst_21 (ContinuousLinearMap.continuousSemilinearMapClass.{u5, u5, u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_20 _inst_21))) f₂))
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_prod_map' ContinuousLinearMap.coe_prod_mapₓ'. -/
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_prod_map' ContinuousLinearMap.coe_prodMap'ₓ'. -/
@[simp, norm_cast]
-theorem coe_prod_map [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (f₁ : M₁ →L[R₁] M₂)
+theorem coe_prodMap' [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (f₁ : M₁ →L[R₁] M₂)
(f₂ : M₃ →L[R₁] M₄) : ⇑(f₁.Prod_map f₂) = Prod.map f₁ f₂ :=
rfl
-#align continuous_linear_map.coe_prod_map' ContinuousLinearMap.coe_prod_map
+#align continuous_linear_map.coe_prod_map' ContinuousLinearMap.coe_prodMap'
/- warning: continuous_linear_map.coprod -> ContinuousLinearMap.coprod is a dubious translation:
lean 3 declaration is
mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab
@@ -365,7 +365,7 @@ section Pi
lean 3 declaration is
forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Finite.{succ u1} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : TopologicalSpace.{u2} R] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_2 _inst_4] [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : ContinuousAdd.{u3} M _inst_6 (AddZeroClass.toHasAdd.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)))] [_inst_8 : ContinuousSMul.{u2, u3} R M (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_4 _inst_5)))) _inst_3 _inst_6] (f : LinearMap.{u2, u2, max u1 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.Function.module.{u1, u2, u2} ι R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_5), Continuous.{max u1 u2, u3} (ι -> R) M (Pi.topologicalSpace.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (a : ι) => _inst_3)) _inst_6 (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.Function.module.{u1, u2, u2} ι R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.Function.module.{u1, u2, u2} ι R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_5) => (ι -> R) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (ι -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.Function.module.{u1, u2, u2} ι R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) f)
but is expected to have type
- forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Finite.{succ u3} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : TopologicalSpace.{u2} R] [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_2 _inst_4] [_inst_6 : TopologicalSpace.{u1} M] [_inst_7 : ContinuousAdd.{u1} M _inst_6 (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)))] [_inst_8 : ContinuousSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (Module.toMulActionWithZero.{u2, u1} R M _inst_2 _inst_4 _inst_5)))) _inst_3 _inst_6] (f : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5155 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5), Continuous.{max u3 u2, u1} (ι -> R) M (Pi.topologicalSpace.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (a : ι) => _inst_3)) _inst_6 (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5155 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5155 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5) (ι -> R) (fun (_x : ι -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (ι -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5155 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) f)
+ forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Finite.{succ u3} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : TopologicalSpace.{u2} R] [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_2 _inst_4] [_inst_6 : TopologicalSpace.{u1} M] [_inst_7 : ContinuousAdd.{u1} M _inst_6 (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)))] [_inst_8 : ContinuousSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (Module.toMulActionWithZero.{u2, u1} R M _inst_2 _inst_4 _inst_5)))) _inst_3 _inst_6] (f : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5), Continuous.{max u3 u2, u1} (ι -> R) M (Pi.topologicalSpace.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (a : ι) => _inst_3)) _inst_6 (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5) (ι -> R) (fun (_x : ι -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (ι -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5153 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) f)
Case conversion may be inaccurate. Consider using '#align linear_map.continuous_on_pi LinearMap.continuous_on_piₓ'. -/
theorem LinearMap.continuous_on_pi {ι : Type _} {R : Type _} {M : Type _} [Finite ι] [Semiring R]
[TopologicalSpace R] [AddCommMonoid M] [Module R M] [TopologicalSpace M] [ContinuousAdd M]
@@ -2157,7 +2157,7 @@ variable (R φ)
lean 3 declaration is
forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {ι : Type.{u2}} (φ : ι -> Type.{u3}) [_inst_8 : forall (i : ι), TopologicalSpace.{u3} (φ i)] [_inst_9 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_10 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_9 i)] {I : Set.{u2} ι} {J : Set.{u2} ι} [_inst_11 : DecidablePred.{succ u2} ι (fun (i : ι) => Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i I)], (Disjoint.{u2} (Set.{u2} ι) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} ι) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.completeBooleanAlgebra.{u2} ι)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u2} (Set.{u2} ι) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u2} (Set.{u2} ι) (Set.booleanAlgebra.{u2} ι))) I J) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) 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u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (Submodule.instInfSetSubmodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) ι (fun (i : ι) => infᵢ.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (Submodule.instInfSetSubmodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i J) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i J) => LinearMap.ker.{u1, u1, max u2 u3, u3, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (ContinuousLinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i)) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u3, u1, u1, max u2 u3, u3} (ContinuousLinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i)) R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i) (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i))) (ContinuousLinearMap.proj.{u1, u2, u3} R _inst_1 ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a) (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i) i))))) (Pi.module.{u2, u3, u1} (Set.Elem.{u2} ι I) (fun (i : Set.Elem.{u2} ι I) => φ (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) i)) R _inst_1 (fun (i : Set.Elem.{u2} ι I) => _inst_9 (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) i)) (fun (i : Set.Elem.{u2} ι I) => _inst_10 (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) i))))
+ forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {ι : Type.{u2}} (φ : ι -> Type.{u3}) [_inst_8 : forall (i : ι), TopologicalSpace.{u3} (φ i)] [_inst_9 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_10 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_9 i)] {I : Set.{u2} ι} {J : Set.{u2} ι} [_inst_11 : DecidablePred.{succ u2} ι (fun (i : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i I)], (Disjoint.{u2} (Set.{u2} ι) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.instCompleteBooleanAlgebraSet.{u2} ι)))))) (BoundedOrder.toOrderBot.{u2} (Set.{u2} ι) (Preorder.toLE.{u2} (Set.{u2} ι) (PartialOrder.toPreorder.{u2} (Set.{u2} ι) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.instCompleteBooleanAlgebraSet.{u2} ι)))))))) (CompleteLattice.toBoundedOrder.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.instCompleteBooleanAlgebraSet.{u2} ι)))))) I J) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.instHasSubsetSet.{u2} ι) (Set.univ.{u2} ι) (Union.union.{u2} (Set.{u2} ι) (Set.instUnionSet.{u2} ι) I J)) -> (ContinuousLinearEquiv.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ (max u2 u3)} (forall (i : ι), φ i) (fun (x : forall (i : ι), φ i) => Membership.mem.{max u2 u3, max u2 u3} (forall (i : ι), φ i) (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (SetLike.instMembership.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (forall (i : ι), φ i) (Submodule.setLike.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)))) x (infᵢ.{max u2 u3, succ 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(fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i J) (fun (h._@.Mathlib.Topology.Algebra.Module.Basic._hyg.34409 : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i J) => LinearMap.ker.{u1, u1, max u2 u3, u3, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (_inst_9 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (ContinuousLinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (Pi.topologicalSpace.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) 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Case conversion may be inaccurate. Consider using '#align continuous_linear_map.infi_ker_proj_equiv ContinuousLinearMap.infᵢKerProjEquivₓ'. -/
/-- If `I` and `J` are complementary index sets, the product of the kernels of the `J`th projections
of `φ` is linearly equivalent to the product over `I`. -/
@@ -4140,7 +4140,7 @@ variable {ι R M}
lean 3 declaration is
forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Unique.{succ u1} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u3} M], Eq.{max (succ (max u1 u3)) (succ u3)} ((ι -> M) -> M) (coeFn.{max (succ (max u1 u3)) (succ u3), max (succ (max u1 u3)) (succ u3)} (ContinuousLinearEquiv.{u2, u2, max u1 u3, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.Function.module.{u1, u2, u3} ι R M _inst_2 _inst_3 _inst_4) _inst_4) (fun (_x : ContinuousLinearEquiv.{u2, u2, max u1 u3, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.Function.module.{u1, u2, u3} ι R M _inst_2 _inst_3 _inst_4) _inst_4) => (ι -> M) -> M) (ContinuousLinearEquiv.hasCoeToFun.{u2, u2, max u1 u3, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.Function.module.{u1, u2, u3} ι R M _inst_2 _inst_3 _inst_4) _inst_4) (ContinuousLinearEquiv.funUnique.{u1, u2, u3} ι R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Function.eval.{succ u1, succ u3} ι (fun (x : ι) => M) (Inhabited.default.{succ u1} ι (Unique.inhabited.{succ u1} ι _inst_1)))
but is expected to have type
- forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Unique.{succ u3} ι] [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], Eq.{max (succ u3) (succ u2)} (forall (ᾰ : ι -> M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : ι -> M) => M) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), succ u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) (ι -> M) (fun (_x : ι -> M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : ι -> M) => M) _x) (ContinuousMapClass.toFunLike.{max u3 u2, max u3 u2, u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) (ι -> M) M (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) _inst_5 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u1, u1, max u3 u2, u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u3 u2, u1, u1, max u3 u2, u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4)))) (ContinuousLinearEquiv.funUnique.{u3, u1, u2} ι R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Function.eval.{succ u3, succ u2} ι (fun (x : ι) => M) (Inhabited.default.{succ u3} ι (Unique.instInhabited.{succ u3} ι _inst_1)))
+ forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Unique.{succ u3} ι] [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], Eq.{max (succ u3) (succ u2)} (forall (ᾰ : ι -> M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : ι -> M) => M) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), succ u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) (ι -> M) (fun (_x : ι -> M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : ι -> M) => M) _x) (ContinuousMapClass.toFunLike.{max u3 u2, max u3 u2, u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) (ι -> M) M (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) _inst_5 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u1, u1, max u3 u2, u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u3 u2, u1, u1, max u3 u2, u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4)))) (ContinuousLinearEquiv.funUnique.{u3, u1, u2} ι R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Function.eval.{succ u3, succ u2} ι (fun (x : ι) => M) (Inhabited.default.{succ u3} ι (Unique.instInhabited.{succ u3} ι _inst_1)))
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_fun_unique ContinuousLinearEquiv.coe_funUniqueₓ'. -/
@[simp]
theorem coe_funUnique : ⇑(funUnique ι R M) = Function.eval default :=
@@ -4151,7 +4151,7 @@ theorem coe_funUnique : ⇑(funUnique ι R M) = Function.eval default :=
lean 3 declaration is
forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Unique.{succ u1} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u3} M], Eq.{max (succ u3) (succ (max u1 u3))} (M -> ι -> M) (coeFn.{max (succ u3) (succ (max u1 u3)), max (succ u3) (succ (max u1 u3))} (ContinuousLinearEquiv.{u2, u2, u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.Function.module.{u1, u2, u3} ι R M _inst_2 _inst_3 _inst_4)) (fun (_x : ContinuousLinearEquiv.{u2, u2, u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.Function.module.{u1, u2, u3} ι R M _inst_2 _inst_3 _inst_4)) => M -> ι -> M) (ContinuousLinearEquiv.hasCoeToFun.{u2, u2, u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.Function.module.{u1, u2, u3} ι R M _inst_2 _inst_3 _inst_4)) (ContinuousLinearEquiv.symm.{u2, u2, max u1 u3, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.Function.module.{u1, u2, u3} ι R M _inst_2 _inst_3 _inst_4) _inst_4 (ContinuousLinearEquiv.funUnique.{u1, u2, u3} ι R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Function.const.{succ u3, succ u1} M ι)
but is expected to have type
- forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Unique.{succ u3} ι] [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], Eq.{max (succ u3) (succ u2)} (forall (ᾰ : M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => ι -> M) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => ι -> M) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u2, max u3 u2} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) M (ι -> M) _inst_5 (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u1, u1, u2, max u3 u2} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u3 u2, u1, u1, u2, max u3 u2} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)))))) (ContinuousLinearEquiv.symm.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4 (ContinuousLinearEquiv.funUnique.{u3, u1, u2} ι R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Function.const.{succ u2, succ u3} M ι)
+ forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Unique.{succ u3} ι] [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], Eq.{max (succ u3) (succ u2)} (forall (ᾰ : M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => ι -> M) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => ι -> M) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u2, max u3 u2} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) M (ι -> M) _inst_5 (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u1, u1, u2, max u3 u2} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u3 u2, u1, u1, u2, max u3 u2} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)))))) (ContinuousLinearEquiv.symm.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61458 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4 (ContinuousLinearEquiv.funUnique.{u3, u1, u2} ι R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Function.const.{succ u2, succ u3} M ι)
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_fun_unique_symm ContinuousLinearEquiv.coe_funUnique_symmₓ'. -/
@[simp]
theorem coe_funUnique_symm : ⇑(funUnique ι R M).symm = Function.const ι :=
@@ -4177,7 +4177,7 @@ def piFinTwo (M : Fin 2 → Type _) [∀ i, AddCommMonoid (M i)] [∀ i, Module
lean 3 declaration is
forall (R : Type.{u1}) (M : Type.{u2}) [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], ContinuousLinearEquiv.{u1, u1, u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) ((Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> M) (Pi.topologicalSpace.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => M) (fun (a : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => _inst_5)) (Pi.addCommMonoid.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => M) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => _inst_3)) (Prod.{u2, u2} M M) (Prod.topologicalSpace.{u2, u2} M M _inst_5 _inst_5) (Prod.addCommMonoid.{u2, u2} M M _inst_3 _inst_3) (Pi.Function.module.{0, u1, u2} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) R M _inst_2 _inst_3 _inst_4) (Prod.module.{u1, u2, u2} R M M _inst_2 _inst_3 _inst_3 _inst_4 _inst_4)
but is expected to have type
- forall (R : Type.{u1}) (M : Type.{u2}) [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], ContinuousLinearEquiv.{u1, u1, u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) ((Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> M) (Pi.topologicalSpace.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M) (fun (a : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_5)) (Pi.addCommMonoid.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_3)) (Prod.{u2, u2} M M) (instTopologicalSpaceProd.{u2, u2} M M _inst_5 _inst_5) (Prod.instAddCommMonoidSum.{u2, u2} M M _inst_3 _inst_3) (Pi.module.{0, u2, u1} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61745 : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M) R _inst_2 (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_3) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_4)) (Prod.module.{u1, u2, u2} R M M _inst_2 _inst_3 _inst_3 _inst_4 _inst_4)
+ forall (R : Type.{u1}) (M : Type.{u2}) [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], ContinuousLinearEquiv.{u1, u1, u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) ((Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> M) (Pi.topologicalSpace.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M) (fun (a : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_5)) (Pi.addCommMonoid.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_3)) (Prod.{u2, u2} M M) (instTopologicalSpaceProd.{u2, u2} M M _inst_5 _inst_5) (Prod.instAddCommMonoidSum.{u2, u2} M M _inst_3 _inst_3) (Pi.module.{0, u2, u1} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61743 : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M) R _inst_2 (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_3) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_4)) (Prod.module.{u1, u2, u2} R M M _inst_2 _inst_3 _inst_3 _inst_4 _inst_4)
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.fin_two_arrow ContinuousLinearEquiv.finTwoArrowₓ'. -/
/-- Continuous linear equivalence between vectors in `M² = fin 2 → M` and `M × M`. -/
@[simps (config := { fullyApplied := false })]
mathlib commit https://github.com/leanprover-community/mathlib/commit/2651125b48fc5c170ab1111afd0817c903b1fc6c
@@ -4041,7 +4041,7 @@ theorem unitsEquivAut_apply (u : Rˣ) (x : R) : unitsEquivAut R u x = x * u :=
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))] (u : Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (x : R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (_x : ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => R -> R) (ContinuousLinearEquiv.hasCoeToFun.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.symm.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : Equiv.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) -> (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Equiv.hasCoeToFun.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.unitsEquivAut.{u1} R _inst_1 _inst_11 _inst_12) u)) x) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))) x ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (coeBase.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (Units.hasCoe.{u1} R (Ring.toMonoid.{u1} R _inst_1))))) (Inv.inv.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (Units.hasInv.{u1} R (Ring.toMonoid.{u1} R _inst_1)) u)))
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))] (u : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) x) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R _inst_11 _inst_11 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u1, u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{u1, u1, u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (ContinuousLinearEquiv.symm.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.unitsEquivAut.{u1} R _inst_1 _inst_11 _inst_12) u)) x) (HMul.hMul.{u1, u1, u1} R ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) x) R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) x (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Inv.inv.{u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Units.instInvUnits.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) u)))
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))] (u : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) x) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R _inst_11 _inst_11 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u1, u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{u1, u1, u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (ContinuousLinearEquiv.symm.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.unitsEquivAut.{u1} R _inst_1 _inst_11 _inst_12) u)) x) (HMul.hMul.{u1, u1, u1} R ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) x) R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) x (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Inv.inv.{u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Units.instInv.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) u)))
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv_aut_apply_symm ContinuousLinearEquiv.unitsEquivAut_apply_symmₓ'. -/
@[simp]
theorem unitsEquivAut_apply_symm (u : Rˣ) (x : R) : (unitsEquivAut R u).symm x = x * ↑u⁻¹ :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/cd8fafa2fac98e1a67097e8a91ad9901cfde48af
@@ -4140,7 +4140,7 @@ variable {ι R M}
lean 3 declaration is
forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Unique.{succ u1} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u3} M], Eq.{max (succ (max u1 u3)) (succ u3)} ((ι -> M) -> M) (coeFn.{max (succ (max u1 u3)) (succ u3), max (succ (max u1 u3)) (succ u3)} (ContinuousLinearEquiv.{u2, u2, max u1 u3, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.Function.module.{u1, u2, u3} ι R M _inst_2 _inst_3 _inst_4) _inst_4) (fun (_x : ContinuousLinearEquiv.{u2, u2, max u1 u3, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.Function.module.{u1, u2, u3} ι R M _inst_2 _inst_3 _inst_4) _inst_4) => (ι -> M) -> M) (ContinuousLinearEquiv.hasCoeToFun.{u2, u2, max u1 u3, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.Function.module.{u1, u2, u3} ι R M _inst_2 _inst_3 _inst_4) _inst_4) (ContinuousLinearEquiv.funUnique.{u1, u2, u3} ι R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Function.eval.{succ u1, succ u3} ι (fun (x : ι) => M) (Inhabited.default.{succ u1} ι (Unique.inhabited.{succ u1} ι _inst_1)))
but is expected to have type
- forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Unique.{succ u3} ι] [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], Eq.{max (succ u3) (succ u2)} (forall (ᾰ : ι -> M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : ι -> M) => M) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), succ u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) (ι -> M) (fun (_x : ι -> M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : ι -> M) => M) _x) (ContinuousMapClass.toFunLike.{max u3 u2, max u3 u2, u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) (ι -> M) M (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (a : ι) => _inst_5)) _inst_5 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u1, u1, max u3 u2, u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u3 u2, u1, u1, max u3 u2, u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4)))) (ContinuousLinearEquiv.funUnique.{u3, u1, u2} ι R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Function.eval.{succ u3, succ u2} ι (fun (x : ι) => M) (Inhabited.default.{succ u3} ι (Unique.instInhabited.{succ u3} ι _inst_1)))
+ forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Unique.{succ u3} ι] [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], Eq.{max (succ u3) (succ u2)} (forall (ᾰ : ι -> M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : ι -> M) => M) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), succ u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) (ι -> M) (fun (_x : ι -> M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : ι -> M) => M) _x) (ContinuousMapClass.toFunLike.{max u3 u2, max u3 u2, u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) (ι -> M) M (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) _inst_5 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u1, u1, max u3 u2, u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u3 u2, u1, u1, max u3 u2, u2} (ContinuousLinearEquiv.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4)))) (ContinuousLinearEquiv.funUnique.{u3, u1, u2} ι R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Function.eval.{succ u3, succ u2} ι (fun (x : ι) => M) (Inhabited.default.{succ u3} ι (Unique.instInhabited.{succ u3} ι _inst_1)))
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_fun_unique ContinuousLinearEquiv.coe_funUniqueₓ'. -/
@[simp]
theorem coe_funUnique : ⇑(funUnique ι R M) = Function.eval default :=
@@ -4151,7 +4151,7 @@ theorem coe_funUnique : ⇑(funUnique ι R M) = Function.eval default :=
lean 3 declaration is
forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Unique.{succ u1} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u3} M], Eq.{max (succ u3) (succ (max u1 u3))} (M -> ι -> M) (coeFn.{max (succ u3) (succ (max u1 u3)), max (succ u3) (succ (max u1 u3))} (ContinuousLinearEquiv.{u2, u2, u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.Function.module.{u1, u2, u3} ι R M _inst_2 _inst_3 _inst_4)) (fun (_x : ContinuousLinearEquiv.{u2, u2, u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.Function.module.{u1, u2, u3} ι R M _inst_2 _inst_3 _inst_4)) => M -> ι -> M) (ContinuousLinearEquiv.hasCoeToFun.{u2, u2, u3, max u1 u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.Function.module.{u1, u2, u3} ι R M _inst_2 _inst_3 _inst_4)) (ContinuousLinearEquiv.symm.{u2, u2, max u1 u3, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (RingHomInvPair.ids.{u2} R _inst_2) (RingHomInvPair.ids.{u2} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.Function.module.{u1, u2, u3} ι R M _inst_2 _inst_3 _inst_4) _inst_4 (ContinuousLinearEquiv.funUnique.{u1, u2, u3} ι R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Function.const.{succ u3, succ u1} M ι)
but is expected to have type
- forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Unique.{succ u3} ι] [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], Eq.{max (succ u3) (succ u2)} (forall (ᾰ : M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => ι -> M) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => ι -> M) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u2, max u3 u2} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) M (ι -> M) _inst_5 (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (a : ι) => _inst_5)) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u1, u1, u2, max u3 u2} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u3 u2, u1, u1, u2, max u3 u2} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)))))) (ContinuousLinearEquiv.symm.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61457 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4 (ContinuousLinearEquiv.funUnique.{u3, u1, u2} ι R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Function.const.{succ u2, succ u3} M ι)
+ forall {ι : Type.{u3}} {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Unique.{succ u3} ι] [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], Eq.{max (succ u3) (succ u2)} (forall (ᾰ : M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => ι -> M) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => ι -> M) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u2, max u3 u2} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) M (ι -> M) _inst_5 (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u1, u1, u2, max u3 u2} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u3 u2, u1, u1, u2, max u3 u2} (ContinuousLinearEquiv.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4))) R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, u2, max u3 u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) M _inst_5 _inst_3 (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) (fun (i : ι) => _inst_3)) _inst_4 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)))))) (ContinuousLinearEquiv.symm.{u1, u1, max u3 u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (ι -> M) (Pi.topologicalSpace.{u3, u2} ι (fun (ᾰ : ι) => M) (fun (a : ι) => _inst_5)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_3)) M _inst_5 _inst_3 (Pi.module.{u3, u2, u1} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61460 : ι) => M) R _inst_2 (fun (i : ι) => _inst_3) (fun (i : ι) => _inst_4)) _inst_4 (ContinuousLinearEquiv.funUnique.{u3, u1, u2} ι R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Function.const.{succ u2, succ u3} M ι)
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_fun_unique_symm ContinuousLinearEquiv.coe_funUnique_symmₓ'. -/
@[simp]
theorem coe_funUnique_symm : ⇑(funUnique ι R M).symm = Function.const ι :=
@@ -4177,7 +4177,7 @@ def piFinTwo (M : Fin 2 → Type _) [∀ i, AddCommMonoid (M i)] [∀ i, Module
lean 3 declaration is
forall (R : Type.{u1}) (M : Type.{u2}) [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], ContinuousLinearEquiv.{u1, u1, u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) ((Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> M) (Pi.topologicalSpace.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => M) (fun (a : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => _inst_5)) (Pi.addCommMonoid.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => M) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => _inst_3)) (Prod.{u2, u2} M M) (Prod.topologicalSpace.{u2, u2} M M _inst_5 _inst_5) (Prod.addCommMonoid.{u2, u2} M M _inst_3 _inst_3) (Pi.Function.module.{0, u1, u2} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) R M _inst_2 _inst_3 _inst_4) (Prod.module.{u1, u2, u2} R M M _inst_2 _inst_3 _inst_3 _inst_4 _inst_4)
but is expected to have type
- forall (R : Type.{u1}) (M : Type.{u2}) [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], ContinuousLinearEquiv.{u1, u1, u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) ((Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> M) (Pi.topologicalSpace.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M) (fun (a : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_5)) (Pi.addCommMonoid.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_3)) (Prod.{u2, u2} M M) (instTopologicalSpaceProd.{u2, u2} M M _inst_5 _inst_5) (Prod.instAddCommMonoidSum.{u2, u2} M M _inst_3 _inst_3) (Pi.module.{0, u2, u1} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61742 : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M) R _inst_2 (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_3) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_4)) (Prod.module.{u1, u2, u2} R M M _inst_2 _inst_3 _inst_3 _inst_4 _inst_4)
+ forall (R : Type.{u1}) (M : Type.{u2}) [_inst_2 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_2 _inst_3] [_inst_5 : TopologicalSpace.{u2} M], ContinuousLinearEquiv.{u1, u1, u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) ((Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> M) (Pi.topologicalSpace.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M) (fun (a : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_5)) (Pi.addCommMonoid.{0, u2} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_3)) (Prod.{u2, u2} M M) (instTopologicalSpaceProd.{u2, u2} M M _inst_5 _inst_5) (Prod.instAddCommMonoidSum.{u2, u2} M M _inst_3 _inst_3) (Pi.module.{0, u2, u1} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.61745 : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => M) R _inst_2 (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_3) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => _inst_4)) (Prod.module.{u1, u2, u2} R M M _inst_2 _inst_3 _inst_3 _inst_4 _inst_4)
Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.fin_two_arrow ContinuousLinearEquiv.finTwoArrowₓ'. -/
/-- Continuous linear equivalence between vectors in `M² = fin 2 → M` and `M × M`. -/
@[simps (config := { fullyApplied := false })]
mathlib commit https://github.com/leanprover-community/mathlib/commit/06a655b5fcfbda03502f9158bbf6c0f1400886f9
@@ -5,7 +5,7 @@ Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov, Fréd
Heather Macbeth
! This file was ported from Lean 3 source module topology.algebra.module.basic
-! leanprover-community/mathlib commit f430769b562e0cedef59ee1ed968d67e0e0c86ba
+! leanprover-community/mathlib commit d64d67d000b974f0d86a2be7918cf800be6271c8
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -21,6 +21,9 @@ import Mathbin.LinearAlgebra.Pi
/-!
# Theory of topological modules and continuous linear maps.
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
We use the class `has_continuous_smul` for topological (semi) modules and topological vector spaces.
In this file we define continuous (semi-)linear maps, as semilinear maps between topological
mathlib commit https://github.com/leanprover-community/mathlib/commit/1a4df69ca1a9a0e5e26bfe12e2b92814216016d0
@@ -2664,7 +2664,7 @@ variable (S) [ContinuousAdd N₃]
lean 3 declaration is
forall {R : Type.{u1}} (S : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_4 : Semiring.{u2} S] {M : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : AddCommMonoid.{u3} M] [_inst_8 : Module.{u1, u3} R M _inst_1 _inst_7] {N₂ : Type.{u4}} [_inst_15 : TopologicalSpace.{u4} N₂] [_inst_16 : AddCommMonoid.{u4} N₂] [_inst_17 : Module.{u1, u4} R N₂ _inst_1 _inst_16] {N₃ : Type.{u5}} [_inst_18 : TopologicalSpace.{u5} N₃] [_inst_19 : AddCommMonoid.{u5} N₃] [_inst_20 : Module.{u1, u5} R N₃ _inst_1 _inst_19] [_inst_24 : Module.{u2, u4} S N₂ _inst_4 _inst_16] [_inst_25 : ContinuousConstSMul.{u2, u4} S N₂ _inst_15 (SMulZeroClass.toHasSmul.{u2, u4} S N₂ (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (SMulWithZero.toSmulZeroClass.{u2, u4} S N₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)))) (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (MulActionWithZero.toSMulWithZero.{u2, u4} S N₂ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (Module.toMulActionWithZero.{u2, u4} S N₂ _inst_4 _inst_16 _inst_24))))] [_inst_26 : SMulCommClass.{u1, u2, u4} R S N₂ (SMulZeroClass.toHasSmul.{u1, u4} R N₂ (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (SMulWithZero.toSmulZeroClass.{u1, u4} R N₂ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (MulActionWithZero.toSMulWithZero.{u1, u4} R N₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (Module.toMulActionWithZero.{u1, u4} R N₂ _inst_1 _inst_16 _inst_17)))) (SMulZeroClass.toHasSmul.{u2, u4} S N₂ (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (SMulWithZero.toSmulZeroClass.{u2, u4} S N₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)))) (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (MulActionWithZero.toSMulWithZero.{u2, u4} S N₂ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (Module.toMulActionWithZero.{u2, u4} S N₂ _inst_4 _inst_16 _inst_24))))] [_inst_27 : Module.{u2, u5} S N₃ _inst_4 _inst_19] [_inst_28 : SMulCommClass.{u1, u2, u5} R S N₃ (SMulZeroClass.toHasSmul.{u1, u5} R N₃ (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (SMulWithZero.toSmulZeroClass.{u1, u5} R N₃ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (MulActionWithZero.toSMulWithZero.{u1, u5} R N₃ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (Module.toMulActionWithZero.{u1, u5} R N₃ _inst_1 _inst_19 _inst_20)))) (SMulZeroClass.toHasSmul.{u2, u5} S N₃ (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (SMulWithZero.toSmulZeroClass.{u2, u5} S N₃ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)))) (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (MulActionWithZero.toSMulWithZero.{u2, u5} S N₃ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (Module.toMulActionWithZero.{u2, u5} S N₃ _inst_4 _inst_19 _inst_27))))] [_inst_29 : ContinuousConstSMul.{u2, u5} S N₃ _inst_18 (SMulZeroClass.toHasSmul.{u2, u5} S N₃ (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (SMulWithZero.toSmulZeroClass.{u2, u5} S N₃ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)))) (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (MulActionWithZero.toSMulWithZero.{u2, u5} S N₃ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (Module.toMulActionWithZero.{u2, u5} S N₃ _inst_4 _inst_19 _inst_27))))] [_inst_33 : ContinuousAdd.{u4} N₂ _inst_15 (AddZeroClass.toHasAdd.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)))] [_inst_34 : ContinuousAdd.{u5} N₃ _inst_18 (AddZeroClass.toHasAdd.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)))], LinearEquiv.{u2, u2, max (max u3 u4) u3 u5, max u3 u4 u5} S S _inst_4 _inst_4 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_4)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_4)) (RingHomInvPair.ids.{u2} S _inst_4) (RingHomInvPair.ids.{u2} S _inst_4) (Prod.{max u3 u4, max u3 u5} (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20)) (ContinuousLinearMap.{u1, u1, u3, max u4 u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 (Prod.{u4, u5} N₂ N₃) (Prod.topologicalSpace.{u4, u5} N₂ N₃ _inst_15 _inst_18) (Prod.addCommMonoid.{u4, u5} N₂ N₃ _inst_16 _inst_19) _inst_8 (Prod.module.{u1, u4, u5} R N₂ N₃ _inst_1 _inst_16 _inst_19 _inst_17 _inst_20)) (Prod.addCommMonoid.{max u3 u4, max u3 u5} (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17 _inst_33) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20 _inst_34)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, max u4 u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 (Prod.{u4, u5} N₂ N₃) (Prod.topologicalSpace.{u4, u5} N₂ N₃ _inst_15 _inst_18) (Prod.addCommMonoid.{u4, u5} N₂ N₃ _inst_16 _inst_19) _inst_8 (Prod.module.{u1, u4, u5} R N₂ N₃ _inst_1 _inst_16 _inst_19 _inst_17 _inst_20) (ContinuousLinearMap.prodₗ._proof_1.{u5, u4} N₂ _inst_15 _inst_16 N₃ _inst_18 _inst_19 _inst_33 _inst_34)) (Prod.module.{u2, max u3 u4, max u3 u5} S (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) _inst_4 (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17 _inst_33) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20 _inst_34) (ContinuousLinearMap.module.{u1, u1, u2, u3, u4} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 N₂ _inst_15 _inst_16 _inst_17 _inst_24 _inst_26 _inst_25 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_33) (ContinuousLinearMap.module.{u1, u1, u2, u3, u5} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 N₃ _inst_18 _inst_19 _inst_20 _inst_27 _inst_28 _inst_29 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_34)) (ContinuousLinearMap.module.{u1, u1, u2, u3, max u4 u5} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 (Prod.{u4, u5} N₂ N₃) (Prod.topologicalSpace.{u4, u5} N₂ N₃ _inst_15 _inst_18) (Prod.addCommMonoid.{u4, u5} N₂ N₃ _inst_16 _inst_19) (Prod.module.{u1, u4, u5} R N₂ N₃ _inst_1 _inst_16 _inst_19 _inst_17 _inst_20) (Prod.module.{u2, u4, u5} S N₂ N₃ _inst_4 _inst_16 _inst_19 _inst_24 _inst_27) (ContinuousLinearMap.prodₗ._proof_2.{u1, u5, u2, u4} R S _inst_1 _inst_4 N₂ _inst_16 _inst_17 N₃ _inst_19 _inst_20 _inst_24 _inst_26 _inst_27 _inst_28) (ContinuousLinearMap.prodₗ._proof_3.{u5, u2, u4} S _inst_4 N₂ _inst_15 _inst_16 N₃ _inst_18 _inst_19 _inst_24 _inst_25 _inst_27 _inst_29) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (ContinuousLinearMap.prodₗ._proof_4.{u5, u4} N₂ _inst_15 _inst_16 N₃ _inst_18 _inst_19 _inst_33 _inst_34))
but is expected to have type
- forall {R : Type.{u1}} (S : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_4 : Semiring.{u2} S] {M : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : AddCommMonoid.{u3} M] [_inst_8 : Module.{u1, u3} R M _inst_1 _inst_7] {N₂ : Type.{u4}} [_inst_15 : TopologicalSpace.{u4} N₂] [_inst_16 : AddCommMonoid.{u4} N₂] [_inst_17 : Module.{u1, u4} R N₂ _inst_1 _inst_16] {N₃ : Type.{u5}} [_inst_18 : TopologicalSpace.{u5} N₃] [_inst_19 : AddCommMonoid.{u5} N₃] [_inst_20 : Module.{u1, u5} R N₃ _inst_1 _inst_19] [_inst_24 : Module.{u2, u4} S N₂ _inst_4 _inst_16] [_inst_25 : ContinuousConstSMul.{u2, u4} S N₂ _inst_15 (SMulZeroClass.toSMul.{u2, u4} S N₂ (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (SMulWithZero.toSMulZeroClass.{u2, u4} S N₂ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (MulActionWithZero.toSMulWithZero.{u2, u4} S N₂ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (Module.toMulActionWithZero.{u2, u4} S N₂ _inst_4 _inst_16 _inst_24))))] [_inst_26 : SMulCommClass.{u1, u2, u4} R S N₂ (SMulZeroClass.toSMul.{u1, u4} R N₂ (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (SMulWithZero.toSMulZeroClass.{u1, u4} R N₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (MulActionWithZero.toSMulWithZero.{u1, u4} R N₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (Module.toMulActionWithZero.{u1, u4} R N₂ _inst_1 _inst_16 _inst_17)))) (SMulZeroClass.toSMul.{u2, u4} S N₂ (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (SMulWithZero.toSMulZeroClass.{u2, u4} S N₂ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (MulActionWithZero.toSMulWithZero.{u2, u4} S N₂ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (Module.toMulActionWithZero.{u2, u4} S N₂ _inst_4 _inst_16 _inst_24))))] [_inst_27 : Module.{u2, u5} S N₃ _inst_4 _inst_19] [_inst_28 : SMulCommClass.{u1, u2, u5} R S N₃ (SMulZeroClass.toSMul.{u1, u5} R N₃ (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (SMulWithZero.toSMulZeroClass.{u1, u5} R N₃ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (MulActionWithZero.toSMulWithZero.{u1, u5} R N₃ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (Module.toMulActionWithZero.{u1, u5} R N₃ _inst_1 _inst_19 _inst_20)))) (SMulZeroClass.toSMul.{u2, u5} S N₃ (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (SMulWithZero.toSMulZeroClass.{u2, u5} S N₃ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (MulActionWithZero.toSMulWithZero.{u2, u5} S N₃ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (Module.toMulActionWithZero.{u2, u5} S N₃ _inst_4 _inst_19 _inst_27))))] [_inst_29 : ContinuousConstSMul.{u2, u5} S N₃ _inst_18 (SMulZeroClass.toSMul.{u2, u5} S N₃ (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (SMulWithZero.toSMulZeroClass.{u2, u5} S N₃ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (MulActionWithZero.toSMulWithZero.{u2, u5} S N₃ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (Module.toMulActionWithZero.{u2, u5} S N₃ _inst_4 _inst_19 _inst_27))))] [_inst_33 : ContinuousAdd.{u4} N₂ _inst_15 (AddZeroClass.toAdd.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)))] [_inst_34 : ContinuousAdd.{u5} N₃ _inst_18 (AddZeroClass.toAdd.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)))], LinearEquiv.{u2, u2, max (max u5 u3) u4 u3, max (max u5 u4) u3} S S _inst_4 _inst_4 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_4)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_4)) (RingHomInvPair.ids.{u2} S _inst_4) (RingHomInvPair.ids.{u2} S _inst_4) (Prod.{max u4 u3, max u5 u3} (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20)) (ContinuousLinearMap.{u1, u1, u3, max u5 u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 (Prod.{u4, u5} N₂ N₃) (instTopologicalSpaceProd.{u4, u5} N₂ N₃ _inst_15 _inst_18) (Prod.instAddCommMonoidSum.{u4, u5} N₂ N₃ _inst_16 _inst_19) _inst_8 (Prod.module.{u1, u4, u5} R N₂ N₃ _inst_1 _inst_16 _inst_19 _inst_17 _inst_20)) (Prod.instAddCommMonoidSum.{max u3 u4, max u3 u5} (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17 _inst_33) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20 _inst_34)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, max u4 u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 (Prod.{u4, u5} N₂ N₃) (instTopologicalSpaceProd.{u4, u5} N₂ N₃ _inst_15 _inst_18) (Prod.instAddCommMonoidSum.{u4, u5} N₂ N₃ _inst_16 _inst_19) _inst_8 (Prod.module.{u1, u4, u5} R N₂ N₃ _inst_1 _inst_16 _inst_19 _inst_17 _inst_20) (instContinuousAddSumInstTopologicalSpaceSumInstAddSum.{u4, u5} N₂ N₃ _inst_15 (AddSemigroup.toAdd.{u4} N₂ (AddMonoid.toAddSemigroup.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) _inst_33 _inst_18 (AddSemigroup.toAdd.{u5} N₃ (AddMonoid.toAddSemigroup.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) _inst_34)) (Prod.module.{u2, max u3 u4, max u3 u5} S (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) _inst_4 (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17 _inst_33) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20 _inst_34) (ContinuousLinearMap.module.{u1, u1, u2, u3, u4} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 N₂ _inst_15 _inst_16 _inst_17 _inst_24 _inst_26 _inst_25 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_33) (ContinuousLinearMap.module.{u1, u1, u2, u3, u5} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 N₃ _inst_18 _inst_19 _inst_20 _inst_27 _inst_28 _inst_29 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_34)) (ContinuousLinearMap.module.{u1, u1, u2, u3, max u4 u5} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 (Prod.{u4, u5} N₂ N₃) (instTopologicalSpaceProd.{u4, u5} N₂ N₃ _inst_15 _inst_18) (Prod.instAddCommMonoidSum.{u4, u5} N₂ N₃ _inst_16 _inst_19) (Prod.module.{u1, u4, u5} R N₂ N₃ _inst_1 _inst_16 _inst_19 _inst_17 _inst_20) (Prod.module.{u2, u4, u5} S N₂ N₃ _inst_4 _inst_16 _inst_19 _inst_24 _inst_27) (Prod.smulCommClass.{u1, u2, u4, u5} R S N₂ N₃ (MulAction.toSMul.{u1, u4} R N₂ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (DistribMulAction.toMulAction.{u1, u4} R N₂ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16) (Module.toDistribMulAction.{u1, u4} R N₂ _inst_1 _inst_16 _inst_17))) (MulAction.toSMul.{u1, u5} R N₃ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (DistribMulAction.toMulAction.{u1, u5} R N₃ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19) (Module.toDistribMulAction.{u1, u5} R N₃ _inst_1 _inst_19 _inst_20))) (MulAction.toSMul.{u2, u4} S N₂ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (DistribMulAction.toMulAction.{u2, u4} S N₂ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16) (Module.toDistribMulAction.{u2, u4} S N₂ _inst_4 _inst_16 _inst_24))) (MulAction.toSMul.{u2, u5} S N₃ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (DistribMulAction.toMulAction.{u2, u5} S N₃ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19) (Module.toDistribMulAction.{u2, u5} S N₃ _inst_4 _inst_19 _inst_27))) _inst_26 _inst_28) (instContinuousConstSMulProdInstTopologicalSpaceProdSmul.{u2, u4, u5} S N₂ N₃ _inst_15 (MulAction.toSMul.{u2, u4} S N₂ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (DistribMulAction.toMulAction.{u2, u4} S N₂ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16) (Module.toDistribMulAction.{u2, u4} S N₂ _inst_4 _inst_16 _inst_24))) _inst_25 _inst_18 (MulAction.toSMul.{u2, u5} S N₃ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (DistribMulAction.toMulAction.{u2, u5} S N₃ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19) (Module.toDistribMulAction.{u2, u5} S N₃ _inst_4 _inst_19 _inst_27))) _inst_29) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (instContinuousAddSumInstTopologicalSpaceSumInstAddSum.{u4, u5} N₂ N₃ _inst_15 (AddSemigroup.toAdd.{u4} N₂ (AddMonoid.toAddSemigroup.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) _inst_33 _inst_18 (AddSemigroup.toAdd.{u5} N₃ (AddMonoid.toAddSemigroup.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) _inst_34))
+ forall {R : Type.{u1}} (S : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_4 : Semiring.{u2} S] {M : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : AddCommMonoid.{u3} M] [_inst_8 : Module.{u1, u3} R M _inst_1 _inst_7] {N₂ : Type.{u4}} [_inst_15 : TopologicalSpace.{u4} N₂] [_inst_16 : AddCommMonoid.{u4} N₂] [_inst_17 : Module.{u1, u4} R N₂ _inst_1 _inst_16] {N₃ : Type.{u5}} [_inst_18 : TopologicalSpace.{u5} N₃] [_inst_19 : AddCommMonoid.{u5} N₃] [_inst_20 : Module.{u1, u5} R N₃ _inst_1 _inst_19] [_inst_24 : Module.{u2, u4} S N₂ _inst_4 _inst_16] [_inst_25 : ContinuousConstSMul.{u2, u4} S N₂ _inst_15 (SMulZeroClass.toSMul.{u2, u4} S N₂ (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (SMulWithZero.toSMulZeroClass.{u2, u4} S N₂ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (MulActionWithZero.toSMulWithZero.{u2, u4} S N₂ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (Module.toMulActionWithZero.{u2, u4} S N₂ _inst_4 _inst_16 _inst_24))))] [_inst_26 : SMulCommClass.{u1, u2, u4} R S N₂ (SMulZeroClass.toSMul.{u1, u4} R N₂ (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (SMulWithZero.toSMulZeroClass.{u1, u4} R N₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (MulActionWithZero.toSMulWithZero.{u1, u4} R N₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (Module.toMulActionWithZero.{u1, u4} R N₂ _inst_1 _inst_16 _inst_17)))) (SMulZeroClass.toSMul.{u2, u4} S N₂ (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (SMulWithZero.toSMulZeroClass.{u2, u4} S N₂ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (MulActionWithZero.toSMulWithZero.{u2, u4} S N₂ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (Module.toMulActionWithZero.{u2, u4} S N₂ _inst_4 _inst_16 _inst_24))))] [_inst_27 : Module.{u2, u5} S N₃ _inst_4 _inst_19] [_inst_28 : SMulCommClass.{u1, u2, u5} R S N₃ (SMulZeroClass.toSMul.{u1, u5} R N₃ (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (SMulWithZero.toSMulZeroClass.{u1, u5} R N₃ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (MulActionWithZero.toSMulWithZero.{u1, u5} R N₃ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (Module.toMulActionWithZero.{u1, u5} R N₃ _inst_1 _inst_19 _inst_20)))) (SMulZeroClass.toSMul.{u2, u5} S N₃ (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (SMulWithZero.toSMulZeroClass.{u2, u5} S N₃ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (MulActionWithZero.toSMulWithZero.{u2, u5} S N₃ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (Module.toMulActionWithZero.{u2, u5} S N₃ _inst_4 _inst_19 _inst_27))))] [_inst_29 : ContinuousConstSMul.{u2, u5} S N₃ _inst_18 (SMulZeroClass.toSMul.{u2, u5} S N₃ (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (SMulWithZero.toSMulZeroClass.{u2, u5} S N₃ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (MulActionWithZero.toSMulWithZero.{u2, u5} S N₃ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (Module.toMulActionWithZero.{u2, u5} S N₃ _inst_4 _inst_19 _inst_27))))] [_inst_33 : ContinuousAdd.{u4} N₂ _inst_15 (AddZeroClass.toAdd.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)))] [_inst_34 : ContinuousAdd.{u5} N₃ _inst_18 (AddZeroClass.toAdd.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)))], LinearEquiv.{u2, u2, max (max u5 u3) u4 u3, max (max u5 u4) u3} S S _inst_4 _inst_4 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_4)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_4)) (RingHomInvPair.ids.{u2} S _inst_4) (RingHomInvPair.ids.{u2} S _inst_4) (Prod.{max u4 u3, max u5 u3} (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20)) (ContinuousLinearMap.{u1, u1, u3, max u5 u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 (Prod.{u4, u5} N₂ N₃) (instTopologicalSpaceProd.{u4, u5} N₂ N₃ _inst_15 _inst_18) (Prod.instAddCommMonoidSum.{u4, u5} N₂ N₃ _inst_16 _inst_19) _inst_8 (Prod.module.{u1, u4, u5} R N₂ N₃ _inst_1 _inst_16 _inst_19 _inst_17 _inst_20)) (Prod.instAddCommMonoidSum.{max u3 u4, max u3 u5} (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17 _inst_33) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20 _inst_34)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, max u4 u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 (Prod.{u4, u5} N₂ N₃) (instTopologicalSpaceProd.{u4, u5} N₂ N₃ _inst_15 _inst_18) (Prod.instAddCommMonoidSum.{u4, u5} N₂ N₃ _inst_16 _inst_19) _inst_8 (Prod.module.{u1, u4, u5} R N₂ N₃ _inst_1 _inst_16 _inst_19 _inst_17 _inst_20) (Prod.continuousAdd.{u4, u5} N₂ N₃ _inst_15 (AddSemigroup.toAdd.{u4} N₂ (AddMonoid.toAddSemigroup.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) _inst_33 _inst_18 (AddSemigroup.toAdd.{u5} N₃ (AddMonoid.toAddSemigroup.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) _inst_34)) (Prod.module.{u2, max u3 u4, max u3 u5} S (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) _inst_4 (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17 _inst_33) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20 _inst_34) (ContinuousLinearMap.module.{u1, u1, u2, u3, u4} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 N₂ _inst_15 _inst_16 _inst_17 _inst_24 _inst_26 _inst_25 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_33) (ContinuousLinearMap.module.{u1, u1, u2, u3, u5} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 N₃ _inst_18 _inst_19 _inst_20 _inst_27 _inst_28 _inst_29 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_34)) (ContinuousLinearMap.module.{u1, u1, u2, u3, max u4 u5} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 (Prod.{u4, u5} N₂ N₃) (instTopologicalSpaceProd.{u4, u5} N₂ N₃ _inst_15 _inst_18) (Prod.instAddCommMonoidSum.{u4, u5} N₂ N₃ _inst_16 _inst_19) (Prod.module.{u1, u4, u5} R N₂ N₃ _inst_1 _inst_16 _inst_19 _inst_17 _inst_20) (Prod.module.{u2, u4, u5} S N₂ N₃ _inst_4 _inst_16 _inst_19 _inst_24 _inst_27) (Prod.smulCommClass.{u1, u2, u4, u5} R S N₂ N₃ (MulAction.toSMul.{u1, u4} R N₂ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (DistribMulAction.toMulAction.{u1, u4} R N₂ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16) (Module.toDistribMulAction.{u1, u4} R N₂ _inst_1 _inst_16 _inst_17))) (MulAction.toSMul.{u1, u5} R N₃ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (DistribMulAction.toMulAction.{u1, u5} R N₃ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19) (Module.toDistribMulAction.{u1, u5} R N₃ _inst_1 _inst_19 _inst_20))) (MulAction.toSMul.{u2, u4} S N₂ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (DistribMulAction.toMulAction.{u2, u4} S N₂ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16) (Module.toDistribMulAction.{u2, u4} S N₂ _inst_4 _inst_16 _inst_24))) (MulAction.toSMul.{u2, u5} S N₃ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (DistribMulAction.toMulAction.{u2, u5} S N₃ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19) (Module.toDistribMulAction.{u2, u5} S N₃ _inst_4 _inst_19 _inst_27))) _inst_26 _inst_28) (Prod.continuousConstSMul.{u2, u4, u5} S N₂ N₃ _inst_15 (MulAction.toSMul.{u2, u4} S N₂ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (DistribMulAction.toMulAction.{u2, u4} S N₂ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16) (Module.toDistribMulAction.{u2, u4} S N₂ _inst_4 _inst_16 _inst_24))) _inst_25 _inst_18 (MulAction.toSMul.{u2, u5} S N₃ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (DistribMulAction.toMulAction.{u2, u5} S N₃ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19) (Module.toDistribMulAction.{u2, u5} S N₃ _inst_4 _inst_19 _inst_27))) _inst_29) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Prod.continuousAdd.{u4, u5} N₂ N₃ _inst_15 (AddSemigroup.toAdd.{u4} N₂ (AddMonoid.toAddSemigroup.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) _inst_33 _inst_18 (AddSemigroup.toAdd.{u5} N₃ (AddMonoid.toAddSemigroup.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) _inst_34))
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.prodₗ ContinuousLinearMap.prodₗₓ'. -/
/-- `continuous_linear_map.prod` as a `linear_equiv`. -/
@[simps apply]
mathlib commit https://github.com/leanprover-community/mathlib/commit/3cacc945118c8c637d89950af01da78307f59325
@@ -45,6 +45,12 @@ section
variable {R : Type _} {M : Type _} [Ring R] [TopologicalSpace R] [TopologicalSpace M]
[AddCommGroup M] [Module R M]
+/- warning: has_continuous_smul.of_nhds_zero -> ContinuousSMul.of_nhds_zero is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_6 : TopologicalRing.{u1} R _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))] [_inst_7 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)], (Filter.Tendsto.{max u1 u2, u2} (Prod.{u1, u2} R M) M (fun (p : Prod.{u1, u2} R M) => SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))) (Prod.fst.{u1, u2} R M p) (Prod.snd.{u1, u2} R M p)) (Filter.prod.{u1, u2} R M (nhds.{u1} R _inst_2 (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))))))) (nhds.{u2} M _inst_3 (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_4)))))))))) (nhds.{u2} M _inst_3 (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_4)))))))))) -> (forall (m : M), Filter.Tendsto.{u1, u2} R M (fun (a : R) => SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))) a m) (nhds.{u1} R _inst_2 (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))))))) (nhds.{u2} M _inst_3 (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_4)))))))))) -> (forall (a : R), Filter.Tendsto.{u2, u2} M M (fun (m : M) => SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))) a m) (nhds.{u2} M _inst_3 (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_4))))))))) (nhds.{u2} M _inst_3 (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_4)))))))))) -> (ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))) _inst_2 _inst_3)
+but is expected to have type
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : TopologicalSpace.{u2} R] [_inst_3 : TopologicalSpace.{u1} M] [_inst_4 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4)] [_inst_6 : TopologicalRing.{u2} R _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))] [_inst_7 : TopologicalAddGroup.{u1} M _inst_3 (AddCommGroup.toAddGroup.{u1} M _inst_4)], (Filter.Tendsto.{max u2 u1, u1} (Prod.{u2, u1} R M) M (fun (p : Prod.{u2, u1} R M) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5))))) (Prod.fst.{u2, u1} R M p) (Prod.snd.{u2, u1} R M p)) (Filter.prod.{u2, u1} R M (nhds.{u2} R _inst_2 (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) (nhds.{u1} M _inst_3 (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))))))) (nhds.{u1} M _inst_3 (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))))))) -> (forall (m : M), Filter.Tendsto.{u2, u1} R M (fun (a : R) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5))))) a m) (nhds.{u2} R _inst_2 (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)))))) (nhds.{u1} M _inst_3 (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))))))) -> (forall (a : R), Filter.Tendsto.{u1, u1} M M (fun (m : M) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5))))) a m) (nhds.{u1} M _inst_3 (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4)))))))) (nhds.{u1} M _inst_3 (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))))))) -> (ContinuousSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5)))) _inst_2 _inst_3)
+Case conversion may be inaccurate. Consider using '#align has_continuous_smul.of_nhds_zero ContinuousSMul.of_nhds_zeroₓ'. -/
theorem ContinuousSMul.of_nhds_zero [TopologicalRing R] [TopologicalAddGroup M]
(hmul : Tendsto (fun p : R × M => p.1 • p.2) (𝓝 0 ×ᶠ 𝓝 0) (𝓝 0))
(hmulleft : ∀ m : M, Tendsto (fun a : R => a • m) (𝓝 0) (𝓝 0))
@@ -105,6 +111,12 @@ section
variable {R : Type _} {M : Type _} [Ring R] [TopologicalSpace R] [TopologicalSpace M]
[AddCommGroup M] [ContinuousAdd M] [Module R M] [ContinuousSMul R M]
+/- warning: submodule.eq_top_of_nonempty_interior' -> Submodule.eq_top_of_nonempty_interior' is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_4)))))] [_inst_6 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_7 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6)))) _inst_2 _inst_3] [_inst_8 : Filter.NeBot.{u1} R (nhdsWithin.{u1} R _inst_2 (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))))) (setOf.{u1} R (fun (x : R) => IsUnit.{u1} R (Ring.toMonoid.{u1} R _inst_1) x)))] (s : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6), (Set.Nonempty.{u2} M (interior.{u2} M _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6)))) s))) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6) s (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6)))
+but is expected to have type
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : TopologicalSpace.{u2} R] [_inst_3 : TopologicalSpace.{u1} M] [_inst_4 : AddCommGroup.{u1} M] [_inst_5 : ContinuousAdd.{u1} M _inst_3 (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_4)))))] [_inst_6 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4)] [_inst_7 : ContinuousSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_6)))) _inst_2 _inst_3] [_inst_8 : Filter.NeBot.{u2} R (nhdsWithin.{u2} R _inst_2 (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (setOf.{u2} R (fun (x : R) => IsUnit.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) x)))] (s : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_6), (Set.Nonempty.{u1} M (interior.{u1} M _inst_3 (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_6) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_6) s))) -> (Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_6) s (Top.top.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_6) (Submodule.instTopSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_6)))
+Case conversion may be inaccurate. Consider using '#align submodule.eq_top_of_nonempty_interior' Submodule.eq_top_of_nonempty_interior'ₓ'. -/
/-- If `M` is a topological module over `R` and `0` is a limit of invertible elements of `R`, then
`⊤` is the only submodule of `M` with a nonempty interior.
This is the case, e.g., if `R` is a nontrivially normed field. -/
@@ -125,6 +137,12 @@ theorem Submodule.eq_top_of_nonempty_interior' [NeBot (𝓝[{ x : R | IsUnit x }
variable (R M)
+/- warning: module.punctured_nhds_ne_bot -> Module.punctured_nhds_neBot is a dubious translation:
+lean 3 declaration is
+ forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Ring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_4)))))] [_inst_6 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_7 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6)))) _inst_2 _inst_3] [_inst_8 : Nontrivial.{u2} M] [_inst_9 : Filter.NeBot.{u1} R (nhdsWithin.{u1} R _inst_2 (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))))) (HasCompl.compl.{u1} (Set.{u1} R) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} R) (Set.booleanAlgebra.{u1} R)) (Singleton.singleton.{u1, u1} R (Set.{u1} R) (Set.hasSingleton.{u1} R) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))))))))] [_inst_10 : NoZeroSMulDivisors.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_4))))) (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6))))] (x : M), Filter.NeBot.{u2} M (nhdsWithin.{u2} M _inst_3 x (HasCompl.compl.{u2} (Set.{u2} M) (BooleanAlgebra.toHasCompl.{u2} (Set.{u2} M) (Set.booleanAlgebra.{u2} M)) (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x)))
+but is expected to have type
+ forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Ring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_4)))))] [_inst_6 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_7 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_4))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6)))) _inst_2 _inst_3] [_inst_8 : Nontrivial.{u2} M] [_inst_9 : Filter.NeBot.{u1} R (nhdsWithin.{u1} R _inst_2 (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (HasCompl.compl.{u1} (Set.{u1} R) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} R) (Set.instBooleanAlgebraSet.{u1} R)) (Singleton.singleton.{u1, u1} R (Set.{u1} R) (Set.instSingletonSet.{u1} R) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))] [_inst_10 : NoZeroSMulDivisors.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} R M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_4))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6))))] (x : M), Filter.NeBot.{u2} M (nhdsWithin.{u2} M _inst_3 x (HasCompl.compl.{u2} (Set.{u2} M) (BooleanAlgebra.toHasCompl.{u2} (Set.{u2} M) (Set.instBooleanAlgebraSet.{u2} M)) (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)))
+Case conversion may be inaccurate. Consider using '#align module.punctured_nhds_ne_bot Module.punctured_nhds_neBotₓ'. -/
/-- Let `R` be a topological ring such that zero is not an isolated point (e.g., a nontrivially
normed field, see `normed_field.punctured_nhds_ne_bot`). Let `M` be a nontrivial module over `R`
such that `c • x = 0` implies `c = 0 ∨ x = 0`. Then `M` has no isolated points. We formulate this
@@ -154,6 +172,12 @@ variable {ι R M₁ M₂ : Type _} [Semiring R] [AddCommMonoid M₁] [AddCommMon
[Module R M₂] [u : TopologicalSpace R] {t : TopologicalSpace M₂} [ContinuousSMul R M₂]
(f : M₁ →ₗ[R] M₂)
+/- warning: has_continuous_smul_induced -> continuousSMul_induced is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : AddCommMonoid.{u3} M₂] [_inst_4 : Module.{u1, u2} R M₁ _inst_1 _inst_2] [_inst_5 : Module.{u1, u3} R M₂ _inst_1 _inst_3] [u : TopologicalSpace.{u1} R] {t : TopologicalSpace.{u3} M₂} [_inst_6 : ContinuousSMul.{u1, u3} R M₂ (SMulZeroClass.toHasSmul.{u1, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M₂ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_3))) (Module.toMulActionWithZero.{u1, u3} R M₂ _inst_1 _inst_3 _inst_5)))) u t] (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5), ContinuousSMul.{u1, u2} R M₁ (SMulZeroClass.toHasSmul.{u1, u2} R M₁ (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M₁ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M₁ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2))) (Module.toMulActionWithZero.{u1, u2} R M₁ _inst_1 _inst_2 _inst_4)))) u (TopologicalSpace.induced.{u2, u3} M₁ M₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M₁ M₂ _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f) t)
+but is expected to have type
+ forall {R : Type.{u3}} {M₁ : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : AddCommMonoid.{u1} M₂] [_inst_4 : Module.{u3, u2} R M₁ _inst_1 _inst_2] [_inst_5 : Module.{u3, u1} R M₂ _inst_1 _inst_3] [u : TopologicalSpace.{u3} R] {t : TopologicalSpace.{u1} M₂} [_inst_6 : ContinuousSMul.{u3, u1} R M₂ (SMulZeroClass.toSMul.{u3, u1} R M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u1} R M₂ (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u1} R M₂ (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_3)) (Module.toMulActionWithZero.{u3, u1} R M₂ _inst_1 _inst_3 _inst_5)))) u t] (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5), ContinuousSMul.{u3, u2} R M₁ (SMulZeroClass.toSMul.{u3, u2} R M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M₁ (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M₁ (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (Module.toMulActionWithZero.{u3, u2} R M₁ _inst_1 _inst_2 _inst_4)))) u (TopologicalSpace.induced.{u2, u1} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M₁ M₂ _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f) t)
+Case conversion may be inaccurate. Consider using '#align has_continuous_smul_induced continuousSMul_inducedₓ'. -/
theorem continuousSMul_induced : @ContinuousSMul R M₁ _ u (t.induced f) :=
{
continuous_smul := by
@@ -216,6 +240,12 @@ theorem Submodule.closure_smul_self_eq (s : Submodule R M) :
variable [ContinuousAdd M]
+/- warning: submodule.topological_closure -> Submodule.topologicalClosure is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))], (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) -> (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5)
+but is expected to have type
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] [_inst_5 : ContinuousConstSMul.{u1, u2} R M _inst_2 (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_3 _inst_4))))] [_inst_6 : ContinuousAdd.{u2} M _inst_2 (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))], (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) -> (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)
+Case conversion may be inaccurate. Consider using '#align submodule.topological_closure Submodule.topologicalClosureₓ'. -/
/-- The (topological-space) closure of a submodule of a topological `R`-module `M` is itself
a submodule. -/
def Submodule.topologicalClosure (s : Submodule R M) : Submodule R M :=
@@ -225,36 +255,78 @@ def Submodule.topologicalClosure (s : Submodule R M) : Submodule R M :=
smul_mem' := fun c x hx => s.closure_smul_self_subset ⟨⟨c, x⟩, ⟨Set.mem_univ _, hx⟩, rfl⟩ }
#align submodule.topological_closure Submodule.topologicalClosure
+/- warning: submodule.topological_closure_coe -> Submodule.topologicalClosure_coe is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))] (s : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5), Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 s)) (closure.{u2} M _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) s))
+but is expected to have type
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] [_inst_5 : ContinuousConstSMul.{u1, u2} R M _inst_2 (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_3 _inst_4))))] [_inst_6 : ContinuousAdd.{u2} M _inst_2 (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))] (_inst_7 : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4), Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7)) (closure.{u2} M _inst_2 (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) _inst_7))
+Case conversion may be inaccurate. Consider using '#align submodule.topological_closure_coe Submodule.topologicalClosure_coeₓ'. -/
@[simp]
theorem Submodule.topologicalClosure_coe (s : Submodule R M) :
(s.topologicalClosure : Set M) = closure (s : Set M) :=
rfl
#align submodule.topological_closure_coe Submodule.topologicalClosure_coe
+/- warning: submodule.le_topological_closure -> Submodule.le_topologicalClosure is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))] (s : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5), LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) s (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 s)
+but is expected to have type
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] [_inst_5 : ContinuousConstSMul.{u1, u2} R M _inst_2 (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_3 _inst_4))))] [_inst_6 : ContinuousAdd.{u2} M _inst_2 (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))] (_inst_7 : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4), LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))))) _inst_7 (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7)
+Case conversion may be inaccurate. Consider using '#align submodule.le_topological_closure Submodule.le_topologicalClosureₓ'. -/
theorem Submodule.le_topologicalClosure (s : Submodule R M) : s ≤ s.topologicalClosure :=
subset_closure
#align submodule.le_topological_closure Submodule.le_topologicalClosure
+/- warning: submodule.is_closed_topological_closure -> Submodule.isClosed_topologicalClosure is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))] (s : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5), IsClosed.{u2} M _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 s))
+but is expected to have type
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] [_inst_5 : ContinuousConstSMul.{u1, u2} R M _inst_2 (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_3 _inst_4))))] [_inst_6 : ContinuousAdd.{u2} M _inst_2 (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))] (_inst_7 : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4), IsClosed.{u2} M _inst_2 (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7))
+Case conversion may be inaccurate. Consider using '#align submodule.is_closed_topological_closure Submodule.isClosed_topologicalClosureₓ'. -/
theorem Submodule.isClosed_topologicalClosure (s : Submodule R M) :
IsClosed (s.topologicalClosure : Set M) := by convert isClosed_closure
#align submodule.is_closed_topological_closure Submodule.isClosed_topologicalClosure
+/- warning: submodule.topological_closure_minimal -> Submodule.topologicalClosure_minimal is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))] (s : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) {t : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5}, (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) s t) -> (IsClosed.{u2} M _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) t)) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 s) t)
+but is expected to have type
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] [_inst_5 : ContinuousConstSMul.{u1, u2} R M _inst_2 (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_3 _inst_4))))] [_inst_6 : ContinuousAdd.{u2} M _inst_2 (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))] (_inst_7 : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) {s : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))))) _inst_7 s) -> (IsClosed.{u2} M _inst_2 (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) s)) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))))) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) s)
+Case conversion may be inaccurate. Consider using '#align submodule.topological_closure_minimal Submodule.topologicalClosure_minimalₓ'. -/
theorem Submodule.topologicalClosure_minimal (s : Submodule R M) {t : Submodule R M} (h : s ≤ t)
(ht : IsClosed (t : Set M)) : s.topologicalClosure ≤ t :=
closure_minimal h ht
#align submodule.topological_closure_minimal Submodule.topologicalClosure_minimal
+/- warning: submodule.topological_closure_mono -> Submodule.topologicalClosure_mono is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))] {s : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5} {t : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5}, (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) s t) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 s) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 t))
+but is expected to have type
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] [_inst_5 : ContinuousConstSMul.{u1, u2} R M _inst_2 (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_3 _inst_4))))] [_inst_6 : ContinuousAdd.{u2} M _inst_2 (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))] {_inst_7 : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {s : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))))) _inst_7 s) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))))) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))
+Case conversion may be inaccurate. Consider using '#align submodule.topological_closure_mono Submodule.topologicalClosure_monoₓ'. -/
theorem Submodule.topologicalClosure_mono {s : Submodule R M} {t : Submodule R M} (h : s ≤ t) :
s.topologicalClosure ≤ t.topologicalClosure :=
s.topologicalClosure_minimal (h.trans t.le_topologicalClosure) t.isClosed_topologicalClosure
#align submodule.topological_closure_mono Submodule.topologicalClosure_mono
+/- warning: is_closed.submodule_topological_closure_eq -> IsClosed.submodule_topologicalClosure_eq is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))] {s : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5}, (IsClosed.{u2} M _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) s)) -> (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 s) s)
+but is expected to have type
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] [_inst_5 : ContinuousConstSMul.{u1, u2} R M _inst_2 (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_3 _inst_4))))] [_inst_6 : ContinuousAdd.{u2} M _inst_2 (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))] {_inst_7 : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, (IsClosed.{u2} M _inst_2 (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) _inst_7)) -> (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) _inst_7)
+Case conversion may be inaccurate. Consider using '#align is_closed.submodule_topological_closure_eq IsClosed.submodule_topologicalClosure_eqₓ'. -/
/-- The topological closure of a closed submodule `s` is equal to `s`. -/
theorem IsClosed.submodule_topologicalClosure_eq {s : Submodule R M} (hs : IsClosed (s : Set M)) :
s.topologicalClosure = s :=
le_antisymm (s.topologicalClosure_minimal rfl.le hs) s.le_topologicalClosure
#align is_closed.submodule_topological_closure_eq IsClosed.submodule_topologicalClosure_eq
+/- warning: submodule.dense_iff_topological_closure_eq_top -> Submodule.dense_iff_topologicalClosure_eq_top is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))] {s : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5}, Iff (Dense.{u2} M _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) s)) (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 s) (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Submodule.hasTop.{u1, u2} R M _inst_1 _inst_4 _inst_5)))
+but is expected to have type
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] [_inst_5 : ContinuousConstSMul.{u1, u2} R M _inst_2 (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_3 _inst_4))))] [_inst_6 : ContinuousAdd.{u2} M _inst_2 (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))] {_inst_7 : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, Iff (Dense.{u2} M _inst_2 (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) _inst_7)) (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.topologicalClosure.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instTopSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)))
+Case conversion may be inaccurate. Consider using '#align submodule.dense_iff_topological_closure_eq_top Submodule.dense_iff_topologicalClosure_eq_topₓ'. -/
/-- A subspace is dense iff its topological closure is the entire space. -/
theorem Submodule.dense_iff_topologicalClosure_eq_top {s : Submodule R M} :
Dense (s : Set M) ↔ s.topologicalClosure = ⊤ :=
@@ -268,6 +340,12 @@ instance {M' : Type _} [AddCommMonoid M'] [Module R M'] [UniformSpace M'] [Conti
CompleteSpace U.topologicalClosure :=
isClosed_closure.completeSpace_coe
+/- warning: submodule.is_closed_or_dense_of_is_coatom -> Submodule.isClosed_or_dense_of_isCoatom is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u1} R] [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u1, u2} R M _inst_1 _inst_4] [_inst_6 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) _inst_2 _inst_3] [_inst_7 : ContinuousAdd.{u2} M _inst_3 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)))] (s : Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5), (IsCoatom.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5))) (Submodule.orderTop.{u1, u2} R M _inst_1 _inst_4 _inst_5) s) -> (Or (IsClosed.{u2} M _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) s)) (Dense.{u2} M _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_4 _inst_5) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_4 _inst_5)))) s)))
+but is expected to have type
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] [_inst_5 : ContinuousConstSMul.{u1, u2} R M _inst_2 (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_3 _inst_4))))] [_inst_6 : ContinuousAdd.{u2} M _inst_2 (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))] (_inst_7 : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4), (IsCoatom.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (Submodule.instOrderTopSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) _inst_7) -> (Or (IsClosed.{u2} M _inst_2 (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) _inst_7)) (Dense.{u2} M _inst_2 (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) _inst_7)))
+Case conversion may be inaccurate. Consider using '#align submodule.is_closed_or_dense_of_is_coatom Submodule.isClosed_or_dense_of_isCoatomₓ'. -/
/-- A maximal proper subspace of a topological module (i.e a `submodule` satisfying `is_coatom`)
is either closed or dense. -/
theorem Submodule.isClosed_or_dense_of_isCoatom (s : Submodule R M) (hs : IsCoatom s) :
@@ -280,6 +358,12 @@ end closure
section Pi
+/- warning: linear_map.continuous_on_pi -> LinearMap.continuous_on_pi is a dubious translation:
+lean 3 declaration is
+ forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Finite.{succ u1} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : TopologicalSpace.{u2} R] [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u2, u3} R M _inst_2 _inst_4] [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : ContinuousAdd.{u3} M _inst_6 (AddZeroClass.toHasAdd.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4)))] [_inst_8 : ContinuousSMul.{u2, u3} R M (SMulZeroClass.toHasSmul.{u2, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} R M (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} R M _inst_2 _inst_4 _inst_5)))) _inst_3 _inst_6] (f : LinearMap.{u2, u2, max u1 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.Function.module.{u1, u2, u2} ι R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_5), Continuous.{max u1 u2, u3} (ι -> R) M (Pi.topologicalSpace.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (a : ι) => _inst_3)) _inst_6 (coeFn.{max (succ (max u1 u2)) (succ u3), max (succ (max u1 u2)) (succ u3)} (LinearMap.{u2, u2, max u1 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.Function.module.{u1, u2, u2} ι R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_5) (fun (_x : LinearMap.{u2, u2, max u1 u2, u3} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.Function.module.{u1, u2, u2} ι R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_5) => (ι -> R) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, u3} R R (ι -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.Function.module.{u1, u2, u2} ι R R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (Semiring.toModule.{u2} R _inst_2)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) f)
+but is expected to have type
+ forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Finite.{succ u3} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : TopologicalSpace.{u2} R] [_inst_4 : AddCommMonoid.{u1} M] [_inst_5 : Module.{u2, u1} R M _inst_2 _inst_4] [_inst_6 : TopologicalSpace.{u1} M] [_inst_7 : ContinuousAdd.{u1} M _inst_6 (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)))] [_inst_8 : ContinuousSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_2)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R _inst_2) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_4)) (Module.toMulActionWithZero.{u2, u1} R M _inst_2 _inst_4 _inst_5)))) _inst_3 _inst_6] (f : LinearMap.{u2, u2, max u3 u2, u1} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5155 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5), Continuous.{max u3 u2, u1} (ι -> R) M (Pi.topologicalSpace.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (a : ι) => _inst_3)) _inst_6 (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), succ u1} (LinearMap.{u2, u2, max u3 u2, u1} R R _inst_2 _inst_2 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5155 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5155 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5) (ι -> R) (fun (_x : ι -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (ι -> R) M _inst_2 _inst_2 (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2)))) _inst_4 (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.Topology.Algebra.Module.Basic._hyg.5155 : ι) => R) R _inst_2 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_2)) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_2))) f)
+Case conversion may be inaccurate. Consider using '#align linear_map.continuous_on_pi LinearMap.continuous_on_piₓ'. -/
theorem LinearMap.continuous_on_pi {ι : Type _} {R : Type _} {M : Type _} [Finite ι] [Semiring R]
[TopologicalSpace R] [AddCommMonoid M] [Module R M] [TopologicalSpace M] [ContinuousAdd M]
[ContinuousSMul R M] (f : (ι → R) →ₗ[R] M) : Continuous f :=
@@ -299,6 +383,7 @@ theorem LinearMap.continuous_on_pi {ι : Type _} {R : Type _} {M : Type _} [Fini
end Pi
+#print ContinuousLinearMap /-
/-- Continuous linear maps between modules. We only put the type classes that are necessary for the
definition, although in applications `M` and `M₂` will be topological modules over the topological
ring `R`. -/
@@ -307,6 +392,7 @@ structure ContinuousLinearMap {R : Type _} {S : Type _} [Semiring R] [Semiring S
[AddCommMonoid M₂] [Module R M] [Module S M₂] extends M →ₛₗ[σ] M₂ where
cont : Continuous to_fun := by continuity
#align continuous_linear_map ContinuousLinearMap
+-/
-- mathport name: «expr →SL[ ] »
notation:25 M " →SL[" σ "] " M₂ => ContinuousLinearMap σ M M₂
@@ -317,6 +403,7 @@ notation:25 M " →L[" R "] " M₂ => ContinuousLinearMap (RingHom.id R) M M₂
-- mathport name: «expr →L⋆[ ] »
notation:25 M " →L⋆[" R "] " M₂ => ContinuousLinearMap (starRingEnd R) M M₂
+#print ContinuousSemilinearMapClass /-
/-- `continuous_semilinear_map_class F σ M M₂` asserts `F` is a type of bundled continuous
`σ`-semilinear maps `M → M₂`. See also `continuous_linear_map_class F R M M₂` for the case where
`σ` is the identity map on `R`. A map `f` between an `R`-module and an `S`-module over a ring
@@ -327,10 +414,12 @@ class ContinuousSemilinearMapClass (F : Type _) {R S : outParam (Type _)} [Semir
(M₂ : outParam (Type _)) [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M]
[Module S M₂] extends SemilinearMapClass F σ M M₂, ContinuousMapClass F M M₂
#align continuous_semilinear_map_class ContinuousSemilinearMapClass
+-/
-- `σ`, `R` and `S` become metavariables, but they are all outparams so it's OK
attribute [nolint dangerous_instance] ContinuousSemilinearMapClass.toContinuousMapClass
+#print ContinuousLinearMapClass /-
/-- `continuous_linear_map_class F R M M₂` asserts `F` is a type of bundled continuous
`R`-linear maps `M → M₂`. This is an abbreviation for
`continuous_semilinear_map_class F (ring_hom.id R) M M₂`. -/
@@ -339,7 +428,9 @@ abbrev ContinuousLinearMapClass (F : Type _) (R : outParam (Type _)) [Semiring R
[TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M] [Module R M₂] :=
ContinuousSemilinearMapClass F (RingHom.id R) M M₂
#align continuous_linear_map_class ContinuousLinearMapClass
+-/
+#print ContinuousLinearEquiv /-
/-- Continuous linear equivalences between modules. We only put the type classes that are necessary
for the definition, although in applications `M` and `M₂` will be topological modules over the
topological semiring `R`. -/
@@ -351,6 +442,7 @@ structure ContinuousLinearEquiv {R : Type _} {S : Type _} [Semiring R] [Semiring
continuous_toFun : Continuous to_fun := by continuity
continuous_invFun : Continuous inv_fun := by continuity
#align continuous_linear_equiv ContinuousLinearEquiv
+-/
-- mathport name: «expr ≃SL[ ] »
notation:50 M " ≃SL[" σ "] " M₂ => ContinuousLinearEquiv σ M M₂
@@ -361,6 +453,7 @@ notation:50 M " ≃L[" R "] " M₂ => ContinuousLinearEquiv (RingHom.id R) M M
-- mathport name: «expr ≃L⋆[ ] »
notation:50 M " ≃L⋆[" R "] " M₂ => ContinuousLinearEquiv (starRingEnd R) M M₂
+#print ContinuousSemilinearEquivClass /-
/-- `continuous_semilinear_equiv_class F σ M M₂` asserts `F` is a type of bundled continuous
`σ`-semilinear equivs `M → M₂`. See also `continuous_linear_equiv_class F R M M₂` for the case
where `σ` is the identity map on `R`. A map `f` between an `R`-module and an `S`-module over a ring
@@ -374,7 +467,9 @@ class ContinuousSemilinearEquivClass (F : Type _) {R : outParam (Type _)} {S : o
map_continuous : ∀ f : F, Continuous f := by continuity
inv_continuous : ∀ f : F, Continuous (inv f) := by continuity
#align continuous_semilinear_equiv_class ContinuousSemilinearEquivClass
+-/
+#print ContinuousLinearEquivClass /-
/-- `continuous_linear_equiv_class F σ M M₂` asserts `F` is a type of bundled continuous
`R`-linear equivs `M → M₂`. This is an abbreviation for
`continuous_semilinear_equiv_class F (ring_hom.id) M M₂`. -/
@@ -383,6 +478,7 @@ abbrev ContinuousLinearEquivClass (F : Type _) (R : outParam (Type _)) [Semiring
[TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M] [Module R M₂] :=
ContinuousSemilinearEquivClass F (RingHom.id R) M M₂
#align continuous_linear_equiv_class ContinuousLinearEquivClass
+-/
namespace ContinuousSemilinearEquivClass
@@ -420,12 +516,18 @@ theorem isClosed_setOf_map_smul : IsClosed { f : M₁ → M₂ | ∀ c x, f (c
exact
isClosed_interᵢ fun c =>
isClosed_interᵢ fun x => isClosed_eq (continuous_apply _) ((continuous_apply _).const_smul _)
-#align is_closed_set_of_map_smul isClosed_setOf_map_smul
+#align is_closed_set_of_map_smul isClosed_setOf_map_smulₓ
end
variable [ContinuousAdd M₂] {σ : R →+* S} {l : Filter α}
+/- warning: linear_map_of_mem_closure_range_coe -> linearMapOfMemClosureRangeCoe is a dubious translation:
+lean 3 declaration is
+ forall {M₁ : Type.{u1}} {M₂ : Type.{u2}} {R : Type.{u3}} {S : Type.{u4}} [_inst_1 : TopologicalSpace.{u2} M₂] [_inst_2 : T2Space.{u2} M₂ _inst_1] [_inst_3 : Semiring.{u3} R] [_inst_4 : Semiring.{u4} S] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_6 : AddCommMonoid.{u2} M₂] [_inst_7 : Module.{u3, u1} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u4, u2} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u4, u2} S M₂ _inst_1 (SMulZeroClass.toHasSmul.{u4, u2} S M₂ (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M₂ (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_4)))) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M₂ (Semiring.toMonoidWithZero.{u4} S _inst_4) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (Module.toMulActionWithZero.{u4, u2} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u2} M₂ _inst_1 (AddZeroClass.toHasAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)))] {σ : RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R _inst_3) (Semiring.toNonAssocSemiring.{u4} S _inst_4)} (f : M₁ -> M₂), (Membership.Mem.{max u1 u2, max u1 u2} (M₁ -> M₂) (Set.{max u1 u2} (M₁ -> M₂)) (Set.hasMem.{max u1 u2} (M₁ -> M₂)) f (closure.{max u1 u2} (M₁ -> M₂) (Pi.topologicalSpace.{u1, u2} M₁ (fun (ᾰ : M₁) => M₂) (fun (a : M₁) => _inst_1)) (Set.range.{max u1 u2, max (succ u1) (succ u2)} (M₁ -> M₂) (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (fun (ᾰ : LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u3, u4, u1, u2} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ))))) -> (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)
+but is expected to have type
+ forall {M₁ : Type.{u1}} {M₂ : Type.{u2}} {R : Type.{u3}} {S : Type.{u4}} [_inst_1 : TopologicalSpace.{u2} M₂] [_inst_2 : T2Space.{u2} M₂ _inst_1] [_inst_3 : Semiring.{u3} R] [_inst_4 : Semiring.{u4} S] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_6 : AddCommMonoid.{u2} M₂] [_inst_7 : Module.{u3, u1} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u4, u2} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u4, u2} S M₂ _inst_1 (SMulZeroClass.toSMul.{u4, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (SMulWithZero.toSMulZeroClass.{u4, u2} S M₂ (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_4)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (MulActionWithZero.toSMulWithZero.{u4, u2} S M₂ (Semiring.toMonoidWithZero.{u4} S _inst_4) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (Module.toMulActionWithZero.{u4, u2} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u2} M₂ _inst_1 (AddZeroClass.toAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)))] {σ : RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R _inst_3) (Semiring.toNonAssocSemiring.{u4} S _inst_4)} (f : M₁ -> M₂), (Membership.mem.{max u1 u2, max u1 u2} (M₁ -> M₂) (Set.{max u1 u2} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) ᾰ)) (Set.instMembershipSet.{max u1 u2} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) ᾰ)) f (closure.{max u1 u2} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) ᾰ) (Pi.topologicalSpace.{u1, u2} M₁ (fun (ᾰ : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) ᾰ) (fun (a : M₁) => _inst_1)) (Set.range.{max u1 u2, max (succ u1) (succ u2)} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) ᾰ) (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) M₁ (fun (ᾰ : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) ᾰ) (LinearMap.instFunLikeLinearMap.{u3, u4, u1, u2} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ))))) -> (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)
+Case conversion may be inaccurate. Consider using '#align linear_map_of_mem_closure_range_coe linearMapOfMemClosureRangeCoeₓ'. -/
/-- Constructs a bundled linear map from a function and a proof that this function belongs to the
closure of the set of linear maps. -/
@[simps (config := { fullyApplied := false })]
@@ -438,6 +540,12 @@ def linearMapOfMemClosureRangeCoe (f : M₁ → M₂)
(Set.range_subset_iff.2 LinearMap.map_smulₛₗ) hf }
#align linear_map_of_mem_closure_range_coe linearMapOfMemClosureRangeCoe
+/- warning: linear_map_of_tendsto -> linearMapOfTendsto is a dubious translation:
+lean 3 declaration is
+ forall {M₁ : Type.{u1}} {M₂ : Type.{u2}} {α : Type.{u3}} {R : Type.{u4}} {S : Type.{u5}} [_inst_1 : TopologicalSpace.{u2} M₂] [_inst_2 : T2Space.{u2} M₂ _inst_1] [_inst_3 : Semiring.{u4} R] [_inst_4 : Semiring.{u5} S] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_6 : AddCommMonoid.{u2} M₂] [_inst_7 : Module.{u4, u1} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u5, u2} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u5, u2} S M₂ _inst_1 (SMulZeroClass.toHasSmul.{u5, u2} S M₂ (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (SMulWithZero.toSmulZeroClass.{u5, u2} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_4)))) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (MulActionWithZero.toSMulWithZero.{u5, u2} S M₂ (Semiring.toMonoidWithZero.{u5} S _inst_4) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (Module.toMulActionWithZero.{u5, u2} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u2} M₂ _inst_1 (AddZeroClass.toHasAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)))] {σ : RingHom.{u4, u5} R S (Semiring.toNonAssocSemiring.{u4} R _inst_3) (Semiring.toNonAssocSemiring.{u5} S _inst_4)} {l : Filter.{u3} α} (f : M₁ -> M₂) (g : α -> (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)) [_inst_11 : Filter.NeBot.{u3} α l], (Filter.Tendsto.{u3, max u1 u2} α (M₁ -> M₂) (fun (a : α) (x : M₁) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (fun (_x : LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u4, u5, u1, u2} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ) (g a) x) l (nhds.{max u1 u2} (M₁ -> M₂) (Pi.topologicalSpace.{u1, u2} M₁ (fun (x : M₁) => M₂) (fun (a : M₁) => _inst_1)) f)) -> (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)
+but is expected to have type
+ forall {M₁ : Type.{u1}} {M₂ : Type.{u2}} {α : Type.{u3}} {R : Type.{u4}} {S : Type.{u5}} [_inst_1 : TopologicalSpace.{u2} M₂] [_inst_2 : T2Space.{u2} M₂ _inst_1] [_inst_3 : Semiring.{u4} R] [_inst_4 : Semiring.{u5} S] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_6 : AddCommMonoid.{u2} M₂] [_inst_7 : Module.{u4, u1} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u5, u2} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u5, u2} S M₂ _inst_1 (SMulZeroClass.toSMul.{u5, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (SMulWithZero.toSMulZeroClass.{u5, u2} S M₂ (MonoidWithZero.toZero.{u5} S (Semiring.toMonoidWithZero.{u5} S _inst_4)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (MulActionWithZero.toSMulWithZero.{u5, u2} S M₂ (Semiring.toMonoidWithZero.{u5} S _inst_4) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)) (Module.toMulActionWithZero.{u5, u2} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u2} M₂ _inst_1 (AddZeroClass.toAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)))] {σ : RingHom.{u4, u5} R S (Semiring.toNonAssocSemiring.{u4} R _inst_3) (Semiring.toNonAssocSemiring.{u5} S _inst_4)} {l : Filter.{u3} α} (f : M₁ -> M₂) (g : α -> (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)) [_inst_11 : Filter.NeBot.{u3} α l], (Filter.Tendsto.{u3, max u1 u2} α (forall (x : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) x) (fun (a : α) (x : M₁) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u5, u1, u2} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ) (g a) x) l (nhds.{max u1 u2} (forall (x : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) x) (Pi.topologicalSpace.{u1, u2} M₁ (fun (x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) x) (fun (a : M₁) => _inst_1)) f)) -> (LinearMap.{u4, u5, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8)
+Case conversion may be inaccurate. Consider using '#align linear_map_of_tendsto linearMapOfTendstoₓ'. -/
/-- Construct a bundled linear map from a pointwise limit of linear maps -/
@[simps (config := { fullyApplied := false })]
def linearMapOfTendsto (f : M₁ → M₂) (g : α → M₁ →ₛₗ[σ] M₂) [l.ne_bot]
@@ -448,6 +556,12 @@ def linearMapOfTendsto (f : M₁ → M₂) (g : α → M₁ →ₛₗ[σ] M₂)
variable (M₁ M₂ σ)
+/- warning: linear_map.is_closed_range_coe -> LinearMap.isClosed_range_coe is a dubious translation:
+lean 3 declaration is
+ forall (M₁ : Type.{u1}) (M₂ : Type.{u2}) {R : Type.{u3}} {S : Type.{u4}} [_inst_1 : TopologicalSpace.{u2} M₂] [_inst_2 : T2Space.{u2} M₂ _inst_1] [_inst_3 : Semiring.{u3} R] [_inst_4 : Semiring.{u4} S] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_6 : AddCommMonoid.{u2} M₂] [_inst_7 : Module.{u3, u1} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u4, u2} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u4, u2} S M₂ _inst_1 (SMulZeroClass.toHasSmul.{u4, u2} S M₂ (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M₂ (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_4)))) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M₂ (Semiring.toMonoidWithZero.{u4} S _inst_4) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6))) (Module.toMulActionWithZero.{u4, u2} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u2} M₂ _inst_1 (AddZeroClass.toHasAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_6)))] (σ : RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R _inst_3) (Semiring.toNonAssocSemiring.{u4} S _inst_4)), IsClosed.{max u1 u2} (M₁ -> M₂) (Pi.topologicalSpace.{u1, u2} M₁ (fun (ᾰ : M₁) => M₂) (fun (a : M₁) => _inst_1)) (Set.range.{max u1 u2, max (succ u1) (succ u2)} (M₁ -> M₂) (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (fun (ᾰ : LinearMap.{u3, u4, u1, u2} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u3, u4, u1, u2} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ)))
+but is expected to have type
+ forall (M₁ : Type.{u4}) (M₂ : Type.{u3}) {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} M₂] [_inst_2 : T2Space.{u3} M₂ _inst_1] [_inst_3 : Semiring.{u2} R] [_inst_4 : Semiring.{u1} S] [_inst_5 : AddCommMonoid.{u4} M₁] [_inst_6 : AddCommMonoid.{u3} M₂] [_inst_7 : Module.{u2, u4} R M₁ _inst_3 _inst_5] [_inst_8 : Module.{u1, u3} S M₂ _inst_4 _inst_6] [_inst_9 : ContinuousConstSMul.{u1, u3} S M₂ _inst_1 (SMulZeroClass.toSMul.{u1, u3} S M₂ (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_6)) (SMulWithZero.toSMulZeroClass.{u1, u3} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_4)) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_6)) (MulActionWithZero.toSMulWithZero.{u1, u3} S M₂ (Semiring.toMonoidWithZero.{u1} S _inst_4) (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_6)) (Module.toMulActionWithZero.{u1, u3} S M₂ _inst_4 _inst_6 _inst_8))))] [_inst_10 : ContinuousAdd.{u3} M₂ _inst_1 (AddZeroClass.toAdd.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_6)))] (σ : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R _inst_3) (Semiring.toNonAssocSemiring.{u1} S _inst_4)), IsClosed.{max u4 u3} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) ᾰ) (Pi.topologicalSpace.{u4, u3} M₁ (fun (ᾰ : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) ᾰ) (fun (a : M₁) => _inst_1)) (Set.range.{max u4 u3, max (succ u4) (succ u3)} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) ᾰ) (LinearMap.{u2, u1, u4, u3} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearMap.{u2, u1, u4, u3} R S _inst_3 _inst_4 σ M₁ M₂ _inst_5 _inst_6 _inst_7 _inst_8) M₁ (fun (ᾰ : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) ᾰ) (LinearMap.instFunLikeLinearMap.{u2, u1, u4, u3} R S M₁ M₂ _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 σ)))
+Case conversion may be inaccurate. Consider using '#align linear_map.is_closed_range_coe LinearMap.isClosed_range_coeₓ'. -/
theorem LinearMap.isClosed_range_coe : IsClosed (Set.range (coeFn : (M₁ →ₛₗ[σ] M₂) → M₁ → M₂)) :=
isClosed_of_closure_subset fun f hf => ⟨linearMapOfMemClosureRangeCoe f hf, rfl⟩
#align linear_map.is_closed_range_coe LinearMap.isClosed_range_coe
@@ -474,12 +588,25 @@ variable {R₁ : Type _} {R₂ : Type _} {R₃ : Type _} [Semiring R₁] [Semiri
instance : Coe (M₁ →SL[σ₁₂] M₂) (M₁ →ₛₗ[σ₁₂] M₂) :=
⟨toLinearMap⟩
+/- warning: continuous_linear_map.to_linear_map_eq_coe clashes with [anonymous] -> [anonymous]
+warning: continuous_linear_map.to_linear_map_eq_coe -> [anonymous] is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.to_linear_map_eq_coe [anonymous]ₓ'. -/
-- make the coercion the preferred form
@[simp]
-theorem toLinearMap_eq_coe (f : M₁ →SL[σ₁₂] M₂) : f.toLinearMap = f :=
+theorem [anonymous] (f : M₁ →SL[σ₁₂] M₂) : f.toLinearMap = f :=
rfl
-#align continuous_linear_map.to_linear_map_eq_coe ContinuousLinearMap.toLinearMap_eq_coe
-
+#align continuous_linear_map.to_linear_map_eq_coe [anonymous]
+
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_injective ContinuousLinearMap.coe_injectiveₓ'. -/
theorem coe_injective : Function.Injective (coe : (M₁ →SL[σ₁₂] M₂) → M₁ →ₛₗ[σ₁₂] M₂) :=
by
intro f g H
@@ -502,58 +629,116 @@ instance toFun : CoeFun (M₁ →SL[σ₁₂] M₂) fun _ => M₁ → M₂ :=
⟨fun f => f.toFun⟩
#align continuous_linear_map.to_fun ContinuousLinearMap.toFun
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_mk ContinuousLinearMap.coe_mkₓ'. -/
@[simp]
theorem coe_mk (f : M₁ →ₛₗ[σ₁₂] M₂) (h) : (mk f h : M₁ →ₛₗ[σ₁₂] M₂) = f :=
rfl
#align continuous_linear_map.coe_mk ContinuousLinearMap.coe_mk
+/- warning: continuous_linear_map.coe_mk' -> ContinuousLinearMap.coe_mk' is a dubious translation:
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+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] (f : LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (h : Continuous.{u2, u1} M₁ M₂ _inst_4 _inst_8 (AddHom.toFun.{u2, u1} M₁ M₂ (AddZeroClass.toAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (AddZeroClass.toAdd.{u1} M₂ (AddMonoid.toAddZeroClass.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9))) (LinearMap.toAddHom.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16 f))), Eq.{max (succ u2) (succ u1)} (forall (a : M₁), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) (ContinuousLinearMap.mk.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f h)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) f)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_mk' ContinuousLinearMap.coe_mk'ₓ'. -/
@[simp]
theorem coe_mk' (f : M₁ →ₛₗ[σ₁₂] M₂) (h) : (mk f h : M₁ → M₂) = f :=
rfl
#align continuous_linear_map.coe_mk' ContinuousLinearMap.coe_mk'
+/- warning: continuous_linear_map.continuous -> ContinuousLinearMap.continuous is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] [_inst_14 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_9] (f : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Continuous.{u3, u4} M₁ M₂ _inst_4 _inst_8 (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) => M₁ -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) f)
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.continuous ContinuousLinearMap.continuousₓ'. -/
@[continuity]
protected theorem continuous (f : M₁ →SL[σ₁₂] M₂) : Continuous f :=
f.2
#align continuous_linear_map.continuous ContinuousLinearMap.continuous
+/- warning: continuous_linear_map.uniform_continuous -> ContinuousLinearMap.uniformContinuous is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {E₁ : Type.{u3}} {E₂ : Type.{u4}} [_inst_18 : UniformSpace.{u3} E₁] [_inst_19 : UniformSpace.{u4} E₂] [_inst_20 : AddCommGroup.{u3} E₁] [_inst_21 : AddCommGroup.{u4} E₂] [_inst_22 : Module.{u1, u3} R₁ E₁ _inst_1 (AddCommGroup.toAddCommMonoid.{u3} E₁ _inst_20)] [_inst_23 : Module.{u2, u4} R₂ E₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} E₂ _inst_21)] [_inst_24 : UniformAddGroup.{u3} E₁ _inst_18 (AddCommGroup.toAddGroup.{u3} E₁ _inst_20)] [_inst_25 : UniformAddGroup.{u4} E₂ _inst_19 (AddCommGroup.toAddGroup.{u4} E₂ _inst_21)] (f : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ E₁ (UniformSpace.toTopologicalSpace.{u3} E₁ _inst_18) (AddCommGroup.toAddCommMonoid.{u3} E₁ _inst_20) E₂ (UniformSpace.toTopologicalSpace.{u4} E₂ _inst_19) (AddCommGroup.toAddCommMonoid.{u4} E₂ _inst_21) _inst_22 _inst_23), UniformContinuous.{u3, u4} E₁ E₂ _inst_18 _inst_19 (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ E₁ (UniformSpace.toTopologicalSpace.{u3} E₁ _inst_18) (AddCommGroup.toAddCommMonoid.{u3} E₁ _inst_20) E₂ (UniformSpace.toTopologicalSpace.{u4} E₂ _inst_19) (AddCommGroup.toAddCommMonoid.{u4} E₂ _inst_21) _inst_22 _inst_23) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ E₁ (UniformSpace.toTopologicalSpace.{u3} E₁ _inst_18) (AddCommGroup.toAddCommMonoid.{u3} E₁ _inst_20) E₂ (UniformSpace.toTopologicalSpace.{u4} E₂ _inst_19) (AddCommGroup.toAddCommMonoid.{u4} E₂ _inst_21) _inst_22 _inst_23) => E₁ -> E₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ E₁ (UniformSpace.toTopologicalSpace.{u3} E₁ _inst_18) (AddCommGroup.toAddCommMonoid.{u3} E₁ _inst_20) E₂ (UniformSpace.toTopologicalSpace.{u4} E₂ _inst_19) (AddCommGroup.toAddCommMonoid.{u4} E₂ _inst_21) _inst_22 _inst_23) f)
+but is expected to have type
+ forall {R₁ : Type.{u2}} {R₂ : Type.{u1}} [_inst_1 : Semiring.{u2} R₁] [_inst_2 : Semiring.{u1} R₂] {σ₁₂ : RingHom.{u2, u1} R₁ R₂ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u1} R₂ _inst_2)} {E₁ : Type.{u4}} {E₂ : Type.{u3}} [_inst_18 : UniformSpace.{u4} E₁] [_inst_19 : UniformSpace.{u3} E₂] [_inst_20 : AddCommGroup.{u4} E₁] [_inst_21 : AddCommGroup.{u3} E₂] [_inst_22 : Module.{u2, u4} R₁ E₁ _inst_1 (AddCommGroup.toAddCommMonoid.{u4} E₁ _inst_20)] [_inst_23 : Module.{u1, u3} R₂ E₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} E₂ _inst_21)] [_inst_24 : UniformAddGroup.{u4} E₁ _inst_18 (AddCommGroup.toAddGroup.{u4} E₁ _inst_20)] [_inst_25 : UniformAddGroup.{u3} E₂ _inst_19 (AddCommGroup.toAddGroup.{u3} E₂ _inst_21)] (f : ContinuousLinearMap.{u2, u1, u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ E₁ (UniformSpace.toTopologicalSpace.{u4} E₁ _inst_18) (AddCommGroup.toAddCommMonoid.{u4} E₁ _inst_20) E₂ (UniformSpace.toTopologicalSpace.{u3} E₂ _inst_19) (AddCommGroup.toAddCommMonoid.{u3} E₂ _inst_21) _inst_22 _inst_23), UniformContinuous.{u4, u3} E₁ E₂ _inst_18 _inst_19 (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (ContinuousLinearMap.{u2, u1, u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ E₁ (UniformSpace.toTopologicalSpace.{u4} E₁ _inst_18) (AddCommGroup.toAddCommMonoid.{u4} E₁ _inst_20) E₂ (UniformSpace.toTopologicalSpace.{u3} E₂ _inst_19) (AddCommGroup.toAddCommMonoid.{u3} E₂ _inst_21) _inst_22 _inst_23) E₁ (fun (_x : E₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E₁) => E₂) _x) (ContinuousMapClass.toFunLike.{max u4 u3, u4, u3} (ContinuousLinearMap.{u2, u1, u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ E₁ (UniformSpace.toTopologicalSpace.{u4} E₁ _inst_18) (AddCommGroup.toAddCommMonoid.{u4} E₁ _inst_20) E₂ (UniformSpace.toTopologicalSpace.{u3} E₂ _inst_19) (AddCommGroup.toAddCommMonoid.{u3} E₂ _inst_21) _inst_22 _inst_23) E₁ E₂ (UniformSpace.toTopologicalSpace.{u4} E₁ _inst_18) (UniformSpace.toTopologicalSpace.{u3} E₂ _inst_19) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u4 u3, u2, u1, u4, u3} (ContinuousLinearMap.{u2, u1, u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ E₁ (UniformSpace.toTopologicalSpace.{u4} E₁ _inst_18) (AddCommGroup.toAddCommMonoid.{u4} E₁ _inst_20) E₂ (UniformSpace.toTopologicalSpace.{u3} E₂ _inst_19) (AddCommGroup.toAddCommMonoid.{u3} E₂ _inst_21) _inst_22 _inst_23) R₁ R₂ _inst_1 _inst_2 σ₁₂ E₁ (UniformSpace.toTopologicalSpace.{u4} E₁ _inst_18) (AddCommGroup.toAddCommMonoid.{u4} E₁ _inst_20) E₂ (UniformSpace.toTopologicalSpace.{u3} E₂ _inst_19) (AddCommGroup.toAddCommMonoid.{u3} E₂ _inst_21) _inst_22 _inst_23 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u1, u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ E₁ (UniformSpace.toTopologicalSpace.{u4} E₁ _inst_18) (AddCommGroup.toAddCommMonoid.{u4} E₁ _inst_20) E₂ (UniformSpace.toTopologicalSpace.{u3} E₂ _inst_19) (AddCommGroup.toAddCommMonoid.{u3} E₂ _inst_21) _inst_22 _inst_23))) f)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.uniform_continuous ContinuousLinearMap.uniformContinuousₓ'. -/
protected theorem uniformContinuous {E₁ E₂ : Type _} [UniformSpace E₁] [UniformSpace E₂]
[AddCommGroup E₁] [AddCommGroup E₂] [Module R₁ E₁] [Module R₂ E₂] [UniformAddGroup E₁]
[UniformAddGroup E₂] (f : E₁ →SL[σ₁₂] E₂) : UniformContinuous f :=
uniformContinuous_addMonoidHom_of_continuous f.Continuous
#align continuous_linear_map.uniform_continuous ContinuousLinearMap.uniformContinuous
+/- warning: continuous_linear_map.coe_inj -> ContinuousLinearMap.coe_inj is a dubious translation:
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+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] {f : ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16} {g : ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16}, Iff (Eq.{max (succ u2) (succ u1)} (LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 g)) (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) f g)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_inj ContinuousLinearMap.coe_injₓ'. -/
@[simp, norm_cast]
theorem coe_inj {f g : M₁ →SL[σ₁₂] M₂} : (f : M₁ →ₛₗ[σ₁₂] M₂) = g ↔ f = g :=
coe_injective.eq_iff
#align continuous_linear_map.coe_inj ContinuousLinearMap.coe_inj
+/- warning: continuous_linear_map.coe_fn_injective -> ContinuousLinearMap.coeFn_injective is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_fn_injective ContinuousLinearMap.coeFn_injectiveₓ'. -/
theorem coeFn_injective : @Function.Injective (M₁ →SL[σ₁₂] M₂) (M₁ → M₂) coeFn :=
FunLike.coe_injective
#align continuous_linear_map.coe_fn_injective ContinuousLinearMap.coeFn_injective
+#print ContinuousLinearMap.Simps.apply /-
/-- See Note [custom simps projection]. We need to specify this projection explicitly in this case,
because it is a composition of multiple projections. -/
def Simps.apply (h : M₁ →SL[σ₁₂] M₂) : M₁ → M₂ :=
h
#align continuous_linear_map.simps.apply ContinuousLinearMap.Simps.apply
+-/
+#print ContinuousLinearMap.Simps.coe /-
/-- See Note [custom simps projection]. -/
def Simps.coe (h : M₁ →SL[σ₁₂] M₂) : M₁ →ₛₗ[σ₁₂] M₂ :=
h
#align continuous_linear_map.simps.coe ContinuousLinearMap.Simps.coe
+-/
initialize_simps_projections ContinuousLinearMap (to_linear_map_to_fun → apply, toLinearMap → coe)
+/- warning: continuous_linear_map.ext -> ContinuousLinearMap.ext 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 continuous_linear_map.ext ContinuousLinearMap.extₓ'. -/
@[ext]
theorem ext {f g : M₁ →SL[σ₁₂] M₂} (h : ∀ x, f x = g x) : f = g :=
FunLike.ext f g h
#align continuous_linear_map.ext ContinuousLinearMap.ext
+/- warning: continuous_linear_map.ext_iff -> ContinuousLinearMap.ext_iff 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 continuous_linear_map.ext_iff ContinuousLinearMap.ext_iffₓ'. -/
theorem ext_iff {f g : M₁ →SL[σ₁₂] M₂} : f = g ↔ ∀ x, f x = g x :=
FunLike.ext_iff
#align continuous_linear_map.ext_iff ContinuousLinearMap.ext_iff
+/- warning: continuous_linear_map.copy -> ContinuousLinearMap.copy 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 continuous_linear_map.copy ContinuousLinearMap.copyₓ'. -/
/-- Copy of a `continuous_linear_map` with a new `to_fun` equal to the old one. Useful to fix
definitional equalities. -/
protected def copy (f : M₁ →SL[σ₁₂] M₂) (f' : M₁ → M₂) (h : f' = ⇑f) : M₁ →SL[σ₁₂] M₂
@@ -562,34 +747,76 @@ protected def copy (f : M₁ →SL[σ₁₂] M₂) (f' : M₁ → M₂) (h : f'
cont := show Continuous f' from h.symm ▸ f.Continuous
#align continuous_linear_map.copy ContinuousLinearMap.copy
+/- warning: continuous_linear_map.coe_copy -> ContinuousLinearMap.coe_copy 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 continuous_linear_map.coe_copy ContinuousLinearMap.coe_copyₓ'. -/
@[simp]
theorem coe_copy (f : M₁ →SL[σ₁₂] M₂) (f' : M₁ → M₂) (h : f' = ⇑f) : ⇑(f.copy f' h) = f' :=
rfl
#align continuous_linear_map.coe_copy ContinuousLinearMap.coe_copy
+/- warning: continuous_linear_map.copy_eq -> ContinuousLinearMap.copy_eq 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 continuous_linear_map.copy_eq ContinuousLinearMap.copy_eqₓ'. -/
theorem copy_eq (f : M₁ →SL[σ₁₂] M₂) (f' : M₁ → M₂) (h : f' = ⇑f) : f.copy f' h = f :=
FunLike.ext' h
#align continuous_linear_map.copy_eq ContinuousLinearMap.copy_eq
+/- warning: continuous_linear_map.map_zero -> ContinuousLinearMap.map_zero 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 continuous_linear_map.map_zero ContinuousLinearMap.map_zeroₓ'. -/
-- make some straightforward lemmas available to `simp`.
protected theorem map_zero (f : M₁ →SL[σ₁₂] M₂) : f (0 : M₁) = 0 :=
map_zero f
#align continuous_linear_map.map_zero ContinuousLinearMap.map_zero
+/- warning: continuous_linear_map.map_add -> ContinuousLinearMap.map_add 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 continuous_linear_map.map_add ContinuousLinearMap.map_addₓ'. -/
protected theorem map_add (f : M₁ →SL[σ₁₂] M₂) (x y : M₁) : f (x + y) = f x + f y :=
map_add f x y
#align continuous_linear_map.map_add ContinuousLinearMap.map_add
+/- warning: continuous_linear_map.map_smulₛₗ -> ContinuousLinearMap.map_smulₛₗ is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_smulₛₗ ContinuousLinearMap.map_smulₛₗₓ'. -/
@[simp]
protected theorem map_smulₛₗ (f : M₁ →SL[σ₁₂] M₂) (c : R₁) (x : M₁) : f (c • x) = σ₁₂ c • f x :=
(toLinearMap _).map_smulₛₗ _ _
#align continuous_linear_map.map_smulₛₗ ContinuousLinearMap.map_smulₛₗ
+/- warning: continuous_linear_map.map_smul -> ContinuousLinearMap.map_smul is a dubious translation:
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+ forall {R₁ : Type.{u3}} [_inst_1 : Semiring.{u3} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] {M₂ : Type.{u2}} [_inst_8 : TopologicalSpace.{u2} M₂] [_inst_9 : AddCommMonoid.{u2} M₂] [_inst_14 : Module.{u3, u1} R₁ M₁ _inst_1 _inst_5] [_inst_18 : Module.{u3, u2} R₁ M₂ _inst_1 _inst_9] (f : ContinuousLinearMap.{u3, u3, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_18) (c : R₁) (x : M₁), Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) (HSMul.hSMul.{u3, u1, u1} R₁ M₁ M₁ (instHSMul.{u3, u1} R₁ M₁ (SMulZeroClass.toSMul.{u3, u1} R₁ M₁ (AddMonoid.toZero.{u1} M₁ (AddCommMonoid.toAddMonoid.{u1} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u1} R₁ M₁ (MonoidWithZero.toZero.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ _inst_1)) (AddMonoid.toZero.{u1} M₁ (AddCommMonoid.toAddMonoid.{u1} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u1} R₁ M₁ (Semiring.toMonoidWithZero.{u3} R₁ _inst_1) (AddMonoid.toZero.{u1} M₁ (AddCommMonoid.toAddMonoid.{u1} M₁ _inst_5)) (Module.toMulActionWithZero.{u3, u1} R₁ M₁ _inst_1 _inst_5 _inst_14))))) c x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousLinearMap.{u3, u3, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_18) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousLinearMap.{u3, u3, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_18) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u1 u2, u3, u3, u1, u2} (ContinuousLinearMap.{u3, u3, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_18) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_18 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_18))) f (HSMul.hSMul.{u3, u1, u1} R₁ M₁ M₁ (instHSMul.{u3, u1} R₁ M₁ (SMulZeroClass.toSMul.{u3, u1} R₁ M₁ (AddMonoid.toZero.{u1} M₁ (AddCommMonoid.toAddMonoid.{u1} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u1} R₁ M₁ (MonoidWithZero.toZero.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ _inst_1)) (AddMonoid.toZero.{u1} M₁ (AddCommMonoid.toAddMonoid.{u1} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u1} R₁ M₁ (Semiring.toMonoidWithZero.{u3} R₁ _inst_1) (AddMonoid.toZero.{u1} M₁ (AddCommMonoid.toAddMonoid.{u1} M₁ _inst_5)) (Module.toMulActionWithZero.{u3, u1} R₁ M₁ _inst_1 _inst_5 _inst_14))))) c x)) (HSMul.hSMul.{u3, u2, u2} R₁ ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (instHSMul.{u3, u2} R₁ ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (SMulZeroClass.toSMul.{u3, u2} R₁ ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_9)) (SMulWithZero.toSMulZeroClass.{u3, u2} R₁ ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (MonoidWithZero.toZero.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ _inst_1)) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_9)) (MulActionWithZero.toSMulWithZero.{u3, u2} R₁ ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (Semiring.toMonoidWithZero.{u3} R₁ _inst_1) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_9)) (Module.toMulActionWithZero.{u3, u2} R₁ ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_1 _inst_9 _inst_18))))) c (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousLinearMap.{u3, u3, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_18) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousLinearMap.{u3, u3, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_18) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u1 u2, u3, u3, u1, u2} (ContinuousLinearMap.{u3, u3, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_18) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_18 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_18))) f x))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_smul ContinuousLinearMap.map_smulₓ'. -/
@[simp]
protected theorem map_smul [Module R₁ M₂] (f : M₁ →L[R₁] M₂) (c : R₁) (x : M₁) :
f (c • x) = c • f x := by simp only [RingHom.id_apply, ContinuousLinearMap.map_smulₛₗ]
#align continuous_linear_map.map_smul ContinuousLinearMap.map_smul
+/- warning: continuous_linear_map.map_smul_of_tower -> ContinuousLinearMap.map_smul_of_tower is a dubious translation:
+lean 3 declaration is
+ forall {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] {M₂ : Type.{u2}} [_inst_8 : TopologicalSpace.{u2} M₂] [_inst_9 : AddCommMonoid.{u2} M₂] {R : Type.{u3}} {S : Type.{u4}} [_inst_18 : Semiring.{u4} S] [_inst_19 : SMul.{u3, u1} R M₁] [_inst_20 : Module.{u4, u1} S M₁ _inst_18 _inst_5] [_inst_21 : SMul.{u3, u2} R M₂] [_inst_22 : Module.{u4, u2} S M₂ _inst_18 _inst_9] [_inst_23 : LinearMap.CompatibleSMul.{u1, u2, u3, u4} M₁ M₂ _inst_5 _inst_9 R S _inst_18 _inst_19 _inst_20 _inst_21 _inst_22] (f : ContinuousLinearMap.{u4, u4, u1, u2} S S _inst_18 _inst_18 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_18)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_20 _inst_22) (c : R) (x : M₁), Eq.{succ u2} M₂ (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousLinearMap.{u4, u4, u1, u2} S S _inst_18 _inst_18 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_18)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_20 _inst_22) (fun (_x : ContinuousLinearMap.{u4, u4, u1, u2} S S _inst_18 _inst_18 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_18)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_20 _inst_22) => M₁ -> M₂) (ContinuousLinearMap.toFun.{u4, u4, u1, u2} S S _inst_18 _inst_18 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_18)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_20 _inst_22) f (SMul.smul.{u3, u1} R M₁ _inst_19 c x)) (SMul.smul.{u3, u2} R M₂ _inst_21 c (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousLinearMap.{u4, u4, u1, u2} S S _inst_18 _inst_18 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_18)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_20 _inst_22) (fun (_x : ContinuousLinearMap.{u4, u4, u1, u2} S S _inst_18 _inst_18 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_18)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_20 _inst_22) => M₁ -> M₂) (ContinuousLinearMap.toFun.{u4, u4, u1, u2} S S _inst_18 _inst_18 (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_18)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_20 _inst_22) f x))
+but is expected to have type
+ forall {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] {R : Type.{u4}} {S : Type.{u3}} [_inst_18 : Semiring.{u3} S] [_inst_19 : SMul.{u4, u2} R M₁] [_inst_20 : Module.{u3, u2} S M₁ _inst_18 _inst_5] [_inst_21 : SMul.{u4, u1} R M₂] [_inst_22 : Module.{u3, u1} S M₂ _inst_18 _inst_9] [_inst_23 : LinearMap.CompatibleSMul.{u2, u1, u4, u3} M₁ M₂ _inst_5 _inst_9 R S _inst_18 _inst_19 _inst_20 _inst_21 _inst_22] (f : ContinuousLinearMap.{u3, u3, u2, u1} S S _inst_18 _inst_18 (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_18)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_20 _inst_22) (c : R) (x : M₁), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) (HSMul.hSMul.{u4, u2, u2} R M₁ M₁ (instHSMul.{u4, u2} R M₁ _inst_19) c x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u3, u3, u2, u1} S S _inst_18 _inst_18 (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_18)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_20 _inst_22) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} S S _inst_18 _inst_18 (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_18)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_20 _inst_22) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} S S _inst_18 _inst_18 (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_18)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_20 _inst_22) S S _inst_18 _inst_18 (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_18)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_20 _inst_22 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} S S _inst_18 _inst_18 (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_18)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_20 _inst_22))) f (HSMul.hSMul.{u4, u2, u2} R M₁ M₁ (instHSMul.{u4, u2} R M₁ _inst_19) c x)) (HSMul.hSMul.{u4, u1, u1} R ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (instHSMul.{u4, u1} R ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_21) c (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u3, u3, u2, u1} S S _inst_18 _inst_18 (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_18)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_20 _inst_22) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} S S _inst_18 _inst_18 (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_18)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_20 _inst_22) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} S S _inst_18 _inst_18 (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_18)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_20 _inst_22) S S _inst_18 _inst_18 (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_18)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_20 _inst_22 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} S S _inst_18 _inst_18 (RingHom.id.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_18)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_20 _inst_22))) f x))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_smul_of_tower ContinuousLinearMap.map_smul_of_towerₓ'. -/
@[simp]
theorem map_smul_of_tower {R S : Type _} [Semiring S] [SMul R M₁] [Module S M₁] [SMul R M₂]
[Module S M₂] [LinearMap.CompatibleSMul M₁ M₂ R S] (f : M₁ →L[S] M₂) (c : R) (x : M₁) :
@@ -597,25 +824,55 @@ theorem map_smul_of_tower {R S : Type _} [Semiring S] [SMul R M₁] [Module S M
LinearMap.CompatibleSMul.map_smul f c x
#align continuous_linear_map.map_smul_of_tower ContinuousLinearMap.map_smul_of_tower
+/- warning: continuous_linear_map.map_sum -> ContinuousLinearMap.map_sum is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] [_inst_14 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_9] {ι : Type.{u5}} (f : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (s : Finset.{u5} ι) (g : ι -> M₁), Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) => M₁ -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) f (Finset.sum.{u3, u5} M₁ ι _inst_5 s (fun (i : ι) => g i))) (Finset.sum.{u4, u5} M₂ ι _inst_9 s (fun (i : ι) => coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) => M₁ -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) f (g i)))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_sum ContinuousLinearMap.map_sumₓ'. -/
protected theorem map_sum {ι : Type _} (f : M₁ →SL[σ₁₂] M₂) (s : Finset ι) (g : ι → M₁) :
f (∑ i in s, g i) = ∑ i in s, f (g i) :=
f.toLinearMap.map_sum
#align continuous_linear_map.map_sum ContinuousLinearMap.map_sum
+/- warning: continuous_linear_map.coe_coe -> ContinuousLinearMap.coe_coe is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] [_inst_14 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_9] (f : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u3) (succ u4)} (M₁ -> M₂) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (fun (_x : LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) ((fun (a : Sort.{max (succ u3) (succ u4)}) (b : Sort.{max (succ u3) (succ u4)}) [self : HasLiftT.{max (succ u3) (succ u4), max (succ u3) (succ u4)} a b] => self.0) (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (HasLiftT.mk.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (CoeTCₓ.coe.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (coeBase.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.LinearMap.coe.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16)))) f)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) => M₁ -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) f)
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] (f : ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) f)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_coe ContinuousLinearMap.coe_coeₓ'. -/
@[simp, norm_cast]
theorem coe_coe (f : M₁ →SL[σ₁₂] M₂) : ⇑(f : M₁ →ₛₗ[σ₁₂] M₂) = f :=
rfl
#align continuous_linear_map.coe_coe ContinuousLinearMap.coe_coe
+/- warning: continuous_linear_map.ext_ring -> ContinuousLinearMap.ext_ring is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ext_ring ContinuousLinearMap.ext_ringₓ'. -/
@[ext]
theorem ext_ring [TopologicalSpace R₁] {f g : R₁ →L[R₁] M₁} (h : f 1 = g 1) : f = g :=
coe_inj.1 <| LinearMap.ext_ring h
#align continuous_linear_map.ext_ring ContinuousLinearMap.ext_ring
+/- warning: continuous_linear_map.ext_ring_iff -> ContinuousLinearMap.ext_ring_iff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ext_ring_iff ContinuousLinearMap.ext_ring_iffₓ'. -/
theorem ext_ring_iff [TopologicalSpace R₁] {f g : R₁ →L[R₁] M₁} : f = g ↔ f 1 = g 1 :=
⟨fun h => h ▸ rfl, ext_ring⟩
#align continuous_linear_map.ext_ring_iff ContinuousLinearMap.ext_ring_iff
+/- warning: continuous_linear_map.eq_on_closure_span -> ContinuousLinearMap.eqOn_closure_span 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 continuous_linear_map.eq_on_closure_span ContinuousLinearMap.eqOn_closure_spanₓ'. -/
/-- If two continuous linear maps are equal on a set `s`, then they are equal on the closure
of the `submodule.span` of this set. -/
theorem eqOn_closure_span [T2Space M₂] {s : Set M₁} {f g : M₁ →SL[σ₁₂] M₂} (h : Set.EqOn f g s) :
@@ -623,6 +880,12 @@ theorem eqOn_closure_span [T2Space M₂] {s : Set M₁} {f g : M₁ →SL[σ₁
(LinearMap.eqOn_span' h).closure f.Continuous g.Continuous
#align continuous_linear_map.eq_on_closure_span ContinuousLinearMap.eqOn_closure_span
+/- warning: continuous_linear_map.ext_on -> ContinuousLinearMap.ext_on is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ext_on ContinuousLinearMap.ext_onₓ'. -/
/-- If the submodule generated by a set `s` is dense in the ambient module, then two continuous
linear maps equal on `s` are equal. -/
theorem ext_on [T2Space M₂] {s : Set M₁} (hs : Dense (Submodule.span R₁ s : Set M₁))
@@ -630,6 +893,12 @@ theorem ext_on [T2Space M₂] {s : Set M₁} (hs : Dense (Submodule.span R₁ s
ext fun x => eqOn_closure_span h (hs x)
#align continuous_linear_map.ext_on ContinuousLinearMap.ext_on
+/- warning: submodule.topological_closure_map -> Submodule.topologicalClosure_map is a dubious translation:
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+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] [_inst_18 : RingHomSurjective.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂] [_inst_19 : TopologicalSpace.{u4} R₁] [_inst_20 : TopologicalSpace.{u3} R₂] [_inst_21 : ContinuousSMul.{u4, u2} R₁ M₁ (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)))) _inst_19 _inst_4] [_inst_22 : ContinuousAdd.{u2} M₁ _inst_4 (AddZeroClass.toAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)))] [_inst_23 : ContinuousSMul.{u3, u1} R₂ M₂ (SMulZeroClass.toSMul.{u3, u1} R₂ M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u3, u1} R₂ M₂ (MonoidWithZero.toZero.{u3} R₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u3, u1} R₂ M₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16)))) _inst_20 _inst_8] [_inst_24 : ContinuousAdd.{u1} M₂ _inst_8 (AddZeroClass.toAdd.{u1} M₂ (AddMonoid.toAddZeroClass.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)))] (f : ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (s : Submodule.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14), LE.le.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (Preorder.toLE.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (PartialOrder.toPreorder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (Submodule.completeLattice.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16))))) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂ _inst_18 (LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f) (Submodule.topologicalClosure.{u4, u2} R₁ M₁ _inst_1 _inst_4 _inst_5 _inst_14 (ContinuousSMul.continuousConstSMul.{u4, u2} R₁ M₁ _inst_19 _inst_4 (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)))) _inst_21) _inst_22 s)) (Submodule.topologicalClosure.{u3, u1} R₂ M₂ _inst_2 _inst_8 _inst_9 _inst_16 (ContinuousSMul.continuousConstSMul.{u3, u1} R₂ M₂ _inst_20 _inst_8 (SMulZeroClass.toSMul.{u3, u1} R₂ M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u3, u1} R₂ M₂ (MonoidWithZero.toZero.{u3} R₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u3, u1} R₂ M₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16)))) _inst_23) _inst_24 (Submodule.map.{u4, u3, u2, u1, max u2 u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂ _inst_18 (LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f) s))
+Case conversion may be inaccurate. Consider using '#align submodule.topological_closure_map Submodule.topologicalClosure_mapₓ'. -/
/-- Under a continuous linear map, the image of the `topological_closure` of a submodule is
contained in the `topological_closure` of its image. -/
theorem Submodule.topologicalClosure_map [RingHomSurjective σ₁₂] [TopologicalSpace R₁]
@@ -640,6 +909,12 @@ theorem Submodule.topologicalClosure_map [RingHomSurjective σ₁₂] [Topologic
image_closure_subset_closure_image f.Continuous
#align submodule.topological_closure_map Submodule.topologicalClosure_map
+/- warning: dense_range.topological_closure_map_submodule -> DenseRange.topologicalClosure_map_submodule is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] [_inst_14 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_9] [_inst_18 : RingHomSurjective.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂] [_inst_19 : TopologicalSpace.{u1} R₁] [_inst_20 : TopologicalSpace.{u2} R₂] [_inst_21 : ContinuousSMul.{u1, u3} R₁ M₁ (SMulZeroClass.toHasSmul.{u1, u3} R₁ M₁ (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5))) (SMulWithZero.toSmulZeroClass.{u1, u3} R₁ M₁ (MulZeroClass.toHasZero.{u1} R₁ (MulZeroOneClass.toMulZeroClass.{u1} R₁ (MonoidWithZero.toMulZeroOneClass.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)))) (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5))) (MulActionWithZero.toSMulWithZero.{u1, u3} R₁ M₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5))) (Module.toMulActionWithZero.{u1, u3} R₁ M₁ _inst_1 _inst_5 _inst_14)))) _inst_19 _inst_4] [_inst_22 : ContinuousAdd.{u3} M₁ _inst_4 (AddZeroClass.toHasAdd.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_5)))] [_inst_23 : ContinuousSMul.{u2, u4} R₂ M₂ (SMulZeroClass.toHasSmul.{u2, u4} R₂ M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (SMulWithZero.toSmulZeroClass.{u2, u4} R₂ M₂ (MulZeroClass.toHasZero.{u2} R₂ (MulZeroOneClass.toMulZeroClass.{u2} R₂ (MonoidWithZero.toMulZeroOneClass.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)))) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (MulActionWithZero.toSMulWithZero.{u2, u4} R₂ M₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (Module.toMulActionWithZero.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)))) _inst_20 _inst_8] [_inst_24 : ContinuousAdd.{u4} M₂ _inst_8 (AddZeroClass.toHasAdd.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9)))] {f : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16}, (DenseRange.{u4, u3} M₂ _inst_8 M₁ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 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M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) ((fun (a : Sort.{max (succ u3) (succ u4)}) (b : Sort.{max (succ u3) (succ u4)}) [self : HasLiftT.{max (succ u3) (succ u4), max (succ u3) (succ u4)} a b] => self.0) (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (HasLiftT.mk.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (CoeTCₓ.coe.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (coeBase.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (LinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.LinearMap.coe.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16)))) f) s)) (Top.top.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) (Submodule.hasTop.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16))))
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] [_inst_18 : RingHomSurjective.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂] [_inst_19 : TopologicalSpace.{u4} R₁] [_inst_20 : TopologicalSpace.{u3} R₂] [_inst_21 : ContinuousSMul.{u4, u2} R₁ M₁ (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)))) _inst_19 _inst_4] [_inst_22 : ContinuousAdd.{u2} M₁ _inst_4 (AddZeroClass.toAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)))] [_inst_23 : ContinuousSMul.{u3, u1} R₂ M₂ (SMulZeroClass.toSMul.{u3, u1} R₂ M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u3, u1} R₂ M₂ (MonoidWithZero.toZero.{u3} R₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u3, u1} R₂ M₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16)))) _inst_20 _inst_8] [_inst_24 : ContinuousAdd.{u1} M₂ _inst_8 (AddZeroClass.toAdd.{u1} M₂ (AddMonoid.toAddZeroClass.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)))] {f : ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16}, (DenseRange.{u1, u2} M₂ _inst_8 M₁ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) f)) -> (forall {s : Submodule.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14}, (Eq.{succ u2} (Submodule.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) (Submodule.topologicalClosure.{u4, u2} R₁ M₁ _inst_1 _inst_4 _inst_5 _inst_14 (ContinuousSMul.continuousConstSMul.{u4, u2} R₁ M₁ _inst_19 _inst_4 (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)))) _inst_21) _inst_22 s) (Top.top.{u2} (Submodule.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) (Submodule.instTopSubmodule.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14))) -> (Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (Submodule.topologicalClosure.{u3, u1} R₂ M₂ _inst_2 _inst_8 _inst_9 _inst_16 (ContinuousSMul.continuousConstSMul.{u3, u1} R₂ M₂ _inst_20 _inst_8 (SMulZeroClass.toSMul.{u3, u1} R₂ M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u3, u1} R₂ M₂ (MonoidWithZero.toZero.{u3} R₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u3, u1} R₂ M₂ (Semiring.toMonoidWithZero.{u3} R₂ _inst_2) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16)))) _inst_23) _inst_24 (Submodule.map.{u4, u3, u2, u1, max u2 u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂ _inst_18 (LinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f) s)) (Top.top.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (Submodule.instTopSubmodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16))))
+Case conversion may be inaccurate. Consider using '#align dense_range.topological_closure_map_submodule DenseRange.topologicalClosure_map_submoduleₓ'. -/
/-- Under a dense continuous linear map, a submodule whose `topological_closure` is `⊤` is sent to
another such submodule. That is, the image of a dense set under a map with dense range is dense.
-/
@@ -667,15 +942,33 @@ instance : MulAction S₂ (M₁ →SL[σ₁₂] M₂)
one_smul f := ext fun x => one_smul _ _
mul_smul a b f := ext fun x => mul_smul _ _ _
+/- warning: continuous_linear_map.smul_apply -> ContinuousLinearMap.smul_apply is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] [_inst_14 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_9] {S₂ : Type.{u5}} [_inst_18 : Monoid.{u5} S₂] [_inst_20 : DistribMulAction.{u5, u4} S₂ M₂ _inst_18 (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9)] [_inst_21 : SMulCommClass.{u2, u5, u4} R₂ S₂ M₂ (SMulZeroClass.toHasSmul.{u2, u4} R₂ M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (SMulWithZero.toSmulZeroClass.{u2, u4} R₂ M₂ (MulZeroClass.toHasZero.{u2} R₂ (MulZeroOneClass.toMulZeroClass.{u2} R₂ (MonoidWithZero.toMulZeroOneClass.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)))) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (MulActionWithZero.toSMulWithZero.{u2, u4} R₂ M₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (Module.toMulActionWithZero.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)))) (SMulZeroClass.toHasSmul.{u5, u4} S₂ M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (DistribSMul.toSmulZeroClass.{u5, u4} S₂ M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9)) (DistribMulAction.toDistribSMul.{u5, u4} S₂ M₂ _inst_18 (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9) _inst_20)))] [_inst_22 : ContinuousConstSMul.{u5, u4} S₂ M₂ _inst_8 (SMulZeroClass.toHasSmul.{u5, u4} S₂ M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (DistribSMul.toSmulZeroClass.{u5, u4} S₂ M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9)) (DistribMulAction.toDistribSMul.{u5, u4} S₂ M₂ _inst_18 (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9) _inst_20)))] (c : S₂) (f : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (x : M₁), Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) => M₁ -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (SMul.smul.{u5, max u3 u4} S₂ (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (MulAction.toHasSmul.{u5, max u3 u4} S₂ (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) _inst_18 (ContinuousLinearMap.mulAction.{u1, u2, u3, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 S₂ _inst_18 _inst_20 _inst_21 _inst_22)) c f) x) (SMul.smul.{u5, u4} S₂ M₂ (SMulZeroClass.toHasSmul.{u5, u4} S₂ M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (DistribSMul.toSmulZeroClass.{u5, u4} S₂ M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9)) (DistribMulAction.toDistribSMul.{u5, u4} S₂ M₂ _inst_18 (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9) _inst_20))) c (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) => M₁ -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) f x))
+but is expected to have type
+ forall {R₁ : Type.{u5}} {R₂ : Type.{u4}} [_inst_1 : Semiring.{u5} R₁] [_inst_2 : Semiring.{u4} R₂] {σ₁₂ : RingHom.{u5, u4} R₁ R₂ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u4} R₂ _inst_2)} {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u2}} [_inst_8 : TopologicalSpace.{u2} M₂] [_inst_9 : AddCommMonoid.{u2} M₂] [_inst_14 : Module.{u5, u3} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u4, u2} R₂ M₂ _inst_2 _inst_9] {S₂ : Type.{u1}} [_inst_18 : Monoid.{u1} S₂] [_inst_20 : DistribMulAction.{u1, u2} S₂ M₂ _inst_18 (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)] [_inst_21 : SMulCommClass.{u4, u1, u2} R₂ S₂ M₂ (SMulZeroClass.toSMul.{u4, u2} R₂ M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₂ M₂ (MonoidWithZero.toZero.{u4} R₂ (Semiring.toMonoidWithZero.{u4} R₂ _inst_2)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₂ M₂ (Semiring.toMonoidWithZero.{u4} R₂ _inst_2) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (Module.toMulActionWithZero.{u4, u2} R₂ M₂ _inst_2 _inst_9 _inst_16)))) (SMulZeroClass.toSMul.{u1, u2} S₂ M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (DistribSMul.toSMulZeroClass.{u1, u2} S₂ M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S₂ M₂ _inst_18 (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9) _inst_20)))] [_inst_22 : ContinuousConstSMul.{u1, u2} S₂ M₂ _inst_8 (SMulZeroClass.toSMul.{u1, u2} S₂ M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (DistribSMul.toSMulZeroClass.{u1, u2} S₂ M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S₂ M₂ _inst_18 (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9) _inst_20)))] (c : S₂) (f : ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (x : M₁), Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u3, u2} (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u5, u4, u3, u2} (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} S₂ (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (instHSMul.{u1, max u3 u2} S₂ (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (MulAction.toSMul.{u1, max u3 u2} S₂ (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) _inst_18 (ContinuousLinearMap.mulAction.{u5, u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 S₂ _inst_18 _inst_20 _inst_21 _inst_22))) c f) x) (HSMul.hSMul.{u1, u2, u2} S₂ ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (instHSMul.{u1, u2} S₂ ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (SMulZeroClass.toSMul.{u1, u2} S₂ ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_9)) (DistribSMul.toSMulZeroClass.{u1, u2} S₂ ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddMonoid.toAddZeroClass.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S₂ ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_18 (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_9) _inst_20)))) c (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u3, u2} (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u5, u4, u3, u2} (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) f x))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_apply ContinuousLinearMap.smul_applyₓ'. -/
theorem smul_apply (c : S₂) (f : M₁ →SL[σ₁₂] M₂) (x : M₁) : (c • f) x = c • f x :=
rfl
#align continuous_linear_map.smul_apply ContinuousLinearMap.smul_apply
+/- warning: continuous_linear_map.coe_smul -> ContinuousLinearMap.coe_smul is a dubious translation:
+lean 3 declaration is
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R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)))) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (MulActionWithZero.toSMulWithZero.{u2, u4} R₂ M₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (Module.toMulActionWithZero.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)))) (SMulZeroClass.toHasSmul.{u5, u4} S₂ M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (DistribSMul.toSmulZeroClass.{u5, u4} S₂ M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9)) (DistribMulAction.toDistribSMul.{u5, u4} S₂ M₂ _inst_18 (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9) _inst_20)))] [_inst_22 : ContinuousConstSMul.{u5, u4} S₂ M₂ _inst_8 (SMulZeroClass.toHasSmul.{u5, u4} S₂ M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ 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+but is expected to have type
+ forall {R₁ : Type.{u5}} {R₂ : Type.{u4}} [_inst_1 : Semiring.{u5} R₁] [_inst_2 : Semiring.{u4} R₂] {σ₁₂ : RingHom.{u5, u4} R₁ R₂ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u4} R₂ _inst_2)} {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u2}} [_inst_8 : TopologicalSpace.{u2} M₂] [_inst_9 : AddCommMonoid.{u2} M₂] [_inst_14 : Module.{u5, u3} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u4, u2} R₂ M₂ _inst_2 _inst_9] {S₂ : Type.{u1}} [_inst_18 : Monoid.{u1} S₂] [_inst_20 : DistribMulAction.{u1, u2} S₂ M₂ _inst_18 (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)] [_inst_21 : SMulCommClass.{u4, u1, u2} R₂ S₂ M₂ (SMulZeroClass.toSMul.{u4, u2} R₂ M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₂ M₂ (MonoidWithZero.toZero.{u4} R₂ (Semiring.toMonoidWithZero.{u4} R₂ _inst_2)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₂ M₂ (Semiring.toMonoidWithZero.{u4} R₂ _inst_2) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (Module.toMulActionWithZero.{u4, u2} R₂ M₂ _inst_2 _inst_9 _inst_16)))) (SMulZeroClass.toSMul.{u1, u2} S₂ M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (DistribSMul.toSMulZeroClass.{u1, u2} S₂ M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S₂ M₂ _inst_18 (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9) _inst_20)))] [_inst_22 : ContinuousConstSMul.{u1, u2} S₂ M₂ _inst_8 (SMulZeroClass.toSMul.{u1, u2} S₂ M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (DistribSMul.toSMulZeroClass.{u1, u2} S₂ M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S₂ M₂ _inst_18 (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9) _inst_20)))] (c : S₂) (f : ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u3) (succ u2)} (LinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.toLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (HSMul.hSMul.{u1, max u3 u2, max u3 u2} S₂ (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (instHSMul.{u1, max u3 u2} S₂ (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (MulAction.toSMul.{u1, max u3 u2} S₂ (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) _inst_18 (ContinuousLinearMap.mulAction.{u5, u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 S₂ _inst_18 _inst_20 _inst_21 _inst_22))) c f)) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} S₂ (LinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (LinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (instHSMul.{u1, max u3 u2} S₂ (LinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ M₂ _inst_5 _inst_9 _inst_14 _inst_16) (LinearMap.instSMulLinearMap.{u5, u4, u1, u3, u2} R₁ R₂ S₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂ _inst_18 _inst_20 _inst_21)) c (ContinuousLinearMap.toLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_smul ContinuousLinearMap.coe_smulₓ'. -/
@[simp, norm_cast]
theorem coe_smul (c : S₂) (f : M₁ →SL[σ₁₂] M₂) : (↑(c • f) : M₁ →ₛₗ[σ₁₂] M₂) = c • f :=
rfl
#align continuous_linear_map.coe_smul ContinuousLinearMap.coe_smul
+/- warning: continuous_linear_map.coe_smul' -> ContinuousLinearMap.coe_smul' is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] [_inst_14 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_9] {S₂ : Type.{u5}} [_inst_18 : Monoid.{u5} S₂] [_inst_20 : DistribMulAction.{u5, u4} S₂ M₂ _inst_18 (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9)] [_inst_21 : SMulCommClass.{u2, u5, u4} R₂ S₂ M₂ (SMulZeroClass.toHasSmul.{u2, u4} R₂ M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (SMulWithZero.toSmulZeroClass.{u2, u4} R₂ M₂ (MulZeroClass.toHasZero.{u2} R₂ (MulZeroOneClass.toMulZeroClass.{u2} R₂ (MonoidWithZero.toMulZeroOneClass.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)))) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (MulActionWithZero.toSMulWithZero.{u2, u4} R₂ M₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (Module.toMulActionWithZero.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)))) (SMulZeroClass.toHasSmul.{u5, u4} S₂ M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (DistribSMul.toSmulZeroClass.{u5, u4} S₂ M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9)) (DistribMulAction.toDistribSMul.{u5, u4} S₂ M₂ _inst_18 (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9) _inst_20)))] [_inst_22 : ContinuousConstSMul.{u5, u4} S₂ M₂ _inst_8 (SMulZeroClass.toHasSmul.{u5, u4} S₂ M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (DistribSMul.toSmulZeroClass.{u5, u4} S₂ M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9)) (DistribMulAction.toDistribSMul.{u5, u4} S₂ M₂ _inst_18 (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9) _inst_20)))] (c : S₂) (f : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{succ (max u3 u4)} (M₁ -> M₂) (coeFn.{succ (max u3 u4), succ (max u3 u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) => M₁ -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (SMul.smul.{u5, max u3 u4} S₂ (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (MulAction.toHasSmul.{u5, max u3 u4} S₂ (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) _inst_18 (ContinuousLinearMap.mulAction.{u1, u2, u3, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 S₂ _inst_18 _inst_20 _inst_21 _inst_22)) c f)) (SMul.smul.{u5, max u3 u4} S₂ (M₁ -> M₂) (Function.hasSMul.{u3, u5, u4} M₁ S₂ M₂ (SMulZeroClass.toHasSmul.{u5, u4} S₂ M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9))) (DistribSMul.toSmulZeroClass.{u5, u4} S₂ M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9)) (DistribMulAction.toDistribSMul.{u5, u4} S₂ M₂ _inst_18 (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_9) _inst_20)))) c (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) => M₁ -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) f))
+but is expected to have type
+ forall {R₁ : Type.{u5}} {R₂ : Type.{u4}} [_inst_1 : Semiring.{u5} R₁] [_inst_2 : Semiring.{u4} R₂] {σ₁₂ : RingHom.{u5, u4} R₁ R₂ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u4} R₂ _inst_2)} {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u2}} [_inst_8 : TopologicalSpace.{u2} M₂] [_inst_9 : AddCommMonoid.{u2} M₂] [_inst_14 : Module.{u5, u3} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u4, u2} R₂ M₂ _inst_2 _inst_9] {S₂ : Type.{u1}} [_inst_18 : Monoid.{u1} S₂] [_inst_20 : DistribMulAction.{u1, u2} S₂ M₂ _inst_18 (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)] [_inst_21 : SMulCommClass.{u4, u1, u2} R₂ S₂ M₂ (SMulZeroClass.toSMul.{u4, u2} R₂ M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₂ M₂ (MonoidWithZero.toZero.{u4} R₂ (Semiring.toMonoidWithZero.{u4} R₂ _inst_2)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₂ M₂ (Semiring.toMonoidWithZero.{u4} R₂ _inst_2) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (Module.toMulActionWithZero.{u4, u2} R₂ M₂ _inst_2 _inst_9 _inst_16)))) (SMulZeroClass.toSMul.{u1, u2} S₂ M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (DistribSMul.toSMulZeroClass.{u1, u2} S₂ M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S₂ M₂ _inst_18 (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9) _inst_20)))] [_inst_22 : ContinuousConstSMul.{u1, u2} S₂ M₂ _inst_8 (SMulZeroClass.toSMul.{u1, u2} S₂ M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (DistribSMul.toSMulZeroClass.{u1, u2} S₂ M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S₂ M₂ _inst_18 (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9) _inst_20)))] (c : S₂) (f : ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u3) (succ u2)} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u3, u2} (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u5, u4, u3, u2} (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} S₂ (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (instHSMul.{u1, max u3 u2} S₂ (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (MulAction.toSMul.{u1, max u3 u2} S₂ (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) _inst_18 (ContinuousLinearMap.mulAction.{u5, u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 S₂ _inst_18 _inst_20 _inst_21 _inst_22))) c f)) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} S₂ (forall (a : M₁), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) a) (forall (ᾰ : M₁), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) ᾰ) (instHSMul.{u1, max u3 u2} S₂ (forall (a : M₁), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) a) (Pi.instSMul.{u3, u2, u1} M₁ S₂ (fun (a : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) a) (fun (i : M₁) => SMulZeroClass.toSMul.{u1, u2} S₂ ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) i) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) i) _inst_9)) (DistribSMul.toSMulZeroClass.{u1, u2} S₂ ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) i) (AddMonoid.toAddZeroClass.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) i) _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S₂ ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) i) _inst_18 (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) i) _inst_9) _inst_20))))) c (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u3, u2} (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u5, u4, u3, u2} (ContinuousLinearMap.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u5, u4, u3, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) f))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_smul' ContinuousLinearMap.coe_smul'ₓ'. -/
@[simp, norm_cast]
theorem coe_smul' (c : S₂) (f : M₁ →SL[σ₁₂] M₂) : ⇑(c • f) = c • f :=
rfl
@@ -696,21 +989,45 @@ instance : Zero (M₁ →SL[σ₁₂] M₂) :=
instance : Inhabited (M₁ →SL[σ₁₂] M₂) :=
⟨0⟩
+/- warning: continuous_linear_map.default_def -> ContinuousLinearMap.default_def is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] [_inst_14 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_9], Eq.{max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (Inhabited.default.{max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.inhabited.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16)) (OfNat.ofNat.{max u3 u4} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) 0 (OfNat.mk.{max u3 u4} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) 0 (Zero.zero.{max u3 u4} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.zero.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))))
+but is expected to have type
+ forall {R₁ : Type.{u2}} {R₂ : Type.{u1}} [_inst_1 : Semiring.{u2} R₁] [_inst_2 : Semiring.{u1} R₂] {σ₁₂ : RingHom.{u2, u1} R₁ R₂ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u1} R₂ _inst_2)} {M₁ : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} M₁] [_inst_5 : AddCommMonoid.{u4} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] [_inst_14 : Module.{u2, u4} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u1, u3} R₂ M₂ _inst_2 _inst_9], Eq.{max (succ u4) (succ u3)} (ContinuousLinearMap.{u2, u1, u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (Inhabited.default.{max (succ u4) (succ u3)} (ContinuousLinearMap.{u2, u1, u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.inhabited.{u2, u1, u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16)) (OfNat.ofNat.{max u4 u3} (ContinuousLinearMap.{u2, u1, u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) 0 (Zero.toOfNat0.{max u4 u3} (ContinuousLinearMap.{u2, u1, u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.zero.{u2, u1, u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16)))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.default_def ContinuousLinearMap.default_defₓ'. -/
@[simp]
theorem default_def : (default : M₁ →SL[σ₁₂] M₂) = 0 :=
rfl
#align continuous_linear_map.default_def ContinuousLinearMap.default_def
+/- warning: continuous_linear_map.zero_apply -> ContinuousLinearMap.zero_apply is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.zero_apply ContinuousLinearMap.zero_applyₓ'. -/
@[simp]
theorem zero_apply (x : M₁) : (0 : M₁ →SL[σ₁₂] M₂) x = 0 :=
rfl
#align continuous_linear_map.zero_apply ContinuousLinearMap.zero_apply
+/- warning: continuous_linear_map.coe_zero -> ContinuousLinearMap.coe_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_zero ContinuousLinearMap.coe_zeroₓ'. -/
@[simp, norm_cast]
theorem coe_zero : ((0 : M₁ →SL[σ₁₂] M₂) : M₁ →ₛₗ[σ₁₂] M₂) = 0 :=
rfl
#align continuous_linear_map.coe_zero ContinuousLinearMap.coe_zero
+/- warning: continuous_linear_map.coe_zero' -> ContinuousLinearMap.coe_zero' is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_zero' ContinuousLinearMap.coe_zero'ₓ'. -/
/- no simp attribute on the next line as simp does not always simplify `0 x` to `0`
when `0` is the zero function, while it does for the zero continuous linear map,
and this is the most important property we care about. -/
@@ -719,14 +1036,24 @@ theorem coe_zero' : ⇑(0 : M₁ →SL[σ₁₂] M₂) = 0 :=
rfl
#align continuous_linear_map.coe_zero' ContinuousLinearMap.coe_zero'
+#print ContinuousLinearMap.uniqueOfLeft /-
instance uniqueOfLeft [Subsingleton M₁] : Unique (M₁ →SL[σ₁₂] M₂) :=
coe_injective.unique
#align continuous_linear_map.unique_of_left ContinuousLinearMap.uniqueOfLeft
+-/
+#print ContinuousLinearMap.uniqueOfRight /-
instance uniqueOfRight [Subsingleton M₂] : Unique (M₁ →SL[σ₁₂] M₂) :=
coe_injective.unique
#align continuous_linear_map.unique_of_right ContinuousLinearMap.uniqueOfRight
+-/
+/- warning: continuous_linear_map.exists_ne_zero -> ContinuousLinearMap.exists_ne_zero 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 continuous_linear_map.exists_ne_zero ContinuousLinearMap.exists_ne_zeroₓ'. -/
theorem exists_ne_zero {f : M₁ →SL[σ₁₂] M₂} (hf : f ≠ 0) : ∃ x, f x ≠ 0 :=
by
by_contra' h
@@ -737,39 +1064,69 @@ section
variable (R₁ M₁)
+#print ContinuousLinearMap.id /-
/-- the identity map as a continuous linear map. -/
def id : M₁ →L[R₁] M₁ :=
⟨LinearMap.id, continuous_id⟩
#align continuous_linear_map.id ContinuousLinearMap.id
+-/
end
instance : One (M₁ →L[R₁] M₁) :=
⟨id R₁ M₁⟩
+#print ContinuousLinearMap.one_def /-
theorem one_def : (1 : M₁ →L[R₁] M₁) = id R₁ M₁ :=
rfl
#align continuous_linear_map.one_def ContinuousLinearMap.one_def
+-/
+/- warning: continuous_linear_map.id_apply -> ContinuousLinearMap.id_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.id_apply ContinuousLinearMap.id_applyₓ'. -/
theorem id_apply (x : M₁) : id R₁ M₁ x = x :=
rfl
#align continuous_linear_map.id_apply ContinuousLinearMap.id_apply
+#print ContinuousLinearMap.coe_id /-
@[simp, norm_cast]
theorem coe_id : (id R₁ M₁ : M₁ →ₗ[R₁] M₁) = LinearMap.id :=
rfl
#align continuous_linear_map.coe_id ContinuousLinearMap.coe_id
+-/
+/- warning: continuous_linear_map.coe_id' -> ContinuousLinearMap.coe_id' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_id' ContinuousLinearMap.coe_id'ₓ'. -/
@[simp, norm_cast]
theorem coe_id' : ⇑(id R₁ M₁) = id :=
rfl
#align continuous_linear_map.coe_id' ContinuousLinearMap.coe_id'
+/- warning: continuous_linear_map.coe_eq_id -> ContinuousLinearMap.coe_eq_id is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_eq_id ContinuousLinearMap.coe_eq_idₓ'. -/
@[simp, norm_cast]
theorem coe_eq_id {f : M₁ →L[R₁] M₁} : (f : M₁ →ₗ[R₁] M₁) = LinearMap.id ↔ f = id _ _ := by
rw [← coe_id, coe_inj]
#align continuous_linear_map.coe_eq_id ContinuousLinearMap.coe_eq_id
+/- warning: continuous_linear_map.one_apply -> ContinuousLinearMap.one_apply is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] (x : M₁), Eq.{succ u2} M₁ (coeFn.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) => M₁ -> M₁) (ContinuousLinearMap.toFun.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (OfNat.ofNat.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) 1 (OfNat.mk.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) 1 (One.one.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.one.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14)))) x) x
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.one_apply ContinuousLinearMap.one_applyₓ'. -/
@[simp]
theorem one_apply (x : M₁) : (1 : M₁ →L[R₁] M₁) x = x :=
rfl
@@ -782,16 +1139,34 @@ variable [ContinuousAdd M₂]
instance : Add (M₁ →SL[σ₁₂] M₂) :=
⟨fun f g => ⟨f + g, f.2.add g.2⟩⟩
+/- warning: continuous_linear_map.add_apply -> ContinuousLinearMap.add_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) g x))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.add_apply ContinuousLinearMap.add_applyₓ'. -/
@[simp]
theorem add_apply (f g : M₁ →SL[σ₁₂] M₂) (x : M₁) : (f + g) x = f x + g x :=
rfl
#align continuous_linear_map.add_apply ContinuousLinearMap.add_apply
+/- warning: continuous_linear_map.coe_add -> ContinuousLinearMap.coe_add is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_add ContinuousLinearMap.coe_addₓ'. -/
@[simp, norm_cast]
theorem coe_add (f g : M₁ →SL[σ₁₂] M₂) : (↑(f + g) : M₁ →ₛₗ[σ₁₂] M₂) = f + g :=
rfl
#align continuous_linear_map.coe_add ContinuousLinearMap.coe_add
+/- warning: continuous_linear_map.coe_add' -> ContinuousLinearMap.coe_add' is a dubious translation:
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+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] [_inst_18 : ContinuousAdd.{u1} M₂ _inst_8 (AddZeroClass.toAdd.{u1} M₂ (AddMonoid.toAddZeroClass.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)))] (f : ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (g : ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : M₁), (fun 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max u2 u1, max u2 u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.add.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 _inst_18)) f g)) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) ᾰ) (forall (ᾰ : M₁), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) ᾰ) (forall (ᾰ : M₁), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) 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_inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) g))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_add' ContinuousLinearMap.coe_add'ₓ'. -/
@[norm_cast]
theorem coe_add' (f g : M₁ →SL[σ₁₂] M₂) : ⇑(f + g) = f + g :=
rfl
@@ -817,17 +1192,35 @@ instance : AddCommMonoid (M₁ →SL[σ₁₂] M₂)
ext
simp [Nat.succ_eq_one_add, add_smul]
+/- warning: continuous_linear_map.coe_sum -> ContinuousLinearMap.coe_sum 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 continuous_linear_map.coe_sum ContinuousLinearMap.coe_sumₓ'. -/
@[simp, norm_cast]
theorem coe_sum {ι : Type _} (t : Finset ι) (f : ι → M₁ →SL[σ₁₂] M₂) :
↑(∑ d in t, f d) = (∑ d in t, f d : M₁ →ₛₗ[σ₁₂] M₂) :=
(AddMonoidHom.mk (coe : (M₁ →SL[σ₁₂] M₂) → M₁ →ₛₗ[σ₁₂] M₂) rfl fun _ _ => rfl).map_sum _ _
#align continuous_linear_map.coe_sum ContinuousLinearMap.coe_sum
+/- warning: continuous_linear_map.coe_sum' -> ContinuousLinearMap.coe_sum' 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 continuous_linear_map.coe_sum' ContinuousLinearMap.coe_sum'ₓ'. -/
@[simp, norm_cast]
theorem coe_sum' {ι : Type _} (t : Finset ι) (f : ι → M₁ →SL[σ₁₂] M₂) :
⇑(∑ d in t, f d) = ∑ d in t, f d := by simp only [← coe_coe, coe_sum, LinearMap.coeFn_sum]
#align continuous_linear_map.coe_sum' ContinuousLinearMap.coe_sum'
+/- warning: continuous_linear_map.sum_apply -> ContinuousLinearMap.sum_apply 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 continuous_linear_map.sum_apply ContinuousLinearMap.sum_applyₓ'. -/
theorem sum_apply {ι : Type _} (t : Finset ι) (f : ι → M₁ →SL[σ₁₂] M₂) (b : M₁) :
(∑ d in t, f d) b = ∑ d in t, f d b := by simp only [coe_sum', Finset.sum_apply]
#align continuous_linear_map.sum_apply ContinuousLinearMap.sum_apply
@@ -836,16 +1229,24 @@ end Add
variable [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃]
+#print ContinuousLinearMap.comp /-
/-- Composition of bounded linear maps. -/
def comp (g : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) : M₁ →SL[σ₁₃] M₃ :=
⟨(g : M₂ →ₛₗ[σ₂₃] M₃).comp ↑f, g.2.comp f.2⟩
#align continuous_linear_map.comp ContinuousLinearMap.comp
+-/
-- mathport name: «expr ∘L »
infixr:80 " ∘L " =>
@ContinuousLinearMap.comp _ _ _ _ _ _ (RingHom.id _) (RingHom.id _) (RingHom.id _) _ _ _ _ _ _ _ _
_ _ _ _ RingHomCompTriple.ids
+/- warning: continuous_linear_map.coe_comp -> ContinuousLinearMap.coe_comp is a dubious translation:
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+but is expected to have type
+ forall {R₁ : Type.{u2}} {R₂ : Type.{u6}} {R₃ : Type.{u5}} [_inst_1 : Semiring.{u2} R₁] [_inst_2 : Semiring.{u6} R₂] [_inst_3 : Semiring.{u5} R₃] {σ₁₂ : RingHom.{u2, u6} R₁ R₂ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2)} {σ₂₃ : RingHom.{u6, u5} R₂ R₃ (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u5} R₃ _inst_3)} {σ₁₃ : RingHom.{u2, u5} R₁ R₃ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u5} R₃ _inst_3)} {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] {M₃ : Type.{u3}} [_inst_10 : TopologicalSpace.{u3} M₃] [_inst_11 : AddCommMonoid.{u3} M₃] [_inst_14 : Module.{u2, u1} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u6, u4} R₂ M₂ _inst_2 _inst_9] [_inst_17 : Module.{u5, u3} R₃ M₃ _inst_3 _inst_11] [_inst_18 : RingHomCompTriple.{u2, u6, u5} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] (h : ContinuousLinearMap.{u6, u5, u4, u3} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17) (f : ContinuousLinearMap.{u2, u6, u1, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u1) (succ u3)} (LinearMap.{u2, u5, u1, u3} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ M₃ _inst_5 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.toLinearMap.{u2, u5, u1, u3} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17 (ContinuousLinearMap.comp.{u2, u6, u5, u1, u4, u3} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_16 _inst_17 _inst_18 h f)) (LinearMap.comp.{u2, u6, u5, u1, u4, u3} R₁ R₂ R₃ M₁ M₂ M₃ _inst_1 _inst_2 _inst_3 _inst_5 _inst_9 _inst_11 _inst_14 _inst_16 _inst_17 σ₁₂ σ₂₃ σ₁₃ _inst_18 (ContinuousLinearMap.toLinearMap.{u6, u5, u4, u3} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17 h) (ContinuousLinearMap.toLinearMap.{u2, u6, u1, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_comp ContinuousLinearMap.coe_compₓ'. -/
@[simp, norm_cast]
theorem coe_comp (h : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) :
(h.comp f : M₁ →ₛₗ[σ₁₃] M₃) = (h : M₂ →ₛₗ[σ₂₃] M₃).comp (f : M₁ →ₛₗ[σ₁₂] M₂) :=
@@ -854,22 +1255,46 @@ theorem coe_comp (h : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂)
include σ₁₃
+/- warning: continuous_linear_map.coe_comp' -> ContinuousLinearMap.coe_comp' is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_comp' ContinuousLinearMap.coe_comp'ₓ'. -/
@[simp, norm_cast]
theorem coe_comp' (h : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) : ⇑(h.comp f) = h ∘ f :=
rfl
#align continuous_linear_map.coe_comp' ContinuousLinearMap.coe_comp'
+/- warning: continuous_linear_map.comp_apply -> ContinuousLinearMap.comp_apply is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_apply ContinuousLinearMap.comp_applyₓ'. -/
theorem comp_apply (g : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) (x : M₁) : (g.comp f) x = g (f x) :=
rfl
#align continuous_linear_map.comp_apply ContinuousLinearMap.comp_apply
omit σ₁₃
+/- warning: continuous_linear_map.comp_id -> ContinuousLinearMap.comp_id is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] [_inst_14 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_9] (f : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.comp.{u1, u1, u2, u3, u3, u4} R₁ R₁ R₂ _inst_1 _inst_1 _inst_2 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) σ₁₂ σ₁₂ M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_14 _inst_16 (RingHomCompTriple.ids.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂) f (ContinuousLinearMap.id.{u1, u3} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14)) f
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] (f : ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.comp.{u4, u4, u3, u2, u2, u1} R₁ R₁ R₂ _inst_1 _inst_1 _inst_2 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) σ₁₂ σ₁₂ M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_14 _inst_16 (RingHomCompTriple.ids.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂) f (ContinuousLinearMap.id.{u4, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14)) f
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_id ContinuousLinearMap.comp_idₓ'. -/
@[simp]
theorem comp_id (f : M₁ →SL[σ₁₂] M₂) : f.comp (id R₁ M₁) = f :=
ext fun x => rfl
#align continuous_linear_map.comp_id ContinuousLinearMap.comp_id
+/- warning: continuous_linear_map.id_comp -> ContinuousLinearMap.id_comp is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] [_inst_14 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_9] (f : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.comp.{u1, u2, u2, u3, u4, u4} R₁ R₂ R₂ _inst_1 _inst_2 _inst_2 σ₁₂ (RingHom.id.{u2} R₂ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)) σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₂ _inst_8 _inst_9 _inst_14 _inst_16 _inst_16 (RingHomCompTriple.right_ids.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂) (ContinuousLinearMap.id.{u2, u4} R₂ _inst_2 M₂ _inst_8 _inst_9 _inst_16) f) f
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] (f : ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.comp.{u4, u3, u3, u2, u1, u1} R₁ R₂ R₂ _inst_1 _inst_2 _inst_2 σ₁₂ (RingHom.id.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₂ _inst_8 _inst_9 _inst_14 _inst_16 _inst_16 (RingHomCompTriple.right_ids.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂) (ContinuousLinearMap.id.{u3, u1} R₂ _inst_2 M₂ _inst_8 _inst_9 _inst_16) f) f
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.id_comp ContinuousLinearMap.id_compₓ'. -/
@[simp]
theorem id_comp (f : M₁ →SL[σ₁₂] M₂) : (id R₂ M₂).comp f = f :=
ext fun x => rfl
@@ -877,6 +1302,12 @@ theorem id_comp (f : M₁ →SL[σ₁₂] M₂) : (id R₂ M₂).comp f = f :=
include σ₁₃
+/- warning: continuous_linear_map.comp_zero -> ContinuousLinearMap.comp_zero is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} {R₃ : Type.{u3}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : Semiring.{u3} R₃] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₃ : RingHom.{u2, u3} R₂ R₃ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {σ₁₃ : RingHom.{u1, u3} R₁ R₃ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {M₁ : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} M₁] [_inst_5 : AddCommMonoid.{u4} M₁] {M₂ : Type.{u5}} [_inst_8 : TopologicalSpace.{u5} M₂] [_inst_9 : AddCommMonoid.{u5} M₂] {M₃ : Type.{u6}} [_inst_10 : TopologicalSpace.{u6} M₃] [_inst_11 : AddCommMonoid.{u6} M₃] [_inst_14 : Module.{u1, u4} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u5} R₂ M₂ _inst_2 _inst_9] [_inst_17 : Module.{u3, u6} R₃ M₃ _inst_3 _inst_11] [_inst_18 : RingHomCompTriple.{u1, u2, u3} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] (g : ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17), Eq.{max (succ u4) (succ u6)} (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_16 _inst_17 _inst_18 g (OfNat.ofNat.{max u4 u5} (ContinuousLinearMap.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) 0 (OfNat.mk.{max u4 u5} (ContinuousLinearMap.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) 0 (Zero.zero.{max u4 u5} (ContinuousLinearMap.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.zero.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))))) (OfNat.ofNat.{max u4 u6} (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) 0 (OfNat.mk.{max u4 u6} (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) 0 (Zero.zero.{max u4 u6} (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.zero.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17))))
+but is expected to have type
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u6}} {R₃ : Type.{u5}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u6} R₂] [_inst_3 : Semiring.{u5} R₃] {σ₁₂ : RingHom.{u1, u6} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2)} {σ₂₃ : RingHom.{u6, u5} R₂ R₃ (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u5} R₃ _inst_3)} {σ₁₃ : RingHom.{u1, u5} R₁ R₃ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u5} R₃ _inst_3)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] {M₃ : Type.{u3}} [_inst_10 : TopologicalSpace.{u3} M₃] [_inst_11 : AddCommMonoid.{u3} M₃] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u6, u4} R₂ M₂ _inst_2 _inst_9] [_inst_17 : Module.{u5, u3} R₃ M₃ _inst_3 _inst_11] [_inst_18 : RingHomCompTriple.{u1, u6, u5} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] (g : ContinuousLinearMap.{u6, u5, u4, u3} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u5, u2, u3} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.comp.{u1, u6, u5, u2, u4, u3} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_16 _inst_17 _inst_18 g (OfNat.ofNat.{max u2 u4} (ContinuousLinearMap.{u1, u6, u2, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) 0 (Zero.toOfNat0.{max u2 u4} (ContinuousLinearMap.{u1, u6, u2, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.zero.{u1, u6, u2, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16)))) (OfNat.ofNat.{max u2 u3} (ContinuousLinearMap.{u1, u5, u2, u3} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) 0 (Zero.toOfNat0.{max u2 u3} (ContinuousLinearMap.{u1, u5, u2, u3} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.zero.{u1, u5, u2, u3} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17)))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_zero ContinuousLinearMap.comp_zeroₓ'. -/
@[simp]
theorem comp_zero (g : M₂ →SL[σ₂₃] M₃) : g.comp (0 : M₁ →SL[σ₁₂] M₂) = 0 :=
by
@@ -884,6 +1315,12 @@ theorem comp_zero (g : M₂ →SL[σ₂₃] M₃) : g.comp (0 : M₁ →SL[σ₁
simp
#align continuous_linear_map.comp_zero ContinuousLinearMap.comp_zero
+/- warning: continuous_linear_map.zero_comp -> ContinuousLinearMap.zero_comp is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} {R₃ : Type.{u3}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : Semiring.{u3} R₃] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₃ : RingHom.{u2, u3} R₂ R₃ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {σ₁₃ : RingHom.{u1, u3} R₁ R₃ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {M₁ : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} M₁] [_inst_5 : AddCommMonoid.{u4} M₁] {M₂ : Type.{u5}} [_inst_8 : TopologicalSpace.{u5} M₂] [_inst_9 : AddCommMonoid.{u5} M₂] {M₃ : Type.{u6}} [_inst_10 : TopologicalSpace.{u6} M₃] [_inst_11 : AddCommMonoid.{u6} M₃] [_inst_14 : Module.{u1, u4} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u5} R₂ M₂ _inst_2 _inst_9] [_inst_17 : Module.{u3, u6} R₃ M₃ _inst_3 _inst_11] [_inst_18 : RingHomCompTriple.{u1, u2, u3} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] (f : ContinuousLinearMap.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u4) (succ u6)} (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_16 _inst_17 _inst_18 (OfNat.ofNat.{max u5 u6} (ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17) 0 (OfNat.mk.{max u5 u6} (ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17) 0 (Zero.zero.{max u5 u6} (ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17) (ContinuousLinearMap.zero.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17)))) f) (OfNat.ofNat.{max u4 u6} (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) 0 (OfNat.mk.{max u4 u6} (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) 0 (Zero.zero.{max u4 u6} (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.zero.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17))))
+but is expected to have type
+ forall {R₁ : Type.{u6}} {R₂ : Type.{u5}} {R₃ : Type.{u1}} [_inst_1 : Semiring.{u6} R₁] [_inst_2 : Semiring.{u5} R₂] [_inst_3 : Semiring.{u1} R₃] {σ₁₂ : RingHom.{u6, u5} R₁ R₂ (Semiring.toNonAssocSemiring.{u6} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u5} R₂ _inst_2)} {σ₂₃ : RingHom.{u5, u1} R₂ R₃ (Semiring.toNonAssocSemiring.{u5} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₃ _inst_3)} {σ₁₃ : RingHom.{u6, u1} R₁ R₃ (Semiring.toNonAssocSemiring.{u6} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u1} R₃ _inst_3)} {M₁ : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} M₁] [_inst_5 : AddCommMonoid.{u4} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u2}} [_inst_10 : TopologicalSpace.{u2} M₃] [_inst_11 : AddCommMonoid.{u2} M₃] [_inst_14 : Module.{u6, u4} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u5, u3} R₂ M₂ _inst_2 _inst_9] [_inst_17 : Module.{u1, u2} R₃ M₃ _inst_3 _inst_11] [_inst_18 : RingHomCompTriple.{u6, u5, u1} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] (f : ContinuousLinearMap.{u6, u5, u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u4) (succ u2)} (ContinuousLinearMap.{u6, u1, u4, u2} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.comp.{u6, u5, u1, u4, u3, u2} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_16 _inst_17 _inst_18 (OfNat.ofNat.{max u3 u2} (ContinuousLinearMap.{u5, u1, u3, u2} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17) 0 (Zero.toOfNat0.{max u3 u2} (ContinuousLinearMap.{u5, u1, u3, u2} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17) (ContinuousLinearMap.zero.{u5, u1, u3, u2} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17))) f) (OfNat.ofNat.{max u4 u2} (ContinuousLinearMap.{u6, u1, u4, u2} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) 0 (Zero.toOfNat0.{max u4 u2} (ContinuousLinearMap.{u6, u1, u4, u2} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.zero.{u6, u1, u4, u2} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17)))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.zero_comp ContinuousLinearMap.zero_compₓ'. -/
@[simp]
theorem zero_comp (f : M₁ →SL[σ₁₂] M₂) : (0 : M₂ →SL[σ₂₃] M₃).comp f = 0 :=
by
@@ -891,6 +1328,12 @@ theorem zero_comp (f : M₁ →SL[σ₁₂] M₂) : (0 : M₂ →SL[σ₂₃] M
simp
#align continuous_linear_map.zero_comp ContinuousLinearMap.zero_comp
+/- warning: continuous_linear_map.comp_add -> ContinuousLinearMap.comp_add is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} {R₃ : Type.{u3}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : Semiring.{u3} R₃] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₃ : RingHom.{u2, u3} R₂ R₃ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {σ₁₃ : RingHom.{u1, u3} R₁ R₃ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {M₁ : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} M₁] [_inst_5 : AddCommMonoid.{u4} M₁] {M₂ : Type.{u5}} [_inst_8 : TopologicalSpace.{u5} M₂] [_inst_9 : AddCommMonoid.{u5} M₂] {M₃ : Type.{u6}} [_inst_10 : TopologicalSpace.{u6} M₃] [_inst_11 : AddCommMonoid.{u6} M₃] [_inst_14 : Module.{u1, u4} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u5} R₂ M₂ _inst_2 _inst_9] [_inst_17 : Module.{u3, u6} R₃ M₃ _inst_3 _inst_11] [_inst_18 : RingHomCompTriple.{u1, u2, u3} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] [_inst_19 : ContinuousAdd.{u5} M₂ _inst_8 (AddZeroClass.toHasAdd.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_9)))] [_inst_20 : ContinuousAdd.{u6} M₃ _inst_10 (AddZeroClass.toHasAdd.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_11)))] (g : ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17) (f₁ : ContinuousLinearMap.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (f₂ : ContinuousLinearMap.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u4) (succ u6)} (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_16 _inst_17 _inst_18 g (HAdd.hAdd.{max u4 u5, max u4 u5, max u4 u5} (ContinuousLinearMap.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (instHAdd.{max u4 u5} (ContinuousLinearMap.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.add.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 _inst_19)) f₁ f₂)) (HAdd.hAdd.{max u4 u6, max u4 u6, max u4 u6} (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (instHAdd.{max u4 u6} (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.add.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17 _inst_20)) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_16 _inst_17 _inst_18 g f₁) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_16 _inst_17 _inst_18 g f₂))
+but is expected to have type
+ forall {R₁ : Type.{u2}} {R₂ : Type.{u4}} {R₃ : Type.{u3}} [_inst_1 : Semiring.{u2} R₁] [_inst_2 : Semiring.{u4} R₂] [_inst_3 : Semiring.{u3} R₃] {σ₁₂ : RingHom.{u2, u4} R₁ R₂ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u4} R₂ _inst_2)} {σ₂₃ : RingHom.{u4, u3} R₂ R₃ (Semiring.toNonAssocSemiring.{u4} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {σ₁₃ : RingHom.{u2, u3} R₁ R₃ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] {M₂ : Type.{u6}} [_inst_8 : TopologicalSpace.{u6} M₂] [_inst_9 : AddCommMonoid.{u6} M₂] {M₃ : Type.{u5}} [_inst_10 : TopologicalSpace.{u5} M₃] [_inst_11 : AddCommMonoid.{u5} M₃] [_inst_14 : Module.{u2, u1} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u4, u6} R₂ M₂ _inst_2 _inst_9] [_inst_17 : Module.{u3, u5} R₃ M₃ _inst_3 _inst_11] [_inst_18 : RingHomCompTriple.{u2, u4, u3} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] [_inst_19 : ContinuousAdd.{u6} M₂ _inst_8 (AddZeroClass.toAdd.{u6} M₂ (AddMonoid.toAddZeroClass.{u6} M₂ (AddCommMonoid.toAddMonoid.{u6} M₂ _inst_9)))] [_inst_20 : ContinuousAdd.{u5} M₃ _inst_10 (AddZeroClass.toAdd.{u5} M₃ (AddMonoid.toAddZeroClass.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_11)))] (g : ContinuousLinearMap.{u4, u3, u6, u5} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17) (f₁ : ContinuousLinearMap.{u2, u4, u1, u6} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (f₂ : ContinuousLinearMap.{u2, u4, u1, u6} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u1) (succ u5)} (ContinuousLinearMap.{u2, u3, u1, u5} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.comp.{u2, u4, u3, u1, u6, u5} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_16 _inst_17 _inst_18 g (HAdd.hAdd.{max u1 u6, max u1 u6, max u1 u6} (ContinuousLinearMap.{u2, u4, u1, u6} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.{u2, u4, u1, u6} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.{u2, u4, u1, u6} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (instHAdd.{max u1 u6} (ContinuousLinearMap.{u2, u4, u1, u6} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousLinearMap.add.{u2, u4, u1, u6} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 _inst_19)) f₁ f₂)) (HAdd.hAdd.{max u1 u5, max u1 u5, max u1 u5} (ContinuousLinearMap.{u2, u3, u1, u5} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.{u2, u3, u1, u5} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.{u2, u3, u1, u5} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (instHAdd.{max u1 u5} (ContinuousLinearMap.{u2, u3, u1, u5} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.add.{u2, u3, u1, u5} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17 _inst_20)) (ContinuousLinearMap.comp.{u2, u4, u3, u1, u6, u5} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_16 _inst_17 _inst_18 g f₁) (ContinuousLinearMap.comp.{u2, u4, u3, u1, u6, u5} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_16 _inst_17 _inst_18 g f₂))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_add ContinuousLinearMap.comp_addₓ'. -/
@[simp]
theorem comp_add [ContinuousAdd M₂] [ContinuousAdd M₃] (g : M₂ →SL[σ₂₃] M₃)
(f₁ f₂ : M₁ →SL[σ₁₂] M₂) : g.comp (f₁ + f₂) = g.comp f₁ + g.comp f₂ :=
@@ -899,6 +1342,12 @@ theorem comp_add [ContinuousAdd M₂] [ContinuousAdd M₃] (g : M₂ →SL[σ₂
simp
#align continuous_linear_map.comp_add ContinuousLinearMap.comp_add
+/- warning: continuous_linear_map.add_comp -> ContinuousLinearMap.add_comp is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} {R₃ : Type.{u3}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : Semiring.{u3} R₃] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₃ : RingHom.{u2, u3} R₂ R₃ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {σ₁₃ : RingHom.{u1, u3} R₁ R₃ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {M₁ : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} M₁] [_inst_5 : AddCommMonoid.{u4} M₁] {M₂ : Type.{u5}} [_inst_8 : TopologicalSpace.{u5} M₂] [_inst_9 : AddCommMonoid.{u5} M₂] {M₃ : Type.{u6}} [_inst_10 : TopologicalSpace.{u6} M₃] [_inst_11 : AddCommMonoid.{u6} M₃] [_inst_14 : Module.{u1, u4} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u5} R₂ M₂ _inst_2 _inst_9] [_inst_17 : Module.{u3, u6} R₃ M₃ _inst_3 _inst_11] [_inst_18 : RingHomCompTriple.{u1, u2, u3} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] [_inst_19 : ContinuousAdd.{u6} M₃ _inst_10 (AddZeroClass.toHasAdd.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_11)))] (g₁ : ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17) (g₂ : ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17) (f : ContinuousLinearMap.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u4) (succ u6)} (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_16 _inst_17 _inst_18 (HAdd.hAdd.{max u5 u6, max u5 u6, max u5 u6} (ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17) (ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17) (ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17) (instHAdd.{max u5 u6} (ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17) (ContinuousLinearMap.add.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17 _inst_19)) g₁ g₂) f) (HAdd.hAdd.{max u4 u6, max u4 u6, max u4 u6} (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (instHAdd.{max u4 u6} (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.add.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17 _inst_19)) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_16 _inst_17 _inst_18 g₁ f) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_16 _inst_17 _inst_18 g₂ f))
+but is expected to have type
+ forall {R₁ : Type.{u2}} {R₂ : Type.{u5}} {R₃ : Type.{u4}} [_inst_1 : Semiring.{u2} R₁] [_inst_2 : Semiring.{u5} R₂] [_inst_3 : Semiring.{u4} R₃] {σ₁₂ : RingHom.{u2, u5} R₁ R₂ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u5} R₂ _inst_2)} {σ₂₃ : RingHom.{u5, u4} R₂ R₃ (Semiring.toNonAssocSemiring.{u5} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3)} {σ₁₃ : RingHom.{u2, u4} R₁ R₃ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3)} {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u6}} [_inst_10 : TopologicalSpace.{u6} M₃] [_inst_11 : AddCommMonoid.{u6} M₃] [_inst_14 : Module.{u2, u1} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u5, u3} R₂ M₂ _inst_2 _inst_9] [_inst_17 : Module.{u4, u6} R₃ M₃ _inst_3 _inst_11] [_inst_18 : RingHomCompTriple.{u2, u5, u4} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] [_inst_19 : ContinuousAdd.{u6} M₃ _inst_10 (AddZeroClass.toAdd.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_11)))] (g₁ : ContinuousLinearMap.{u5, u4, u3, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17) (g₂ : ContinuousLinearMap.{u5, u4, u3, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17) (f : ContinuousLinearMap.{u2, u5, u1, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u1) (succ u6)} (ContinuousLinearMap.{u2, u4, u1, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.comp.{u2, u5, u4, u1, u3, u6} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_16 _inst_17 _inst_18 (HAdd.hAdd.{max u3 u6, max u3 u6, max u3 u6} (ContinuousLinearMap.{u5, u4, u3, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17) (ContinuousLinearMap.{u5, u4, u3, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17) (ContinuousLinearMap.{u5, u4, u3, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17) (instHAdd.{max u3 u6} (ContinuousLinearMap.{u5, u4, u3, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17) (ContinuousLinearMap.add.{u5, u4, u3, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17 _inst_19)) g₁ g₂) f) (HAdd.hAdd.{max u1 u6, max u1 u6, max u1 u6} (ContinuousLinearMap.{u2, u4, u1, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.{u2, u4, u1, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.{u2, u4, u1, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (instHAdd.{max u1 u6} (ContinuousLinearMap.{u2, u4, u1, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17) (ContinuousLinearMap.add.{u2, u4, u1, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_17 _inst_19)) (ContinuousLinearMap.comp.{u2, u5, u4, u1, u3, u6} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_16 _inst_17 _inst_18 g₁ f) (ContinuousLinearMap.comp.{u2, u5, u4, u1, u3, u6} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_16 _inst_17 _inst_18 g₂ f))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.add_comp ContinuousLinearMap.add_compₓ'. -/
@[simp]
theorem add_comp [ContinuousAdd M₃] (g₁ g₂ : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) :
(g₁ + g₂).comp f = g₁.comp f + g₂.comp f := by
@@ -908,6 +1357,12 @@ theorem add_comp [ContinuousAdd M₃] (g₁ g₂ : M₂ →SL[σ₂₃] M₃) (f
omit σ₁₃
+/- warning: continuous_linear_map.comp_assoc -> ContinuousLinearMap.comp_assoc is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} {R₃ : Type.{u3}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : Semiring.{u3} R₃] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₃ : RingHom.{u2, u3} R₂ R₃ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {σ₁₃ : RingHom.{u1, u3} R₁ R₃ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {M₁ : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} M₁] [_inst_5 : AddCommMonoid.{u4} M₁] {M₂ : Type.{u5}} [_inst_8 : TopologicalSpace.{u5} M₂] [_inst_9 : AddCommMonoid.{u5} M₂] {M₃ : Type.{u6}} [_inst_10 : TopologicalSpace.{u6} M₃] [_inst_11 : AddCommMonoid.{u6} M₃] {M₄ : Type.{u7}} [_inst_12 : TopologicalSpace.{u7} M₄] [_inst_13 : AddCommMonoid.{u7} M₄] [_inst_14 : Module.{u1, u4} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u5} R₂ M₂ _inst_2 _inst_9] [_inst_17 : Module.{u3, u6} R₃ M₃ _inst_3 _inst_11] [_inst_18 : RingHomCompTriple.{u1, u2, u3} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] {R₄ : Type.{u8}} [_inst_19 : Semiring.{u8} R₄] [_inst_20 : Module.{u8, u7} R₄ M₄ _inst_19 _inst_13] {σ₁₄ : RingHom.{u1, u8} R₁ R₄ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u8} R₄ _inst_19)} {σ₂₄ : RingHom.{u2, u8} R₂ R₄ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u8} R₄ _inst_19)} {σ₃₄ : RingHom.{u3, u8} R₃ R₄ (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3) (Semiring.toNonAssocSemiring.{u8} R₄ _inst_19)} [_inst_21 : RingHomCompTriple.{u1, u3, u8} R₁ R₃ R₄ _inst_1 _inst_3 _inst_19 σ₁₃ σ₃₄ σ₁₄] [_inst_22 : RingHomCompTriple.{u2, u3, u8} R₂ R₃ R₄ _inst_2 _inst_3 _inst_19 σ₂₃ σ₃₄ σ₂₄] [_inst_23 : RingHomCompTriple.{u1, u2, u8} R₁ R₂ R₄ _inst_1 _inst_2 _inst_19 σ₁₂ σ₂₄ σ₁₄] (h : ContinuousLinearMap.{u3, u8, u6, u7} R₃ R₄ _inst_3 _inst_19 σ₃₄ M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_17 _inst_20) (g : ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17) (f : ContinuousLinearMap.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u4) (succ u7)} (ContinuousLinearMap.{u1, u8, u4, u7} R₁ R₄ _inst_1 _inst_19 σ₁₄ M₁ _inst_4 _inst_5 M₄ _inst_12 _inst_13 _inst_14 _inst_20) (ContinuousLinearMap.comp.{u1, u2, u8, u4, u5, u7} R₁ R₂ R₄ _inst_1 _inst_2 _inst_19 σ₁₂ σ₂₄ σ₁₄ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₄ _inst_12 _inst_13 _inst_14 _inst_16 _inst_20 _inst_23 (ContinuousLinearMap.comp.{u2, u3, u8, u5, u6, u7} R₂ R₃ R₄ _inst_2 _inst_3 _inst_19 σ₂₃ σ₃₄ σ₂₄ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_16 _inst_17 _inst_20 _inst_22 h g) f) (ContinuousLinearMap.comp.{u1, u3, u8, u4, u6, u7} R₁ R₃ R₄ _inst_1 _inst_3 _inst_19 σ₁₃ σ₃₄ σ₁₄ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_14 _inst_17 _inst_20 _inst_21 h (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_16 _inst_17 _inst_18 g f))
+but is expected to have type
+ forall {R₁ : Type.{u6}} {R₂ : Type.{u5}} {R₃ : Type.{u4}} [_inst_1 : Semiring.{u6} R₁] [_inst_2 : Semiring.{u5} R₂] [_inst_3 : Semiring.{u4} R₃] {σ₁₂ : RingHom.{u6, u5} R₁ R₂ (Semiring.toNonAssocSemiring.{u6} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u5} R₂ _inst_2)} {σ₂₃ : RingHom.{u5, u4} R₂ R₃ (Semiring.toNonAssocSemiring.{u5} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3)} {σ₁₃ : RingHom.{u6, u4} R₁ R₃ (Semiring.toNonAssocSemiring.{u6} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3)} {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] {M₂ : Type.{u2}} [_inst_8 : TopologicalSpace.{u2} M₂] [_inst_9 : AddCommMonoid.{u2} M₂] {M₃ : Type.{u3}} [_inst_10 : TopologicalSpace.{u3} M₃] [_inst_11 : AddCommMonoid.{u3} M₃] {M₄ : Type.{u7}} [_inst_12 : TopologicalSpace.{u7} M₄] [_inst_13 : AddCommMonoid.{u7} M₄] [_inst_14 : Module.{u6, u1} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u5, u2} R₂ M₂ _inst_2 _inst_9] [_inst_17 : Module.{u4, u3} R₃ M₃ _inst_3 _inst_11] [_inst_18 : RingHomCompTriple.{u6, u5, u4} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] {R₄ : Type.{u8}} [_inst_19 : Semiring.{u8} R₄] [_inst_20 : Module.{u8, u7} R₄ M₄ _inst_19 _inst_13] {σ₁₄ : RingHom.{u6, u8} R₁ R₄ (Semiring.toNonAssocSemiring.{u6} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u8} R₄ _inst_19)} {σ₂₄ : RingHom.{u5, u8} R₂ R₄ (Semiring.toNonAssocSemiring.{u5} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u8} R₄ _inst_19)} {σ₃₄ : RingHom.{u4, u8} R₃ R₄ (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3) (Semiring.toNonAssocSemiring.{u8} R₄ _inst_19)} [_inst_21 : RingHomCompTriple.{u6, u4, u8} R₁ R₃ R₄ _inst_1 _inst_3 _inst_19 σ₁₃ σ₃₄ σ₁₄] [_inst_22 : RingHomCompTriple.{u5, u4, u8} R₂ R₃ R₄ _inst_2 _inst_3 _inst_19 σ₂₃ σ₃₄ σ₂₄] [_inst_23 : RingHomCompTriple.{u6, u5, u8} R₁ R₂ R₄ _inst_1 _inst_2 _inst_19 σ₁₂ σ₂₄ σ₁₄] (h : ContinuousLinearMap.{u4, u8, u3, u7} R₃ R₄ _inst_3 _inst_19 σ₃₄ M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_17 _inst_20) (g : ContinuousLinearMap.{u5, u4, u2, u3} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_16 _inst_17) (f : ContinuousLinearMap.{u6, u5, u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16), Eq.{max (succ u1) (succ u7)} (ContinuousLinearMap.{u6, u8, u1, u7} R₁ R₄ _inst_1 _inst_19 σ₁₄ M₁ _inst_4 _inst_5 M₄ _inst_12 _inst_13 _inst_14 _inst_20) (ContinuousLinearMap.comp.{u6, u5, u8, u1, u2, u7} R₁ R₂ R₄ _inst_1 _inst_2 _inst_19 σ₁₂ σ₂₄ σ₁₄ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₄ _inst_12 _inst_13 _inst_14 _inst_16 _inst_20 _inst_23 (ContinuousLinearMap.comp.{u5, u4, u8, u2, u3, u7} R₂ R₃ R₄ _inst_2 _inst_3 _inst_19 σ₂₃ σ₃₄ σ₂₄ M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_16 _inst_17 _inst_20 _inst_22 h g) f) (ContinuousLinearMap.comp.{u6, u4, u8, u1, u3, u7} R₁ R₃ R₄ _inst_1 _inst_3 _inst_19 σ₁₃ σ₃₄ σ₁₄ M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_14 _inst_17 _inst_20 _inst_21 h (ContinuousLinearMap.comp.{u6, u5, u4, u1, u2, u3} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_16 _inst_17 _inst_18 g f))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_assoc ContinuousLinearMap.comp_assocₓ'. -/
theorem comp_assoc {R₄ : Type _} [Semiring R₄] [Module R₄ M₄] {σ₁₄ : R₁ →+* R₄} {σ₂₄ : R₂ →+* R₄}
{σ₃₄ : R₃ →+* R₄} [RingHomCompTriple σ₁₃ σ₃₄ σ₁₄] [RingHomCompTriple σ₂₃ σ₃₄ σ₂₄]
[RingHomCompTriple σ₁₂ σ₂₄ σ₁₄] (h : M₃ →SL[σ₃₄] M₄) (g : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) :
@@ -918,15 +1373,33 @@ theorem comp_assoc {R₄ : Type _} [Semiring R₄] [Module R₄ M₄] {σ₁₄
instance : Mul (M₁ →L[R₁] M₁) :=
⟨comp⟩
+/- warning: continuous_linear_map.mul_def -> ContinuousLinearMap.mul_def is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] (f : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (g : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14), Eq.{succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (HMul.hMul.{u2, u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (instHMul.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.mul.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14)) f g) (ContinuousLinearMap.comp.{u1, u1, u1, u2, u2, u2} R₁ R₁ R₁ _inst_1 _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14 _inst_14 (RingHomCompTriple.right_ids.{u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) f g)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.mul_def ContinuousLinearMap.mul_defₓ'. -/
theorem mul_def (f g : M₁ →L[R₁] M₁) : f * g = f.comp g :=
rfl
#align continuous_linear_map.mul_def ContinuousLinearMap.mul_def
+/- warning: continuous_linear_map.coe_mul -> ContinuousLinearMap.coe_mul is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] (f : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (g : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14), Eq.{succ u2} (M₁ -> M₁) (coeFn.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) => M₁ -> M₁) (ContinuousLinearMap.toFun.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (HMul.hMul.{u2, u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (instHMul.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.mul.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14)) f g)) (Function.comp.{succ u2, succ u2, succ u2} M₁ M₁ M₁ (coeFn.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) => M₁ -> M₁) (ContinuousLinearMap.toFun.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) f) (coeFn.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) => M₁ -> M₁) (ContinuousLinearMap.toFun.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) g))
+but is expected to have type
+ forall {R₁ : Type.{u2}} [_inst_1 : Semiring.{u2} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_14 : Module.{u2, u1} R₁ M₁ _inst_1 _inst_5] (f : ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (g : ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14), Eq.{succ u1} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₁) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₁) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ M₁ _inst_4 _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14))) (HMul.hMul.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (instHMul.{u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.mul.{u2, u1} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14)) f g)) (Function.comp.{succ u1, succ u1, succ u1} M₁ M₁ M₁ (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₁) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ M₁ _inst_4 _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14))) f) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₁) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ M₁ _inst_4 _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14))) g))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_mul ContinuousLinearMap.coe_mulₓ'. -/
@[simp]
theorem coe_mul (f g : M₁ →L[R₁] M₁) : ⇑(f * g) = f ∘ g :=
rfl
#align continuous_linear_map.coe_mul ContinuousLinearMap.coe_mul
+/- warning: continuous_linear_map.mul_apply -> ContinuousLinearMap.mul_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+ forall {R₁ : Type.{u2}} [_inst_1 : Semiring.{u2} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_14 : Module.{u2, u1} R₁ M₁ _inst_1 _inst_5] (f : ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (g : ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (x : M₁), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₁) x) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₁) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ M₁ _inst_4 _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14))) (HMul.hMul.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (instHMul.{u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.mul.{u2, u1} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14)) f g) x) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₁) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ M₁ _inst_4 _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14))) f (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₁) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ M₁ _inst_4 _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14))) g x))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.mul_apply ContinuousLinearMap.mul_applyₓ'. -/
theorem mul_apply (f g : M₁ →L[R₁] M₁) (x : M₁) : (f * g) x = f (g x) :=
rfl
#align continuous_linear_map.mul_apply ContinuousLinearMap.mul_apply
@@ -950,6 +1423,12 @@ instance [ContinuousAdd M₁] : Semiring (M₁ →L[R₁] M₁) :=
left_distrib := fun f g h => ext fun x => map_add f (g x) (h x)
right_distrib := fun _ _ _ => ext fun _ => LinearMap.add_apply _ _ _ }
+/- warning: continuous_linear_map.to_linear_map_ring_hom -> ContinuousLinearMap.toLinearMapRingHom is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : ContinuousAdd.{u2} M₁ _inst_4 (AddZeroClass.toHasAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)))], RingHom.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (LinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ M₁ _inst_5 _inst_5 _inst_14 _inst_14) (Semiring.toNonAssocSemiring.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.semiring.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19)) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ M₁ _inst_5 _inst_5 _inst_14 _inst_14) (Module.End.semiring.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14))
+but is expected to have type
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : ContinuousAdd.{u2} M₁ _inst_4 (AddZeroClass.toAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)))], RingHom.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (LinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ M₁ _inst_5 _inst_5 _inst_14 _inst_14) (Semiring.toNonAssocSemiring.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.semiring.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19)) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ M₁ _inst_5 _inst_5 _inst_14 _inst_14) (Module.End.semiring.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.to_linear_map_ring_hom ContinuousLinearMap.toLinearMapRingHomₓ'. -/
/-- `continuous_linear_map.to_linear_map` as a `ring_hom`.-/
@[simps]
def toLinearMapRingHom [ContinuousAdd M₁] : (M₁ →L[R₁] M₁) →+* M₁ →ₗ[R₁] M₁
@@ -965,6 +1444,12 @@ section ApplyAction
variable [ContinuousAdd M₁]
+/- warning: continuous_linear_map.apply_module -> ContinuousLinearMap.applyModule is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : ContinuousAdd.{u2} M₁ _inst_4 (AddZeroClass.toHasAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)))], Module.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (ContinuousLinearMap.semiring.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19) _inst_5
+but is expected to have type
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : ContinuousAdd.{u2} M₁ _inst_4 (AddZeroClass.toAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)))], Module.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (ContinuousLinearMap.semiring.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19) _inst_5
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.apply_module ContinuousLinearMap.applyModuleₓ'. -/
/-- The tautological action by `M₁ →L[R₁] M₁` on `M`.
This generalizes `function.End.apply_mul_action`. -/
@@ -972,41 +1457,83 @@ instance applyModule : Module (M₁ →L[R₁] M₁) M₁ :=
Module.compHom _ toLinearMapRingHom
#align continuous_linear_map.apply_module ContinuousLinearMap.applyModule
+/- warning: continuous_linear_map.smul_def -> ContinuousLinearMap.smul_def is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : ContinuousAdd.{u2} M₁ _inst_4 (AddZeroClass.toHasAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)))] (f : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (a : M₁), Eq.{succ u2} M₁ (SMul.smul.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (SMulZeroClass.toHasSmul.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (SMulWithZero.toSmulZeroClass.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (MulZeroClass.toHasZero.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (MulZeroOneClass.toMulZeroClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (MonoidWithZero.toMulZeroOneClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (Semiring.toMonoidWithZero.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.semiring.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19))))) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (MulActionWithZero.toSMulWithZero.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (Semiring.toMonoidWithZero.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.semiring.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19)) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (Module.toMulActionWithZero.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (ContinuousLinearMap.semiring.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19) _inst_5 (ContinuousLinearMap.applyModule.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19))))) f a) (coeFn.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) => M₁ -> M₁) (ContinuousLinearMap.toFun.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) f a)
+but is expected to have type
+ forall {R₁ : Type.{u2}} [_inst_1 : Semiring.{u2} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_14 : Module.{u2, u1} R₁ M₁ _inst_1 _inst_5] [_inst_19 : ContinuousAdd.{u1} M₁ _inst_4 (AddZeroClass.toAdd.{u1} M₁ (AddMonoid.toAddZeroClass.{u1} M₁ (AddCommMonoid.toAddMonoid.{u1} M₁ _inst_5)))] (f : ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (a : M₁), Eq.{succ u1} M₁ (HSMul.hSMul.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ M₁ (instHSMul.{u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (SMulZeroClass.toSMul.{u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (AddMonoid.toZero.{u1} M₁ (AddCommMonoid.toAddMonoid.{u1} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (ContinuousLinearMap.zero.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (AddMonoid.toZero.{u1} M₁ (AddCommMonoid.toAddMonoid.{u1} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (ContinuousLinearMap.monoidWithZero.{u2, u1} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14) (AddMonoid.toZero.{u1} M₁ (AddCommMonoid.toAddMonoid.{u1} M₁ _inst_5)) (Module.toMulActionWithZero.{u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (ContinuousLinearMap.semiring.{u2, u1} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19) _inst_5 (ContinuousLinearMap.applyModule.{u2, u1} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19)))))) f a) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₁) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ M₁ _inst_4 _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14))) f a)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_def ContinuousLinearMap.smul_defₓ'. -/
@[simp]
protected theorem smul_def (f : M₁ →L[R₁] M₁) (a : M₁) : f • a = f a :=
rfl
#align continuous_linear_map.smul_def ContinuousLinearMap.smul_def
+/- warning: continuous_linear_map.apply_has_faithful_smul -> ContinuousLinearMap.applyFaithfulSMul is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : ContinuousAdd.{u2} M₁ _inst_4 (AddZeroClass.toHasAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)))], FaithfulSMul.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (SMulZeroClass.toHasSmul.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (SMulWithZero.toSmulZeroClass.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (MulZeroClass.toHasZero.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (MulZeroOneClass.toMulZeroClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (MonoidWithZero.toMulZeroOneClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (Semiring.toMonoidWithZero.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.semiring.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19))))) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (MulActionWithZero.toSMulWithZero.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (Semiring.toMonoidWithZero.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.semiring.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19)) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (Module.toMulActionWithZero.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (ContinuousLinearMap.semiring.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19) _inst_5 (ContinuousLinearMap.applyModule.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19)))))
+but is expected to have type
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : ContinuousAdd.{u2} M₁ _inst_4 (AddZeroClass.toAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)))], FaithfulSMul.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (SMulZeroClass.toSMul.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (ContinuousLinearMap.zero.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (ContinuousLinearMap.monoidWithZero.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (Module.toMulActionWithZero.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (ContinuousLinearMap.semiring.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19) _inst_5 (ContinuousLinearMap.applyModule.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19)))))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.apply_has_faithful_smul ContinuousLinearMap.applyFaithfulSMulₓ'. -/
/-- `continuous_linear_map.apply_module` is faithful. -/
-instance apply_faithfulSMul : FaithfulSMul (M₁ →L[R₁] M₁) M₁ :=
+instance applyFaithfulSMul : FaithfulSMul (M₁ →L[R₁] M₁) M₁ :=
⟨fun _ _ => ContinuousLinearMap.ext⟩
-#align continuous_linear_map.apply_has_faithful_smul ContinuousLinearMap.apply_faithfulSMul
-
-instance apply_sMulCommClass : SMulCommClass R₁ (M₁ →L[R₁] M₁) M₁
+#align continuous_linear_map.apply_has_faithful_smul ContinuousLinearMap.applyFaithfulSMul
+
+/- warning: continuous_linear_map.apply_smul_comm_class -> ContinuousLinearMap.applySMulCommClass is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : ContinuousAdd.{u2} M₁ _inst_4 (AddZeroClass.toHasAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)))], SMulCommClass.{u1, u2, u2} R₁ (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (SMulZeroClass.toHasSmul.{u1, u2} R₁ M₁ (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (SMulWithZero.toSmulZeroClass.{u1, u2} R₁ M₁ (MulZeroClass.toHasZero.{u1} R₁ (MulZeroOneClass.toMulZeroClass.{u1} R₁ (MonoidWithZero.toMulZeroOneClass.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)))) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (MulActionWithZero.toSMulWithZero.{u1, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (Module.toMulActionWithZero.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)))) (SMulZeroClass.toHasSmul.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (SMulWithZero.toSmulZeroClass.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (MulZeroClass.toHasZero.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (MulZeroOneClass.toMulZeroClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (MonoidWithZero.toMulZeroOneClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (Semiring.toMonoidWithZero.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.semiring.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19))))) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (MulActionWithZero.toSMulWithZero.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (Semiring.toMonoidWithZero.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.semiring.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19)) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (Module.toMulActionWithZero.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (ContinuousLinearMap.semiring.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19) _inst_5 (ContinuousLinearMap.applyModule.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19)))))
+but is expected to have type
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : ContinuousAdd.{u2} M₁ _inst_4 (AddZeroClass.toAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)))], SMulCommClass.{u1, u2, u2} R₁ (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (SMulZeroClass.toSMul.{u1, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} R₁ M₁ (MonoidWithZero.toZero.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (Module.toMulActionWithZero.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)))) (SMulZeroClass.toSMul.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (ContinuousLinearMap.zero.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (ContinuousLinearMap.monoidWithZero.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (Module.toMulActionWithZero.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (ContinuousLinearMap.semiring.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19) _inst_5 (ContinuousLinearMap.applyModule.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19)))))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.apply_smul_comm_class ContinuousLinearMap.applySMulCommClassₓ'. -/
+instance applySMulCommClass : SMulCommClass R₁ (M₁ →L[R₁] M₁) M₁
where smul_comm r e m := (e.map_smul r m).symm
-#align continuous_linear_map.apply_smul_comm_class ContinuousLinearMap.apply_sMulCommClass
-
-instance apply_smul_comm_class' : SMulCommClass (M₁ →L[R₁] M₁) R₁ M₁
+#align continuous_linear_map.apply_smul_comm_class ContinuousLinearMap.applySMulCommClass
+
+/- warning: continuous_linear_map.apply_smul_comm_class' -> ContinuousLinearMap.applySMulCommClass' is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : ContinuousAdd.{u2} M₁ _inst_4 (AddZeroClass.toHasAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)))], SMulCommClass.{u2, u1, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) R₁ M₁ (SMulZeroClass.toHasSmul.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (SMulWithZero.toSmulZeroClass.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (MulZeroClass.toHasZero.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (MulZeroOneClass.toMulZeroClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (MonoidWithZero.toMulZeroOneClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (Semiring.toMonoidWithZero.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.semiring.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19))))) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (MulActionWithZero.toSMulWithZero.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (Semiring.toMonoidWithZero.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (ContinuousLinearMap.semiring.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19)) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (Module.toMulActionWithZero.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (ContinuousLinearMap.semiring.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19) _inst_5 (ContinuousLinearMap.applyModule.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19))))) (SMulZeroClass.toHasSmul.{u1, u2} R₁ M₁ (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (SMulWithZero.toSmulZeroClass.{u1, u2} R₁ M₁ (MulZeroClass.toHasZero.{u1} R₁ (MulZeroOneClass.toMulZeroClass.{u1} R₁ (MonoidWithZero.toMulZeroOneClass.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)))) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (MulActionWithZero.toSMulWithZero.{u1, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5))) (Module.toMulActionWithZero.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14))))
+but is expected to have type
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : ContinuousAdd.{u2} M₁ _inst_4 (AddZeroClass.toAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)))], SMulCommClass.{u2, u1, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) R₁ M₁ (SMulZeroClass.toSMul.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (ContinuousLinearMap.zero.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (ContinuousLinearMap.monoidWithZero.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (Module.toMulActionWithZero.{u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₁ _inst_4 _inst_5 _inst_14 _inst_14) M₁ (ContinuousLinearMap.semiring.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19) _inst_5 (ContinuousLinearMap.applyModule.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 _inst_19))))) (SMulZeroClass.toSMul.{u1, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} R₁ M₁ (MonoidWithZero.toZero.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)) (Module.toMulActionWithZero.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14))))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.apply_smul_comm_class' ContinuousLinearMap.applySMulCommClass'ₓ'. -/
+instance applySMulCommClass' : SMulCommClass (M₁ →L[R₁] M₁) R₁ M₁
where smul_comm := ContinuousLinearMap.map_smul
-#align continuous_linear_map.apply_smul_comm_class' ContinuousLinearMap.apply_smul_comm_class'
+#align continuous_linear_map.apply_smul_comm_class' ContinuousLinearMap.applySMulCommClass'
instance : ContinuousConstSMul (M₁ →L[R₁] M₁) M₁ :=
⟨ContinuousLinearMap.continuous⟩
end ApplyAction
+/- warning: continuous_linear_map.prod -> ContinuousLinearMap.prod is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u4}} [_inst_10 : TopologicalSpace.{u4} M₃] [_inst_11 : AddCommMonoid.{u4} M₃] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u1, u4} R₁ M₃ _inst_1 _inst_11], (ContinuousLinearMap.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) -> (ContinuousLinearMap.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) -> (ContinuousLinearMap.{u1, u1, u2, max u3 u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 (Prod.{u3, u4} M₂ M₃) (Prod.topologicalSpace.{u3, u4} M₂ M₃ _inst_8 _inst_10) (Prod.addCommMonoid.{u3, u4} M₂ M₃ _inst_9 _inst_11) _inst_14 (Prod.module.{u1, u3, u4} R₁ M₂ M₃ _inst_1 _inst_9 _inst_11 _inst_19 _inst_20))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.prod ContinuousLinearMap.prodₓ'. -/
/-- The cartesian product of two bounded linear maps, as a bounded linear map. -/
protected def prod [Module R₁ M₂] [Module R₁ M₃] (f₁ : M₁ →L[R₁] M₂) (f₂ : M₁ →L[R₁] M₃) :
M₁ →L[R₁] M₂ × M₃ :=
⟨(f₁ : M₁ →ₗ[R₁] M₂).Prod f₂, f₁.2.prod_mk f₂.2⟩
#align continuous_linear_map.prod ContinuousLinearMap.prod
+/- warning: continuous_linear_map.coe_prod -> ContinuousLinearMap.coe_prod is a dubious translation:
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+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u4}} [_inst_10 : TopologicalSpace.{u4} M₃] [_inst_11 : AddCommMonoid.{u4} M₃] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u1, u4} R₁ M₃ _inst_1 _inst_11] (f₁ : ContinuousLinearMap.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) (f₂ : ContinuousLinearMap.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20), Eq.{max (succ u2) (succ (max u3 u4))} (LinearMap.{u1, u1, u2, max u3 u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_prod ContinuousLinearMap.coe_prodₓ'. -/
@[simp, norm_cast]
theorem coe_prod [Module R₁ M₂] [Module R₁ M₃] (f₁ : M₁ →L[R₁] M₂) (f₂ : M₁ →L[R₁] M₃) :
(f₁.Prod f₂ : M₁ →ₗ[R₁] M₂ × M₃) = LinearMap.prod f₁ f₂ :=
rfl
#align continuous_linear_map.coe_prod ContinuousLinearMap.coe_prod
+/- warning: continuous_linear_map.prod_apply -> ContinuousLinearMap.prod_apply is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u4}} [_inst_10 : TopologicalSpace.{u4} M₃] [_inst_11 : AddCommMonoid.{u4} M₃] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u1, u4} R₁ M₃ _inst_1 _inst_11] (f₁ : ContinuousLinearMap.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) (f₂ : ContinuousLinearMap.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) (x : M₁), Eq.{max (succ u3) (succ u4)} (Prod.{u3, u4} M₂ M₃) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 u4))} (ContinuousLinearMap.{u1, u1, u2, max u3 u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 (Prod.{u3, u4} M₂ M₃) (Prod.topologicalSpace.{u3, u4} M₂ M₃ _inst_8 _inst_10) (Prod.addCommMonoid.{u3, u4} M₂ M₃ _inst_9 _inst_11) _inst_14 (Prod.module.{u1, u3, u4} R₁ M₂ M₃ _inst_1 _inst_9 _inst_11 _inst_19 _inst_20)) (fun (_x : ContinuousLinearMap.{u1, u1, u2, max u3 u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 (Prod.{u3, u4} M₂ M₃) (Prod.topologicalSpace.{u3, u4} M₂ M₃ _inst_8 _inst_10) (Prod.addCommMonoid.{u3, u4} M₂ M₃ _inst_9 _inst_11) _inst_14 (Prod.module.{u1, u3, u4} R₁ M₂ M₃ _inst_1 _inst_9 _inst_11 _inst_19 _inst_20)) => M₁ -> (Prod.{u3, u4} M₂ M₃)) (ContinuousLinearMap.toFun.{u1, u1, u2, max u3 u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 (Prod.{u3, u4} M₂ M₃) (Prod.topologicalSpace.{u3, u4} M₂ M₃ _inst_8 _inst_10) (Prod.addCommMonoid.{u3, u4} M₂ M₃ _inst_9 _inst_11) _inst_14 (Prod.module.{u1, u3, u4} R₁ M₂ M₃ _inst_1 _inst_9 _inst_11 _inst_19 _inst_20)) (ContinuousLinearMap.prod.{u1, u2, u3, u4} R₁ _inst_1 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_19 _inst_20 f₁ f₂) x) (Prod.mk.{u3, u4} M₂ M₃ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) => M₁ -> M₂) (ContinuousLinearMap.toFun.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) f₁ x) (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (ContinuousLinearMap.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) => M₁ -> M₃) (ContinuousLinearMap.toFun.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) f₂ x))
+but is expected to have type
+ forall {R₁ : Type.{u4}} [_inst_1 : Semiring.{u4} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u2}} [_inst_10 : TopologicalSpace.{u2} M₃] [_inst_11 : AddCommMonoid.{u2} M₃] [_inst_14 : Module.{u4, u1} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u4, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u4, u2} R₁ M₃ _inst_1 _inst_11] (f₁ : ContinuousLinearMap.{u4, u4, u1, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) (f₂ : ContinuousLinearMap.{u4, u4, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) (x : M₁), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => Prod.{u3, u2} M₂ M₃) x) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u1, max (succ u3) (succ u2)} (ContinuousLinearMap.{u4, u4, u1, max u2 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 (Prod.{u3, u2} M₂ M₃) (instTopologicalSpaceProd.{u3, u2} M₂ M₃ _inst_8 _inst_10) (Prod.instAddCommMonoidSum.{u3, u2} M₂ M₃ _inst_9 _inst_11) _inst_14 (Prod.module.{u4, u3, u2} R₁ M₂ M₃ _inst_1 _inst_9 _inst_11 _inst_19 _inst_20)) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => Prod.{u3, u2} M₂ M₃) _x) (ContinuousMapClass.toFunLike.{max (max u1 u3) u2, u1, max u3 u2} (ContinuousLinearMap.{u4, u4, u1, max u2 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 (Prod.{u3, u2} M₂ M₃) (instTopologicalSpaceProd.{u3, u2} M₂ M₃ _inst_8 _inst_10) (Prod.instAddCommMonoidSum.{u3, u2} M₂ M₃ _inst_9 _inst_11) _inst_14 (Prod.module.{u4, u3, u2} R₁ M₂ M₃ _inst_1 _inst_9 _inst_11 _inst_19 _inst_20)) M₁ (Prod.{u3, u2} M₂ M₃) _inst_4 (instTopologicalSpaceProd.{u3, u2} M₂ M₃ _inst_8 _inst_10) (ContinuousSemilinearMapClass.toContinuousMapClass.{max (max u1 u3) u2, u4, u4, u1, max u3 u2} (ContinuousLinearMap.{u4, u4, u1, max u2 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 (Prod.{u3, u2} M₂ M₃) (instTopologicalSpaceProd.{u3, u2} M₂ M₃ _inst_8 _inst_10) (Prod.instAddCommMonoidSum.{u3, u2} M₂ M₃ _inst_9 _inst_11) _inst_14 (Prod.module.{u4, u3, u2} R₁ M₂ M₃ _inst_1 _inst_9 _inst_11 _inst_19 _inst_20)) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 (Prod.{u3, u2} M₂ M₃) (instTopologicalSpaceProd.{u3, u2} M₂ M₃ _inst_8 _inst_10) (Prod.instAddCommMonoidSum.{u3, u2} M₂ M₃ _inst_9 _inst_11) _inst_14 (Prod.module.{u4, u3, u2} R₁ M₂ M₃ _inst_1 _inst_9 _inst_11 _inst_19 _inst_20) (ContinuousLinearMap.continuousSemilinearMapClass.{u4, 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(x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u1 u3, u1, u3} (ContinuousLinearMap.{u4, u4, u1, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u1 u3, u4, u4, u1, u3} (ContinuousLinearMap.{u4, u4, u1, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u1, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19))) f₁ x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousLinearMap.{u4, u4, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₃) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousLinearMap.{u4, u4, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) M₁ M₃ _inst_4 _inst_10 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u1 u2, u4, u4, u1, u2} (ContinuousLinearMap.{u4, u4, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20))) f₂ x))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.prod_apply ContinuousLinearMap.prod_applyₓ'. -/
@[simp, norm_cast]
theorem prod_apply [Module R₁ M₂] [Module R₁ M₃] (f₁ : M₁ →L[R₁] M₂) (f₂ : M₁ →L[R₁] M₃) (x : M₁) :
f₁.Prod f₂ x = (f₁ x, f₂ x) :=
@@ -1017,11 +1544,23 @@ section
variable (R₁ M₁ M₂)
+/- warning: continuous_linear_map.inl -> ContinuousLinearMap.inl is a dubious translation:
+lean 3 declaration is
+ forall (R₁ : Type.{u1}) [_inst_1 : Semiring.{u1} R₁] (M₁ : Type.{u2}) [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] (M₂ : Type.{u3}) [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9], ContinuousLinearMap.{u1, u1, u2, max u2 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) _inst_14 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)
+but is expected to have type
+ forall (R₁ : Type.{u1}) [_inst_1 : Semiring.{u1} R₁] (M₁ : Type.{u2}) [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] (M₂ : Type.{u3}) [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9], ContinuousLinearMap.{u1, u1, u2, max u3 u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 (Prod.{u2, u3} M₁ M₂) (instTopologicalSpaceProd.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.instAddCommMonoidSum.{u2, u3} M₁ M₂ _inst_5 _inst_9) _inst_14 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.inl ContinuousLinearMap.inlₓ'. -/
/-- The left injection into a product is a continuous linear map. -/
def inl [Module R₁ M₂] : M₁ →L[R₁] M₁ × M₂ :=
(id R₁ M₁).Prod 0
#align continuous_linear_map.inl ContinuousLinearMap.inl
+/- warning: continuous_linear_map.inr -> ContinuousLinearMap.inr is a dubious translation:
+lean 3 declaration is
+ forall (R₁ : Type.{u1}) [_inst_1 : Semiring.{u1} R₁] (M₁ : Type.{u2}) [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] (M₂ : Type.{u3}) [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9], ContinuousLinearMap.{u1, u1, u3, max u2 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) _inst_19 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)
+but is expected to have type
+ forall (R₁ : Type.{u1}) [_inst_1 : Semiring.{u1} R₁] (M₁ : Type.{u2}) [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] (M₂ : Type.{u3}) [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9], ContinuousLinearMap.{u1, u1, u3, max u3 u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 (Prod.{u2, u3} M₁ M₂) (instTopologicalSpaceProd.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.instAddCommMonoidSum.{u2, u3} M₁ M₂ _inst_5 _inst_9) _inst_19 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.inr ContinuousLinearMap.inrₓ'. -/
/-- The right injection into a product is a continuous linear map. -/
def inr [Module R₁ M₂] : M₂ →L[R₁] M₁ × M₂ :=
(0 : M₂ →L[R₁] M₁).Prod (id R₁ M₂)
@@ -1031,49 +1570,99 @@ end
variable {F : Type _}
+/- warning: continuous_linear_map.inl_apply -> ContinuousLinearMap.inl_apply is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.inl_apply ContinuousLinearMap.inl_applyₓ'. -/
@[simp]
theorem inl_apply [Module R₁ M₂] (x : M₁) : inl R₁ M₁ M₂ x = (x, 0) :=
rfl
#align continuous_linear_map.inl_apply ContinuousLinearMap.inl_apply
+/- warning: continuous_linear_map.inr_apply -> ContinuousLinearMap.inr_apply is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9] (x : M₂), Eq.{max (succ u2) (succ u3)} (Prod.{u2, u3} M₁ M₂) (coeFn.{max (succ u3) (succ (max u2 u3)), max (succ u3) (succ (max u2 u3))} (ContinuousLinearMap.{u1, u1, u3, max u2 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) _inst_19 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)) (fun (_x : ContinuousLinearMap.{u1, u1, u3, max u2 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) _inst_19 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)) => M₂ -> (Prod.{u2, u3} M₁ M₂)) (ContinuousLinearMap.toFun.{u1, u1, u3, max u2 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) _inst_19 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)) (ContinuousLinearMap.inr.{u1, u2, u3} R₁ _inst_1 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) x) (Prod.mk.{u2, u3} M₁ M₂ (OfNat.ofNat.{u2} M₁ 0 (OfNat.mk.{u2} M₁ 0 (Zero.zero.{u2} M₁ (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_5)))))) x)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.inr_apply ContinuousLinearMap.inr_applyₓ'. -/
@[simp]
theorem inr_apply [Module R₁ M₂] (x : M₂) : inr R₁ M₁ M₂ x = (0, x) :=
rfl
#align continuous_linear_map.inr_apply ContinuousLinearMap.inr_apply
+/- warning: continuous_linear_map.coe_inl -> ContinuousLinearMap.coe_inl is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+ forall {R₁ : Type.{u3}} [_inst_1 : Semiring.{u3} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] {M₂ : Type.{u2}} [_inst_8 : TopologicalSpace.{u2} M₂] [_inst_9 : AddCommMonoid.{u2} M₂] [_inst_14 : Module.{u3, u1} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u3, u2} R₁ M₂ _inst_1 _inst_9], Eq.{max (succ u1) (succ u2)} (LinearMap.{u3, u3, u1, max u1 u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) M₁ (Prod.{u1, u2} M₁ M₂) _inst_5 (Prod.instAddCommMonoidSum.{u1, u2} M₁ M₂ _inst_5 _inst_9) _inst_14 (Prod.module.{u3, u1, u2} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)) (ContinuousLinearMap.toLinearMap.{u3, u3, u1, max u1 u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) M₁ _inst_4 _inst_5 (Prod.{u1, u2} M₁ M₂) (instTopologicalSpaceProd.{u1, u2} M₁ M₂ _inst_4 _inst_8) (Prod.instAddCommMonoidSum.{u1, u2} M₁ M₂ _inst_5 _inst_9) _inst_14 (Prod.module.{u3, u1, u2} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) (ContinuousLinearMap.inl.{u3, u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19)) (LinearMap.inl.{u3, u1, u2} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_inl ContinuousLinearMap.coe_inlₓ'. -/
@[simp, norm_cast]
theorem coe_inl [Module R₁ M₂] : (inl R₁ M₁ M₂ : M₁ →ₗ[R₁] M₁ × M₂) = LinearMap.inl R₁ M₁ M₂ :=
rfl
#align continuous_linear_map.coe_inl ContinuousLinearMap.coe_inl
+/- warning: continuous_linear_map.coe_inr -> ContinuousLinearMap.coe_inr is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9], Eq.{max (succ u3) (succ (max u2 u3))} (LinearMap.{u1, u1, u3, max u2 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ (Prod.{u2, u3} M₁ M₂) _inst_9 (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) _inst_19 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)) ((fun (a : Sort.{max (succ u3) (succ (max u2 u3))}) (b : Sort.{max (succ u3) (succ (max u2 u3))}) [self : HasLiftT.{max (succ u3) (succ (max u2 u3)), max (succ u3) (succ (max u2 u3))} a b] => self.0) (ContinuousLinearMap.{u1, u1, u3, max u2 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) _inst_19 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)) (LinearMap.{u1, u1, u3, max u2 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ (Prod.{u2, u3} M₁ M₂) _inst_9 (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) _inst_19 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)) (HasLiftT.mk.{max (succ u3) (succ (max u2 u3)), max (succ u3) (succ (max u2 u3))} (ContinuousLinearMap.{u1, u1, u3, max u2 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) _inst_19 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)) (LinearMap.{u1, u1, u3, max u2 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ (Prod.{u2, u3} M₁ M₂) _inst_9 (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) _inst_19 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)) (CoeTCₓ.coe.{max (succ u3) (succ (max u2 u3)), max (succ u3) (succ (max u2 u3))} (ContinuousLinearMap.{u1, u1, u3, max u2 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) _inst_19 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)) (LinearMap.{u1, u1, u3, max u2 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ (Prod.{u2, u3} M₁ M₂) _inst_9 (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) _inst_19 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)) (coeBase.{max (succ u3) (succ (max u2 u3)), max (succ u3) (succ (max u2 u3))} (ContinuousLinearMap.{u1, u1, u3, max u2 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) _inst_19 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)) (LinearMap.{u1, u1, u3, max u2 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ (Prod.{u2, u3} M₁ M₂) _inst_9 (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) _inst_19 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)) (ContinuousLinearMap.LinearMap.coe.{u1, u1, u3, max u2 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) _inst_19 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19))))) (ContinuousLinearMap.inr.{u1, u2, u3} R₁ _inst_1 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19)) (LinearMap.inr.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)
+but is expected to have type
+ forall {R₁ : Type.{u3}} [_inst_1 : Semiring.{u3} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] {M₂ : Type.{u2}} [_inst_8 : TopologicalSpace.{u2} M₂] [_inst_9 : AddCommMonoid.{u2} M₂] [_inst_14 : Module.{u3, u1} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u3, u2} R₁ M₂ _inst_1 _inst_9], Eq.{max (succ u1) (succ u2)} (LinearMap.{u3, u3, u2, max u1 u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) M₂ (Prod.{u1, u2} M₁ M₂) _inst_9 (Prod.instAddCommMonoidSum.{u1, u2} M₁ M₂ _inst_5 _inst_9) _inst_19 (Prod.module.{u3, u1, u2} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)) (ContinuousLinearMap.toLinearMap.{u3, u3, u2, max u1 u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) M₂ _inst_8 _inst_9 (Prod.{u1, u2} M₁ M₂) (instTopologicalSpaceProd.{u1, u2} M₁ M₂ _inst_4 _inst_8) (Prod.instAddCommMonoidSum.{u1, u2} M₁ M₂ _inst_5 _inst_9) _inst_19 (Prod.module.{u3, u1, u2} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) (ContinuousLinearMap.inr.{u3, u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19)) (LinearMap.inr.{u3, u1, u2} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_inr ContinuousLinearMap.coe_inrₓ'. -/
@[simp, norm_cast]
theorem coe_inr [Module R₁ M₂] : (inr R₁ M₁ M₂ : M₂ →ₗ[R₁] M₁ × M₂) = LinearMap.inr R₁ M₁ M₂ :=
rfl
#align continuous_linear_map.coe_inr ContinuousLinearMap.coe_inr
+/- warning: continuous_linear_map.is_closed_ker -> ContinuousLinearMap.isClosed_ker is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] [_inst_14 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_9] {F : Type.{u5}} [_inst_19 : T1Space.{u4} M₂ _inst_8] [_inst_20 : ContinuousSemilinearMapClass.{u5, u1, u2, u3, u4} F R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16] (f : F), IsClosed.{u3} M₁ _inst_4 ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Submodule.{u1, u3} R₁ M₁ _inst_1 _inst_5 _inst_14) (Set.{u3} M₁) (HasLiftT.mk.{succ u3, succ u3} (Submodule.{u1, u3} R₁ M₁ _inst_1 _inst_5 _inst_14) (Set.{u3} M₁) (CoeTCₓ.coe.{succ u3, succ u3} (Submodule.{u1, u3} R₁ M₁ _inst_1 _inst_5 _inst_14) (Set.{u3} M₁) (SetLike.Set.hasCoeT.{u3, u3} (Submodule.{u1, u3} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u3} R₁ M₁ _inst_1 _inst_5 _inst_14)))) (LinearMap.ker.{u1, u2, u3, u4, u5} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂ F (ContinuousSemilinearMapClass.toSemilinearMapClass.{u5, u1, u2, u3, u4} F R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 _inst_20) f))
+but is expected to have type
+ forall {R₁ : Type.{u3}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u3} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u3, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] {M₂ : Type.{u5}} [_inst_8 : TopologicalSpace.{u5} M₂] [_inst_9 : AddCommMonoid.{u5} M₂] [_inst_14 : Module.{u3, u1} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u5} R₂ M₂ _inst_2 _inst_9] {F : Type.{u4}} [_inst_19 : T1Space.{u5} M₂ _inst_8] [_inst_20 : ContinuousSemilinearMapClass.{u4, u3, u2, u1, u5} F R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16] (f : F), IsClosed.{u1} M₁ _inst_4 (SetLike.coe.{u1, u1} (Submodule.{u3, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u3, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (LinearMap.ker.{u3, u2, u1, u5, u4} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂ F (ContinuousSemilinearMapClass.toSemilinearMapClass.{u4, u3, u2, u1, u5} F R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 _inst_20) f))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.is_closed_ker ContinuousLinearMap.isClosed_kerₓ'. -/
theorem isClosed_ker [T1Space M₂] [ContinuousSemilinearMapClass F σ₁₂ M₁ M₂] (f : F) :
IsClosed (ker f : Set M₁) :=
continuous_iff_isClosed.1 (map_continuous f) _ isClosed_singleton
#align continuous_linear_map.is_closed_ker ContinuousLinearMap.isClosed_ker
+/- warning: continuous_linear_map.is_complete_ker -> ContinuousLinearMap.isComplete_ker is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] [_inst_16 : Module.{u2, u3} R₂ M₂ _inst_2 _inst_9] {F : Type.{u4}} {M' : Type.{u5}} [_inst_19 : UniformSpace.{u5} M'] [_inst_20 : CompleteSpace.{u5} M' _inst_19] [_inst_21 : AddCommMonoid.{u5} M'] [_inst_22 : Module.{u1, u5} R₁ M' _inst_1 _inst_21] [_inst_23 : T1Space.{u3} M₂ _inst_8] [_inst_24 : ContinuousSemilinearMapClass.{u4, u1, u2, u5, u3} F R₁ R₂ _inst_1 _inst_2 σ₁₂ M' (UniformSpace.toTopologicalSpace.{u5} M' _inst_19) _inst_21 M₂ _inst_8 _inst_9 _inst_22 _inst_16] (f : F), IsComplete.{u5} M' _inst_19 ((fun (a : Type.{u5}) (b : Type.{u5}) [self : HasLiftT.{succ u5, succ u5} a b] => self.0) (Submodule.{u1, u5} R₁ M' _inst_1 _inst_21 _inst_22) (Set.{u5} M') (HasLiftT.mk.{succ u5, succ u5} (Submodule.{u1, u5} R₁ M' _inst_1 _inst_21 _inst_22) (Set.{u5} M') (CoeTCₓ.coe.{succ u5, succ u5} (Submodule.{u1, u5} R₁ M' _inst_1 _inst_21 _inst_22) (Set.{u5} M') (SetLike.Set.hasCoeT.{u5, u5} (Submodule.{u1, u5} R₁ M' _inst_1 _inst_21 _inst_22) M' (Submodule.setLike.{u1, u5} R₁ M' _inst_1 _inst_21 _inst_22)))) (LinearMap.ker.{u1, u2, u5, u3, u4} R₁ R₂ M' M₂ _inst_1 _inst_2 _inst_21 _inst_9 _inst_22 _inst_16 σ₁₂ F (ContinuousSemilinearMapClass.toSemilinearMapClass.{u4, u1, u2, u5, u3} F R₁ R₂ _inst_1 _inst_2 σ₁₂ M' (UniformSpace.toTopologicalSpace.{u5} M' _inst_19) _inst_21 M₂ _inst_8 _inst_9 _inst_22 _inst_16 _inst_24) f))
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u1} R₂] {σ₁₂ : RingHom.{u4, u1} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u1} R₂ _inst_2)} {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] [_inst_16 : Module.{u1, u3} R₂ M₂ _inst_2 _inst_9] {F : Type.{u2}} {M' : Type.{u5}} [_inst_19 : UniformSpace.{u5} M'] [_inst_20 : CompleteSpace.{u5} M' _inst_19] [_inst_21 : AddCommMonoid.{u5} M'] [_inst_22 : Module.{u4, u5} R₁ M' _inst_1 _inst_21] [_inst_23 : T1Space.{u3} M₂ _inst_8] [_inst_24 : ContinuousSemilinearMapClass.{u2, u4, u1, u5, u3} F R₁ R₂ _inst_1 _inst_2 σ₁₂ M' (UniformSpace.toTopologicalSpace.{u5} M' _inst_19) _inst_21 M₂ _inst_8 _inst_9 _inst_22 _inst_16] (f : F), IsComplete.{u5} M' _inst_19 (SetLike.coe.{u5, u5} (Submodule.{u4, u5} R₁ M' _inst_1 _inst_21 _inst_22) M' (Submodule.setLike.{u4, u5} R₁ M' _inst_1 _inst_21 _inst_22) (LinearMap.ker.{u4, u1, u5, u3, u2} R₁ R₂ M' M₂ _inst_1 _inst_2 _inst_21 _inst_9 _inst_22 _inst_16 σ₁₂ F (ContinuousSemilinearMapClass.toSemilinearMapClass.{u2, u4, u1, u5, u3} F R₁ R₂ _inst_1 _inst_2 σ₁₂ M' (UniformSpace.toTopologicalSpace.{u5} M' _inst_19) _inst_21 M₂ _inst_8 _inst_9 _inst_22 _inst_16 _inst_24) f))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.is_complete_ker ContinuousLinearMap.isComplete_kerₓ'. -/
theorem isComplete_ker {M' : Type _} [UniformSpace M'] [CompleteSpace M'] [AddCommMonoid M']
[Module R₁ M'] [T1Space M₂] [ContinuousSemilinearMapClass F σ₁₂ M' M₂] (f : F) :
IsComplete (ker f : Set M') :=
(isClosed_ker f).IsComplete
#align continuous_linear_map.is_complete_ker ContinuousLinearMap.isComplete_ker
+#print ContinuousLinearMap.completeSpace_ker /-
instance (priority := 100) completeSpace_ker {M' : Type _} [UniformSpace M'] [CompleteSpace M']
[AddCommMonoid M'] [Module R₁ M'] [T1Space M₂] [ContinuousSemilinearMapClass F σ₁₂ M' M₂]
(f : F) : CompleteSpace (ker f) :=
(isClosed_ker f).completeSpace_coe
#align continuous_linear_map.complete_space_ker ContinuousLinearMap.completeSpace_ker
+-/
+/- warning: continuous_linear_map.ker_prod -> ContinuousLinearMap.ker_prod is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u4}} [_inst_10 : TopologicalSpace.{u4} M₃] [_inst_11 : AddCommMonoid.{u4} M₃] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u1, u4} R₁ M₃ _inst_1 _inst_11] (f : ContinuousLinearMap.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) (g : ContinuousLinearMap.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20), Eq.{succ u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) (LinearMap.ker.{u1, u1, u2, max u3 u4, max u2 u3 u4} R₁ R₁ M₁ (Prod.{u3, u4} M₂ M₃) _inst_1 _inst_1 _inst_5 (Prod.addCommMonoid.{u3, u4} M₂ M₃ _inst_9 _inst_11) _inst_14 (Prod.module.{u1, u3, u4} R₁ M₂ M₃ _inst_1 _inst_9 _inst_11 _inst_19 _inst_20) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (ContinuousLinearMap.{u1, u1, u2, max u3 u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 (Prod.{u3, u4} M₂ M₃) (Prod.topologicalSpace.{u3, u4} M₂ M₃ _inst_8 _inst_10) (Prod.addCommMonoid.{u3, u4} M₂ M₃ _inst_9 _inst_11) _inst_14 (Prod.module.{u1, u3, u4} R₁ M₂ M₃ _inst_1 _inst_9 _inst_11 _inst_19 _inst_20)) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u3 u4, u1, u1, u2, max u3 u4} (ContinuousLinearMap.{u1, u1, u2, max u3 u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 (Prod.{u3, u4} M₂ M₃) (Prod.topologicalSpace.{u3, u4} M₂ M₃ _inst_8 _inst_10) (Prod.addCommMonoid.{u3, u4} M₂ M₃ _inst_9 _inst_11) _inst_14 (Prod.module.{u1, u3, u4} R₁ M₂ M₃ _inst_1 _inst_9 _inst_11 _inst_19 _inst_20)) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 (Prod.{u3, u4} M₂ M₃) (Prod.topologicalSpace.{u3, u4} M₂ M₃ _inst_8 _inst_10) (Prod.addCommMonoid.{u3, u4} M₂ M₃ _inst_9 _inst_11) _inst_14 (Prod.module.{u1, u3, u4} R₁ M₂ M₃ _inst_1 _inst_9 _inst_11 _inst_19 _inst_20) (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, max u3 u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 (Prod.{u3, u4} M₂ M₃) (Prod.topologicalSpace.{u3, u4} M₂ M₃ _inst_8 _inst_10) (Prod.addCommMonoid.{u3, u4} M₂ M₃ _inst_9 _inst_11) _inst_14 (Prod.module.{u1, u3, u4} R₁ M₂ M₃ _inst_1 _inst_9 _inst_11 _inst_19 _inst_20))) (ContinuousLinearMap.prod.{u1, u2, u3, u4} R₁ _inst_1 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_19 _inst_20 f g)) (Inf.inf.{u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) (Submodule.hasInf.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R₁ R₁ M₁ M₂ _inst_1 _inst_1 _inst_5 _inst_9 _inst_14 _inst_19 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (ContinuousLinearMap.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u3, u1, u1, u2, u3} (ContinuousLinearMap.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19)) f) (LinearMap.ker.{u1, u1, u2, u4, max u2 u4} R₁ R₁ M₁ M₃ _inst_1 _inst_1 _inst_5 _inst_11 _inst_14 _inst_20 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (ContinuousLinearMap.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u1, u1, u2, u4} (ContinuousLinearMap.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20)) g))
+but is expected to have type
+ forall {R₁ : Type.{u4}} [_inst_1 : Semiring.{u4} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u2}} [_inst_10 : TopologicalSpace.{u2} M₃] [_inst_11 : AddCommMonoid.{u2} M₃] [_inst_14 : Module.{u4, u1} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u4, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u4, u2} R₁ M₃ _inst_1 _inst_11] (f : ContinuousLinearMap.{u4, u4, u1, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) (g : ContinuousLinearMap.{u4, u4, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20), Eq.{succ u1} (Submodule.{u4, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (LinearMap.ker.{u4, u4, u1, max u3 u2, max (max u1 u3) u2} R₁ R₁ M₁ (Prod.{u3, u2} M₂ M₃) _inst_1 _inst_1 _inst_5 (Prod.instAddCommMonoidSum.{u3, u2} M₂ M₃ _inst_9 _inst_11) _inst_14 (Prod.module.{u4, u3, u2} R₁ M₂ M₃ _inst_1 _inst_9 _inst_11 _inst_19 _inst_20) (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) (ContinuousLinearMap.{u4, u4, u1, max u2 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 (Prod.{u3, u2} M₂ M₃) (instTopologicalSpaceProd.{u3, u2} M₂ M₃ _inst_8 _inst_10) (Prod.instAddCommMonoidSum.{u3, u2} M₂ M₃ _inst_9 _inst_11) _inst_14 (Prod.module.{u4, u3, u2} R₁ M₂ M₃ _inst_1 _inst_9 _inst_11 _inst_19 _inst_20)) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max (max u1 u3) u2, u4, u4, u1, max u3 u2} (ContinuousLinearMap.{u4, u4, u1, max u2 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 (Prod.{u3, u2} M₂ M₃) (instTopologicalSpaceProd.{u3, u2} M₂ M₃ _inst_8 _inst_10) (Prod.instAddCommMonoidSum.{u3, u2} M₂ M₃ _inst_9 _inst_11) _inst_14 (Prod.module.{u4, u3, u2} R₁ M₂ M₃ _inst_1 _inst_9 _inst_11 _inst_19 _inst_20)) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 (Prod.{u3, u2} M₂ M₃) (instTopologicalSpaceProd.{u3, u2} M₂ M₃ _inst_8 _inst_10) (Prod.instAddCommMonoidSum.{u3, u2} M₂ M₃ _inst_9 _inst_11) _inst_14 (Prod.module.{u4, u3, u2} R₁ M₂ M₃ _inst_1 _inst_9 _inst_11 _inst_19 _inst_20) (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u1, max u3 u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 (Prod.{u3, u2} M₂ M₃) (instTopologicalSpaceProd.{u3, u2} M₂ M₃ _inst_8 _inst_10) (Prod.instAddCommMonoidSum.{u3, u2} M₂ M₃ _inst_9 _inst_11) _inst_14 (Prod.module.{u4, u3, u2} R₁ M₂ M₃ _inst_1 _inst_9 _inst_11 _inst_19 _inst_20))) (ContinuousLinearMap.prod.{u4, u1, u3, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_19 _inst_20 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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ker_prod ContinuousLinearMap.ker_prodₓ'. -/
@[simp]
theorem ker_prod [Module R₁ M₂] [Module R₁ M₃] (f : M₁ →L[R₁] M₂) (g : M₁ →L[R₁] M₃) :
ker (f.Prod g) = ker f ⊓ ker g :=
LinearMap.ker_prod f g
#align continuous_linear_map.ker_prod ContinuousLinearMap.ker_prod
+/- warning: continuous_linear_map.cod_restrict -> ContinuousLinearMap.codRestrict 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 continuous_linear_map.cod_restrict ContinuousLinearMap.codRestrictₓ'. -/
/-- Restrict codomain of a continuous linear map. -/
def codRestrict (f : M₁ →SL[σ₁₂] M₂) (p : Submodule R₂ M₂) (h : ∀ x, f x ∈ p) : M₁ →SL[σ₁₂] p
where
@@ -1081,51 +1670,101 @@ def codRestrict (f : M₁ →SL[σ₁₂] M₂) (p : Submodule R₂ M₂) (h :
toLinearMap := (f : M₁ →ₛₗ[σ₁₂] M₂).codRestrict p h
#align continuous_linear_map.cod_restrict ContinuousLinearMap.codRestrict
+/- warning: continuous_linear_map.coe_cod_restrict -> ContinuousLinearMap.coe_codRestrict is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_cod_restrict ContinuousLinearMap.coe_codRestrictₓ'. -/
@[norm_cast]
theorem coe_codRestrict (f : M₁ →SL[σ₁₂] M₂) (p : Submodule R₂ M₂) (h : ∀ x, f x ∈ p) :
(f.codRestrict p h : M₁ →ₛₗ[σ₁₂] p) = (f : M₁ →ₛₗ[σ₁₂] M₂).codRestrict p h :=
rfl
#align continuous_linear_map.coe_cod_restrict ContinuousLinearMap.coe_codRestrict
+/- warning: continuous_linear_map.coe_cod_restrict_apply -> ContinuousLinearMap.coe_codRestrict_apply 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 continuous_linear_map.coe_cod_restrict_apply ContinuousLinearMap.coe_codRestrict_applyₓ'. -/
@[simp]
theorem coe_codRestrict_apply (f : M₁ →SL[σ₁₂] M₂) (p : Submodule R₂ M₂) (h : ∀ x, f x ∈ p) (x) :
(f.codRestrict p h x : M₂) = f x :=
rfl
#align continuous_linear_map.coe_cod_restrict_apply ContinuousLinearMap.coe_codRestrict_apply
+/- warning: continuous_linear_map.ker_cod_restrict -> ContinuousLinearMap.ker_codRestrict is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] [_inst_14 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_9] (f : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (p : Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) (h : forall (x : M₁), Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} 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_inst_4 _inst_5 (coeSort.{succ u4, succ (succ u4)} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)) p) (Subtype.topologicalSpace.{u4} M₂ (fun (x : M₂) => Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)) x p) _inst_8) (Submodule.addCommMonoid.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16 p) _inst_14 (Submodule.module.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16 p)) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u4, u1, u2, u3, u4} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 (coeSort.{succ u4, succ (succ u4)} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)) p) (Subtype.topologicalSpace.{u4} M₂ (fun (x : M₂) => Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)) x p) _inst_8) (Submodule.addCommMonoid.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16 p) _inst_14 (Submodule.module.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16 p)) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 (coeSort.{succ u4, succ (succ u4)} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)) p) (Subtype.topologicalSpace.{u4} M₂ (fun (x : M₂) => Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)) x p) _inst_8) (Submodule.addCommMonoid.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16 p) _inst_14 (Submodule.module.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16 p) (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 (coeSort.{succ u4, succ (succ u4)} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)) p) (Subtype.topologicalSpace.{u4} M₂ (fun (x : M₂) => Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16)) x p) _inst_8) (Submodule.addCommMonoid.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16 p) _inst_14 (Submodule.module.{u2, u4} R₂ M₂ _inst_2 _inst_9 _inst_16 p))) (ContinuousLinearMap.codRestrict.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 f p h)) (LinearMap.ker.{u1, u2, u3, u4, max u3 u4} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_5 _inst_9 _inst_14 _inst_16 σ₁₂ (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u4, u1, u2, u3, u4} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16)) f)
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_14 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_5] [_inst_16 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_9] (f : ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (p : Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (h : forall (x : M₁), Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) M₁ M₂ _inst_4 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16))) f x) p), Eq.{succ u2} (Submodule.{u4, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) 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(SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16)) x p) _inst_8) (Submodule.addCommMonoid.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16 p) _inst_14 (Submodule.module.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16 p)) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 (Subtype.{succ u1} M₂ (fun (x : M₂) => Membership.mem.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16)) x p)) (instTopologicalSpaceSubtype.{u1} M₂ (fun (x : M₂) => Membership.mem.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16)) x p) _inst_8) (Submodule.addCommMonoid.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16 p) _inst_14 (Submodule.module.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16 p)) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 (Subtype.{succ u1} M₂ (fun (x : M₂) => Membership.mem.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16)) x p)) (instTopologicalSpaceSubtype.{u1} M₂ (fun (x : M₂) => Membership.mem.{u1, u1} M₂ (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16)) x p) _inst_8) (Submodule.addCommMonoid.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16 p) _inst_14 (Submodule.module.{u3, u1} R₂ M₂ _inst_2 _inst_9 _inst_16 p) (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ 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(ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_16)) f)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ker_cod_restrict ContinuousLinearMap.ker_codRestrictₓ'. -/
@[simp]
theorem ker_codRestrict (f : M₁ →SL[σ₁₂] M₂) (p : Submodule R₂ M₂) (h : ∀ x, f x ∈ p) :
ker (f.codRestrict p h) = ker f :=
(f : M₁ →ₛₗ[σ₁₂] M₂).ker_codRestrict p h
#align continuous_linear_map.ker_cod_restrict ContinuousLinearMap.ker_codRestrict
+#print Submodule.subtypeL /-
/-- `submodule.subtype` as a `continuous_linear_map`. -/
def Submodule.subtypeL (p : Submodule R₁ M₁) : p →L[R₁] M₁
where
cont := continuous_subtype_val
toLinearMap := p.Subtype
#align submodule.subtypeL Submodule.subtypeL
+-/
+/- warning: submodule.coe_subtypeL -> Submodule.coe_subtypeL 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 submodule.coe_subtypeL Submodule.coe_subtypeLₓ'. -/
@[simp, norm_cast]
theorem Submodule.coe_subtypeL (p : Submodule R₁ M₁) : (p.subtypeL : p →ₗ[R₁] M₁) = p.Subtype :=
rfl
#align submodule.coe_subtypeL Submodule.coe_subtypeL
+/- warning: submodule.coe_subtypeL' -> Submodule.coe_subtypeL' is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+ forall {R₁ : Type.{u2}} [_inst_1 : Semiring.{u2} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_14 : Module.{u2, u1} R₁ M₁ _inst_1 _inst_5] (p : Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14), Eq.{succ u1} (forall (ᾰ : Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) => M₁) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (instTopologicalSpaceSubtype.{u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ 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+Case conversion may be inaccurate. Consider using '#align submodule.coe_subtypeL' Submodule.coe_subtypeL'ₓ'. -/
@[simp]
theorem Submodule.coe_subtypeL' (p : Submodule R₁ M₁) : ⇑p.subtypeL = p.Subtype :=
rfl
#align submodule.coe_subtypeL' Submodule.coe_subtypeL'
+/- warning: submodule.subtypeL_apply -> Submodule.subtypeL_apply is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] (p : Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) p), Eq.{succ u2} M₁ (coeFn.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) p) (Subtype.topologicalSpace.{u2} M₁ (fun (x : M₁) => Membership.Mem.{u2, u2} M₁ (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) p) (Subtype.topologicalSpace.{u2} M₁ (fun (x : M₁) => Membership.Mem.{u2, u2} M₁ (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14) => (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) p) -> M₁) (ContinuousLinearMap.toFun.{u1, u1, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) p) (Subtype.topologicalSpace.{u2} M₁ (fun (x : M₁) => Membership.Mem.{u2, u2} M₁ (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14) (Submodule.subtypeL.{u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 p) x) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) p) M₁ (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) p) M₁ (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) p) M₁ (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) p) M₁ (coeSubtype.{succ u2} M₁ (fun (x : M₁) => Membership.Mem.{u2, u2} M₁ (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p))))) x)
+but is expected to have type
+ forall {R₁ : Type.{u2}} [_inst_1 : Semiring.{u2} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_14 : Module.{u2, u1} R₁ M₁ _inst_1 _inst_5] (p : Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (x : Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) => M₁) x) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 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+Case conversion may be inaccurate. Consider using '#align submodule.subtypeL_apply Submodule.subtypeL_applyₓ'. -/
@[simp, norm_cast]
theorem Submodule.subtypeL_apply (p : Submodule R₁ M₁) (x : p) : p.subtypeL x = x :=
rfl
#align submodule.subtypeL_apply Submodule.subtypeL_apply
+/- warning: submodule.range_subtypeL -> Submodule.range_subtypeL 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 submodule.range_subtypeL Submodule.range_subtypeLₓ'. -/
@[simp]
theorem Submodule.range_subtypeL (p : Submodule R₁ M₁) : range p.subtypeL = p :=
Submodule.range_subtype _
#align submodule.range_subtypeL Submodule.range_subtypeL
+/- warning: submodule.ker_subtypeL -> Submodule.ker_subtypeL is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] (p : Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14), Eq.{succ u2} (Submodule.{u1, u2} R₁ (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) p) _inst_1 (Submodule.addCommMonoid.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14 p) (Submodule.module.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14 p)) (LinearMap.ker.{u1, u1, u2, u2, u2} R₁ R₁ (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u1, u2} R₁ M₁ _inst_1 _inst_5 _inst_14)) p) M₁ _inst_1 _inst_1 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+but is expected to have type
+ forall {R₁ : Type.{u2}} [_inst_1 : Semiring.{u2} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] [_inst_14 : Module.{u2, u1} R₁ M₁ _inst_1 _inst_5] (p : Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14), Eq.{succ u1} (Submodule.{u2, u1} R₁ (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p)) (LinearMap.ker.{u2, u2, u1, u1, u1} R₁ R₁ (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) M₁ _inst_1 _inst_1 (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (instTopologicalSpaceSubtype.{u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14) (ContinuousSemilinearMapClass.toSemilinearMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (instTopologicalSpaceSubtype.{u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (instTopologicalSpaceSubtype.{u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p)) (instTopologicalSpaceSubtype.{u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) M₁ (Submodule.setLike.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14)) x p) _inst_4) (Submodule.addCommMonoid.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) M₁ _inst_4 _inst_5 (Submodule.module.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14 p) _inst_14)) (Submodule.subtypeL.{u2, u1} R₁ _inst_1 M₁ _inst_4 _inst_5 _inst_14 p)) (Bot.bot.{u1} (Submodule.{u2, u1} R₁ (Subtype.{succ u1} M₁ (fun (x : M₁) => Membership.mem.{u1, u1} M₁ (Submodule.{u2, u1} R₁ M₁ _inst_1 _inst_5 _inst_14) (SetLike.instMembership.{u1, u1} 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+Case conversion may be inaccurate. Consider using '#align submodule.ker_subtypeL Submodule.ker_subtypeLₓ'. -/
@[simp]
theorem Submodule.ker_subtypeL (p : Submodule R₁ M₁) : ker p.subtypeL = ⊥ :=
Submodule.ker_subtype _
@@ -1133,6 +1772,12 @@ theorem Submodule.ker_subtypeL (p : Submodule R₁ M₁) : ker p.subtypeL = ⊥
variable (R₁ M₁ M₂)
+/- warning: continuous_linear_map.fst -> ContinuousLinearMap.fst is a dubious translation:
+lean 3 declaration is
+ forall (R₁ : Type.{u1}) [_inst_1 : Semiring.{u1} R₁] (M₁ : Type.{u2}) [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] (M₂ : Type.{u3}) [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9], ContinuousLinearMap.{u1, u1, max u2 u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) M₁ _inst_4 _inst_5 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) _inst_14
+but is expected to have type
+ forall (R₁ : Type.{u1}) [_inst_1 : Semiring.{u1} R₁] (M₁ : Type.{u2}) [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] (M₂ : Type.{u3}) [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9], ContinuousLinearMap.{u1, u1, max u3 u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u3} M₁ M₂) (instTopologicalSpaceProd.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.instAddCommMonoidSum.{u2, u3} M₁ M₂ _inst_5 _inst_9) M₁ _inst_4 _inst_5 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) _inst_14
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.fst ContinuousLinearMap.fstₓ'. -/
/-- `prod.fst` as a `continuous_linear_map`. -/
def fst [Module R₁ M₂] : M₁ × M₂ →L[R₁] M₁
where
@@ -1140,6 +1785,12 @@ def fst [Module R₁ M₂] : M₁ × M₂ →L[R₁] M₁
toLinearMap := LinearMap.fst R₁ M₁ M₂
#align continuous_linear_map.fst ContinuousLinearMap.fst
+/- warning: continuous_linear_map.snd -> ContinuousLinearMap.snd is a dubious translation:
+lean 3 declaration is
+ forall (R₁ : Type.{u1}) [_inst_1 : Semiring.{u1} R₁] (M₁ : Type.{u2}) [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] (M₂ : Type.{u3}) [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9], ContinuousLinearMap.{u1, u1, max u2 u3, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) M₂ _inst_8 _inst_9 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) _inst_19
+but is expected to have type
+ forall (R₁ : Type.{u1}) [_inst_1 : Semiring.{u1} R₁] (M₁ : Type.{u2}) [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] (M₂ : Type.{u3}) [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9], ContinuousLinearMap.{u1, u1, max u3 u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u3} M₁ M₂) (instTopologicalSpaceProd.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.instAddCommMonoidSum.{u2, u3} M₁ M₂ _inst_5 _inst_9) M₂ _inst_8 _inst_9 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) _inst_19
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.snd ContinuousLinearMap.sndₓ'. -/
/-- `prod.snd` as a `continuous_linear_map`. -/
def snd [Module R₁ M₂] : M₁ × M₂ →L[R₁] M₂
where
@@ -1149,79 +1800,163 @@ def snd [Module R₁ M₂] : M₁ × M₂ →L[R₁] M₂
variable {R₁ M₁ M₂}
+/- warning: continuous_linear_map.coe_fst -> ContinuousLinearMap.coe_fst 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 continuous_linear_map.coe_fst ContinuousLinearMap.coe_fstₓ'. -/
@[simp, norm_cast]
theorem coe_fst [Module R₁ M₂] : ↑(fst R₁ M₁ M₂) = LinearMap.fst R₁ M₁ M₂ :=
rfl
#align continuous_linear_map.coe_fst ContinuousLinearMap.coe_fst
+/- warning: continuous_linear_map.coe_fst' -> ContinuousLinearMap.coe_fst' is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_fst' ContinuousLinearMap.coe_fst'ₓ'. -/
@[simp, norm_cast]
theorem coe_fst' [Module R₁ M₂] : ⇑(fst R₁ M₁ M₂) = Prod.fst :=
rfl
#align continuous_linear_map.coe_fst' ContinuousLinearMap.coe_fst'
+/- warning: continuous_linear_map.coe_snd -> ContinuousLinearMap.coe_snd 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 continuous_linear_map.coe_snd ContinuousLinearMap.coe_sndₓ'. -/
@[simp, norm_cast]
theorem coe_snd [Module R₁ M₂] : ↑(snd R₁ M₁ M₂) = LinearMap.snd R₁ M₁ M₂ :=
rfl
#align continuous_linear_map.coe_snd ContinuousLinearMap.coe_snd
+/- warning: continuous_linear_map.coe_snd' -> ContinuousLinearMap.coe_snd' is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9], Eq.{max (succ (max u2 u3)) (succ u3)} ((Prod.{u2, u3} M₁ M₂) -> M₂) (coeFn.{max (succ (max u2 u3)) (succ u3), max (succ (max u2 u3)) (succ u3)} (ContinuousLinearMap.{u1, u1, max u2 u3, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) M₂ _inst_8 _inst_9 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) _inst_19) (fun (_x : ContinuousLinearMap.{u1, u1, max u2 u3, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) M₂ _inst_8 _inst_9 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) _inst_19) => (Prod.{u2, u3} M₁ M₂) -> M₂) (ContinuousLinearMap.toFun.{u1, u1, max u2 u3, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) M₂ _inst_8 _inst_9 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) _inst_19) (ContinuousLinearMap.snd.{u1, u2, u3} R₁ _inst_1 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19)) (Prod.snd.{u2, u3} M₁ M₂)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_snd' ContinuousLinearMap.coe_snd'ₓ'. -/
@[simp, norm_cast]
theorem coe_snd' [Module R₁ M₂] : ⇑(snd R₁ M₁ M₂) = Prod.snd :=
rfl
#align continuous_linear_map.coe_snd' ContinuousLinearMap.coe_snd'
+/- warning: continuous_linear_map.fst_prod_snd -> ContinuousLinearMap.fst_prod_snd is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9], Eq.{succ (max u2 u3)} (ContinuousLinearMap.{u1, u1, max u2 u3, max u2 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)) (ContinuousLinearMap.prod.{u1, max u2 u3, u2, u3} R₁ _inst_1 (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) _inst_14 _inst_19 (ContinuousLinearMap.fst.{u1, u2, u3} R₁ _inst_1 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) (ContinuousLinearMap.snd.{u1, u2, u3} R₁ _inst_1 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19)) (ContinuousLinearMap.id.{u1, max u2 u3} R₁ _inst_1 (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19))
+but is expected to have type
+ forall {R₁ : Type.{u3}} [_inst_1 : Semiring.{u3} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] {M₂ : Type.{u2}} [_inst_8 : TopologicalSpace.{u2} M₂] [_inst_9 : AddCommMonoid.{u2} M₂] [_inst_14 : Module.{u3, u1} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u3, u2} R₁ M₂ _inst_1 _inst_9], Eq.{max (succ u1) (succ u2)} (ContinuousLinearMap.{u3, u3, max u1 u2, max u2 u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) (Prod.{u1, u2} M₁ M₂) (instTopologicalSpaceProd.{u1, u2} M₁ M₂ _inst_4 _inst_8) (Prod.instAddCommMonoidSum.{u1, u2} M₁ M₂ _inst_5 _inst_9) (Prod.{u1, u2} M₁ M₂) (instTopologicalSpaceProd.{u1, u2} M₁ M₂ _inst_4 _inst_8) (Prod.instAddCommMonoidSum.{u1, u2} M₁ M₂ _inst_5 _inst_9) (Prod.module.{u3, u1, u2} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) (Prod.module.{u3, u1, u2} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19)) (ContinuousLinearMap.prod.{u3, max u1 u2, u1, u2} R₁ _inst_1 (Prod.{u1, u2} M₁ M₂) (instTopologicalSpaceProd.{u1, u2} M₁ M₂ _inst_4 _inst_8) (Prod.instAddCommMonoidSum.{u1, u2} M₁ M₂ _inst_5 _inst_9) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 (Prod.module.{u3, u1, u2} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) _inst_14 _inst_19 (ContinuousLinearMap.fst.{u3, u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) (ContinuousLinearMap.snd.{u3, u1, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19)) (ContinuousLinearMap.id.{u3, max u2 u1} R₁ _inst_1 (Prod.{u1, u2} M₁ M₂) (instTopologicalSpaceProd.{u1, u2} M₁ M₂ _inst_4 _inst_8) (Prod.instAddCommMonoidSum.{u1, u2} M₁ M₂ _inst_5 _inst_9) (Prod.module.{u3, u1, u2} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.fst_prod_snd ContinuousLinearMap.fst_prod_sndₓ'. -/
@[simp]
theorem fst_prod_snd [Module R₁ M₂] : (fst R₁ M₁ M₂).Prod (snd R₁ M₁ M₂) = id R₁ (M₁ × M₂) :=
ext fun ⟨x, y⟩ => rfl
#align continuous_linear_map.fst_prod_snd ContinuousLinearMap.fst_prod_snd
+/- warning: continuous_linear_map.fst_comp_prod -> ContinuousLinearMap.fst_comp_prod is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u4}} [_inst_10 : TopologicalSpace.{u4} M₃] [_inst_11 : AddCommMonoid.{u4} M₃] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u1, u4} R₁ M₃ _inst_1 _inst_11] (f : ContinuousLinearMap.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) (g : ContinuousLinearMap.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) (ContinuousLinearMap.comp.{u1, u1, u1, u2, max u3 u4, u3} R₁ R₁ R₁ _inst_1 _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 (Prod.{u3, u4} M₂ M₃) (Prod.topologicalSpace.{u3, u4} M₂ M₃ _inst_8 _inst_10) (Prod.addCommMonoid.{u3, u4} M₂ M₃ _inst_9 _inst_11) M₂ _inst_8 _inst_9 _inst_14 (Prod.module.{u1, u3, u4} R₁ M₂ M₃ _inst_1 _inst_9 _inst_11 _inst_19 _inst_20) _inst_19 (RingHomCompTriple.right_ids.{u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (ContinuousLinearMap.fst.{u1, u3, u4} R₁ _inst_1 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20) (ContinuousLinearMap.prod.{u1, u2, u3, u4} R₁ _inst_1 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_19 _inst_20 f g)) f
+but is expected to have type
+ forall {R₁ : Type.{u4}} [_inst_1 : Semiring.{u4} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u2}} [_inst_10 : TopologicalSpace.{u2} M₃] [_inst_11 : AddCommMonoid.{u2} M₃] [_inst_14 : Module.{u4, u1} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u4, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u4, u2} R₁ M₃ _inst_1 _inst_11] (f : ContinuousLinearMap.{u4, u4, u1, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) (g : ContinuousLinearMap.{u4, u4, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20), Eq.{max (succ u1) (succ u3)} (ContinuousLinearMap.{u4, u4, u1, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) (ContinuousLinearMap.comp.{u4, u4, u4, u1, max u3 u2, u3} R₁ R₁ R₁ _inst_1 _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 (Prod.{u3, u2} M₂ M₃) (instTopologicalSpaceProd.{u3, u2} M₂ M₃ _inst_8 _inst_10) (Prod.instAddCommMonoidSum.{u3, u2} M₂ M₃ _inst_9 _inst_11) M₂ _inst_8 _inst_9 _inst_14 (Prod.module.{u4, u3, u2} R₁ M₂ M₃ _inst_1 _inst_9 _inst_11 _inst_19 _inst_20) _inst_19 (RingHomCompTriple.ids.{u4, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1))) (ContinuousLinearMap.fst.{u4, u3, u2} R₁ _inst_1 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20) (ContinuousLinearMap.prod.{u4, u1, u3, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_19 _inst_20 f g)) f
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.fst_comp_prod ContinuousLinearMap.fst_comp_prodₓ'. -/
@[simp]
theorem fst_comp_prod [Module R₁ M₂] [Module R₁ M₃] (f : M₁ →L[R₁] M₂) (g : M₁ →L[R₁] M₃) :
(fst R₁ M₂ M₃).comp (f.Prod g) = f :=
ext fun x => rfl
#align continuous_linear_map.fst_comp_prod ContinuousLinearMap.fst_comp_prod
+/- warning: continuous_linear_map.snd_comp_prod -> ContinuousLinearMap.snd_comp_prod is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u4}} [_inst_10 : TopologicalSpace.{u4} M₃] [_inst_11 : AddCommMonoid.{u4} M₃] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u1, u4} R₁ M₃ _inst_1 _inst_11] (f : ContinuousLinearMap.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) (g : ContinuousLinearMap.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20), Eq.{max (succ u2) (succ u4)} (ContinuousLinearMap.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) (ContinuousLinearMap.comp.{u1, u1, u1, u2, max u3 u4, u4} R₁ R₁ R₁ _inst_1 _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 (Prod.{u3, u4} M₂ M₃) (Prod.topologicalSpace.{u3, u4} M₂ M₃ _inst_8 _inst_10) (Prod.addCommMonoid.{u3, u4} M₂ M₃ _inst_9 _inst_11) M₃ _inst_10 _inst_11 _inst_14 (Prod.module.{u1, u3, u4} R₁ M₂ M₃ _inst_1 _inst_9 _inst_11 _inst_19 _inst_20) _inst_20 (RingHomCompTriple.right_ids.{u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (ContinuousLinearMap.snd.{u1, u3, u4} R₁ _inst_1 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20) (ContinuousLinearMap.prod.{u1, u2, u3, u4} R₁ _inst_1 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_19 _inst_20 f g)) g
+but is expected to have type
+ forall {R₁ : Type.{u4}} [_inst_1 : Semiring.{u4} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u2}} [_inst_10 : TopologicalSpace.{u2} M₃] [_inst_11 : AddCommMonoid.{u2} M₃] [_inst_14 : Module.{u4, u1} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u4, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u4, u2} R₁ M₃ _inst_1 _inst_11] (f : ContinuousLinearMap.{u4, u4, u1, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) (g : ContinuousLinearMap.{u4, u4, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20), Eq.{max (succ u1) (succ u2)} (ContinuousLinearMap.{u4, u4, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) (ContinuousLinearMap.comp.{u4, u4, u4, u1, max u3 u2, u2} R₁ R₁ R₁ _inst_1 _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 (Prod.{u3, u2} M₂ M₃) (instTopologicalSpaceProd.{u3, u2} M₂ M₃ _inst_8 _inst_10) (Prod.instAddCommMonoidSum.{u3, u2} M₂ M₃ _inst_9 _inst_11) M₃ _inst_10 _inst_11 _inst_14 (Prod.module.{u4, u3, u2} R₁ M₂ M₃ _inst_1 _inst_9 _inst_11 _inst_19 _inst_20) _inst_20 (RingHomCompTriple.ids.{u4, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1))) (ContinuousLinearMap.snd.{u4, u3, u2} R₁ _inst_1 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20) (ContinuousLinearMap.prod.{u4, u1, u3, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_19 _inst_20 f g)) g
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.snd_comp_prod ContinuousLinearMap.snd_comp_prodₓ'. -/
@[simp]
theorem snd_comp_prod [Module R₁ M₂] [Module R₁ M₃] (f : M₁ →L[R₁] M₂) (g : M₁ →L[R₁] M₃) :
(snd R₁ M₂ M₃).comp (f.Prod g) = g :=
ext fun x => rfl
#align continuous_linear_map.snd_comp_prod ContinuousLinearMap.snd_comp_prod
+/- warning: continuous_linear_map.prod_map -> ContinuousLinearMap.prodMap is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u4}} [_inst_10 : TopologicalSpace.{u4} M₃] [_inst_11 : AddCommMonoid.{u4} M₃] {M₄ : Type.{u5}} [_inst_12 : TopologicalSpace.{u5} M₄] [_inst_13 : AddCommMonoid.{u5} M₄] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u1, u4} R₁ M₃ _inst_1 _inst_11] [_inst_21 : Module.{u1, u5} R₁ M₄ _inst_1 _inst_13], (ContinuousLinearMap.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) -> (ContinuousLinearMap.{u1, u1, u4, u5} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_20 _inst_21) -> (ContinuousLinearMap.{u1, u1, max u2 u4, max u3 u5} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u4} M₁ M₃) (Prod.topologicalSpace.{u2, u4} M₁ M₃ _inst_4 _inst_10) (Prod.addCommMonoid.{u2, u4} M₁ M₃ _inst_5 _inst_11) (Prod.{u3, u5} M₂ M₄) (Prod.topologicalSpace.{u3, u5} M₂ M₄ _inst_8 _inst_12) (Prod.addCommMonoid.{u3, u5} M₂ M₄ _inst_9 _inst_13) (Prod.module.{u1, u2, u4} R₁ M₁ M₃ _inst_1 _inst_5 _inst_11 _inst_14 _inst_20) (Prod.module.{u1, u3, u5} R₁ M₂ M₄ _inst_1 _inst_9 _inst_13 _inst_19 _inst_21))
+but is expected to have type
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u4}} [_inst_10 : TopologicalSpace.{u4} M₃] [_inst_11 : AddCommMonoid.{u4} M₃] {M₄ : Type.{u5}} [_inst_12 : TopologicalSpace.{u5} M₄] [_inst_13 : AddCommMonoid.{u5} M₄] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u1, u4} R₁ M₃ _inst_1 _inst_11] [_inst_21 : Module.{u1, u5} R₁ M₄ _inst_1 _inst_13], (ContinuousLinearMap.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) -> (ContinuousLinearMap.{u1, u1, u4, u5} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_20 _inst_21) -> (ContinuousLinearMap.{u1, u1, max u4 u2, max u5 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u4} M₁ M₃) (instTopologicalSpaceProd.{u2, u4} M₁ M₃ _inst_4 _inst_10) (Prod.instAddCommMonoidSum.{u2, u4} M₁ M₃ _inst_5 _inst_11) (Prod.{u3, u5} M₂ M₄) (instTopologicalSpaceProd.{u3, u5} M₂ M₄ _inst_8 _inst_12) (Prod.instAddCommMonoidSum.{u3, u5} M₂ M₄ _inst_9 _inst_13) (Prod.module.{u1, u2, u4} R₁ M₁ M₃ _inst_1 _inst_5 _inst_11 _inst_14 _inst_20) (Prod.module.{u1, u3, u5} R₁ M₂ M₄ _inst_1 _inst_9 _inst_13 _inst_19 _inst_21))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.prod_map ContinuousLinearMap.prodMapₓ'. -/
/-- `prod.map` of two continuous linear maps. -/
def prodMap [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (f₁ : M₁ →L[R₁] M₂) (f₂ : M₃ →L[R₁] M₄) :
M₁ × M₃ →L[R₁] M₂ × M₄ :=
(f₁.comp (fst R₁ M₁ M₃)).Prod (f₂.comp (snd R₁ M₁ M₃))
#align continuous_linear_map.prod_map ContinuousLinearMap.prodMap
+/- warning: continuous_linear_map.coe_prod_map -> ContinuousLinearMap.coe_prodMap is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u4}} [_inst_10 : TopologicalSpace.{u4} M₃] [_inst_11 : AddCommMonoid.{u4} M₃] {M₄ : Type.{u5}} [_inst_12 : TopologicalSpace.{u5} M₄] [_inst_13 : AddCommMonoid.{u5} M₄] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u1, u4} R₁ M₃ _inst_1 _inst_11] [_inst_21 : Module.{u1, u5} R₁ M₄ _inst_1 _inst_13] (f₁ : ContinuousLinearMap.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) (f₂ : ContinuousLinearMap.{u1, u1, u4, u5} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_20 _inst_21), 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_prod_map ContinuousLinearMap.coe_prodMapₓ'. -/
@[simp, norm_cast]
theorem coe_prodMap [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (f₁ : M₁ →L[R₁] M₂)
(f₂ : M₃ →L[R₁] M₄) : ↑(f₁.Prod_map f₂) = (f₁ : M₁ →ₗ[R₁] M₂).Prod_map (f₂ : M₃ →ₗ[R₁] M₄) :=
rfl
#align continuous_linear_map.coe_prod_map ContinuousLinearMap.coe_prodMap
+/- warning: continuous_linear_map.coe_prod_map' -> ContinuousLinearMap.coe_prod_map is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u4}} [_inst_10 : TopologicalSpace.{u4} M₃] [_inst_11 : AddCommMonoid.{u4} M₃] {M₄ : Type.{u5}} [_inst_12 : TopologicalSpace.{u5} M₄] [_inst_13 : AddCommMonoid.{u5} M₄] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u1, u4} R₁ M₃ _inst_1 _inst_11] [_inst_21 : Module.{u1, u5} R₁ M₄ _inst_1 _inst_13] (f₁ : ContinuousLinearMap.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) (f₂ : ContinuousLinearMap.{u1, u1, u4, u5} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_20 _inst_21), Eq.{max (succ (max u2 u4)) (succ (max u3 u5))} ((Prod.{u2, u4} M₁ M₃) -> (Prod.{u3, u5} M₂ M₄)) (coeFn.{max (succ (max u2 u4)) (succ (max u3 u5)), max (succ (max u2 u4)) (succ (max u3 u5))} (ContinuousLinearMap.{u1, u1, max u2 u4, max u3 u5} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u4} M₁ M₃) (Prod.topologicalSpace.{u2, u4} M₁ M₃ _inst_4 _inst_10) (Prod.addCommMonoid.{u2, u4} M₁ M₃ _inst_5 _inst_11) (Prod.{u3, u5} M₂ M₄) (Prod.topologicalSpace.{u3, u5} M₂ M₄ _inst_8 _inst_12) (Prod.addCommMonoid.{u3, u5} M₂ M₄ _inst_9 _inst_13) (Prod.module.{u1, u2, u4} R₁ M₁ M₃ _inst_1 _inst_5 _inst_11 _inst_14 _inst_20) (Prod.module.{u1, u3, u5} R₁ M₂ M₄ _inst_1 _inst_9 _inst_13 _inst_19 _inst_21)) (fun (_x : ContinuousLinearMap.{u1, u1, max u2 u4, max u3 u5} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u4} M₁ M₃) (Prod.topologicalSpace.{u2, u4} M₁ M₃ _inst_4 _inst_10) (Prod.addCommMonoid.{u2, u4} M₁ M₃ _inst_5 _inst_11) (Prod.{u3, u5} M₂ M₄) (Prod.topologicalSpace.{u3, u5} M₂ M₄ _inst_8 _inst_12) (Prod.addCommMonoid.{u3, u5} M₂ M₄ _inst_9 _inst_13) (Prod.module.{u1, u2, u4} R₁ M₁ M₃ _inst_1 _inst_5 _inst_11 _inst_14 _inst_20) (Prod.module.{u1, u3, u5} R₁ M₂ M₄ _inst_1 _inst_9 _inst_13 _inst_19 _inst_21)) => (Prod.{u2, u4} M₁ M₃) -> (Prod.{u3, u5} M₂ M₄)) (ContinuousLinearMap.toFun.{u1, u1, max u2 u4, max u3 u5} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u4} M₁ M₃) (Prod.topologicalSpace.{u2, u4} M₁ M₃ _inst_4 _inst_10) (Prod.addCommMonoid.{u2, u4} M₁ M₃ _inst_5 _inst_11) (Prod.{u3, u5} M₂ M₄) (Prod.topologicalSpace.{u3, u5} M₂ M₄ _inst_8 _inst_12) (Prod.addCommMonoid.{u3, u5} M₂ M₄ _inst_9 _inst_13) (Prod.module.{u1, u2, u4} R₁ M₁ M₃ _inst_1 _inst_5 _inst_11 _inst_14 _inst_20) (Prod.module.{u1, u3, u5} R₁ M₂ M₄ _inst_1 _inst_9 _inst_13 _inst_19 _inst_21)) (ContinuousLinearMap.prodMap.{u1, u2, u3, u4, u5} R₁ _inst_1 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_14 _inst_19 _inst_20 _inst_21 f₁ f₂)) (Prod.map.{u2, u3, u4, u5} M₁ M₂ M₃ M₄ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) => M₁ -> M₂) (ContinuousLinearMap.toFun.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) f₁) (coeFn.{max (succ u4) (succ u5), max (succ u4) (succ u5)} (ContinuousLinearMap.{u1, u1, u4, u5} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_20 _inst_21) (fun (_x : ContinuousLinearMap.{u1, u1, u4, u5} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_20 _inst_21) => M₃ -> M₄) (ContinuousLinearMap.toFun.{u1, u1, u4, u5} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_20 _inst_21) f₂))
+but is expected to have type
+ forall {R₁ : Type.{u5}} [_inst_1 : Semiring.{u5} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] {M₂ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₂] [_inst_9 : AddCommMonoid.{u4} M₂] {M₃ : Type.{u3}} [_inst_10 : TopologicalSpace.{u3} M₃] [_inst_11 : AddCommMonoid.{u3} M₃] {M₄ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₄] [_inst_13 : AddCommMonoid.{u2} M₄] [_inst_14 : Module.{u5, u1} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u5, u4} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u5, u3} R₁ M₃ _inst_1 _inst_11] [_inst_21 : Module.{u5, u2} R₁ M₄ _inst_1 _inst_13] (f₁ : ContinuousLinearMap.{u5, u5, u1, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19) (f₂ : ContinuousLinearMap.{u5, u5, u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_20 _inst_21), 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_inst_19 (ContinuousLinearMap.continuousSemilinearMapClass.{u5, u5, u1, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_14 _inst_19))) f₁) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (ContinuousLinearMap.{u5, u5, u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_20 _inst_21) M₃ (fun (_x : M₃) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₃) => M₄) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u3, u2} (ContinuousLinearMap.{u5, u5, u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_20 _inst_21) M₃ M₄ _inst_10 _inst_12 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u5, u5, u3, u2} (ContinuousLinearMap.{u5, u5, u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_20 _inst_21) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_20 _inst_21 (ContinuousLinearMap.continuousSemilinearMapClass.{u5, u5, u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) M₃ _inst_10 _inst_11 M₄ _inst_12 _inst_13 _inst_20 _inst_21))) f₂))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_prod_map' ContinuousLinearMap.coe_prod_mapₓ'. -/
@[simp, norm_cast]
-theorem coe_prod_map' [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (f₁ : M₁ →L[R₁] M₂)
+theorem coe_prod_map [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (f₁ : M₁ →L[R₁] M₂)
(f₂ : M₃ →L[R₁] M₄) : ⇑(f₁.Prod_map f₂) = Prod.map f₁ f₂ :=
rfl
-#align continuous_linear_map.coe_prod_map' ContinuousLinearMap.coe_prod_map'
-
+#align continuous_linear_map.coe_prod_map' ContinuousLinearMap.coe_prod_map
+
+/- warning: continuous_linear_map.coprod -> ContinuousLinearMap.coprod is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u4}} [_inst_10 : TopologicalSpace.{u4} M₃] [_inst_11 : AddCommMonoid.{u4} M₃] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u1, u4} R₁ M₃ _inst_1 _inst_11] [_inst_21 : ContinuousAdd.{u4} M₃ _inst_10 (AddZeroClass.toHasAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_11)))], (ContinuousLinearMap.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) -> (ContinuousLinearMap.{u1, u1, u3, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20) -> (ContinuousLinearMap.{u1, u1, max u2 u3, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) M₃ _inst_10 _inst_11 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) _inst_20)
+but is expected to have type
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u4}} [_inst_10 : TopologicalSpace.{u4} M₃] [_inst_11 : AddCommMonoid.{u4} M₃] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u1, u4} R₁ M₃ _inst_1 _inst_11] [_inst_21 : ContinuousAdd.{u4} M₃ _inst_10 (AddZeroClass.toAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_11)))], (ContinuousLinearMap.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) -> (ContinuousLinearMap.{u1, u1, u3, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20) -> (ContinuousLinearMap.{u1, u1, max u3 u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u3} M₁ M₂) (instTopologicalSpaceProd.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.instAddCommMonoidSum.{u2, u3} M₁ M₂ _inst_5 _inst_9) M₃ _inst_10 _inst_11 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) _inst_20)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coprod ContinuousLinearMap.coprodₓ'. -/
/-- The continuous linear map given by `(x, y) ↦ f₁ x + f₂ y`. -/
def coprod [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃] (f₁ : M₁ →L[R₁] M₃)
(f₂ : M₂ →L[R₁] M₃) : M₁ × M₂ →L[R₁] M₃ :=
⟨LinearMap.coprod f₁ f₂, (f₁.cont.comp continuous_fst).add (f₂.cont.comp continuous_snd)⟩
#align continuous_linear_map.coprod ContinuousLinearMap.coprod
+/- warning: continuous_linear_map.coe_coprod -> ContinuousLinearMap.coe_coprod is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u4}} [_inst_10 : TopologicalSpace.{u4} M₃] [_inst_11 : AddCommMonoid.{u4} M₃] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u1, u4} R₁ M₃ _inst_1 _inst_11] [_inst_21 : ContinuousAdd.{u4} M₃ _inst_10 (AddZeroClass.toHasAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_11)))] (f₁ : ContinuousLinearMap.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) (f₂ : ContinuousLinearMap.{u1, u1, u3, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 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_inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20)))) f₂))
+but is expected to have type
+ forall {R₁ : Type.{u4}} [_inst_1 : Semiring.{u4} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u2}} [_inst_10 : TopologicalSpace.{u2} M₃] [_inst_11 : AddCommMonoid.{u2} M₃] [_inst_14 : Module.{u4, u1} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u4, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u4, u2} R₁ M₃ _inst_1 _inst_11] [_inst_21 : ContinuousAdd.{u2} M₃ _inst_10 (AddZeroClass.toAdd.{u2} M₃ (AddMonoid.toAddZeroClass.{u2} M₃ (AddCommMonoid.toAddMonoid.{u2} M₃ _inst_11)))] (f₁ : ContinuousLinearMap.{u4, u4, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) (f₂ : ContinuousLinearMap.{u4, u4, u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20), Eq.{max (max (succ u1) (succ u3)) (succ u2)} (LinearMap.{u4, u4, max u1 u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) (Prod.{u1, u3} M₁ M₂) M₃ (Prod.instAddCommMonoidSum.{u1, u3} M₁ M₂ _inst_5 _inst_9) _inst_11 (Prod.module.{u4, u1, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) _inst_20) (ContinuousLinearMap.toLinearMap.{u4, u4, max u1 u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) (Prod.{u1, u3} M₁ M₂) (instTopologicalSpaceProd.{u1, u3} M₁ M₂ _inst_4 _inst_8) (Prod.instAddCommMonoidSum.{u1, u3} M₁ M₂ _inst_5 _inst_9) M₃ _inst_10 _inst_11 (Prod.module.{u4, u1, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) _inst_20 (ContinuousLinearMap.coprod.{u4, u1, u3, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_19 _inst_20 _inst_21 f₁ f₂)) (LinearMap.coprod.{u4, u1, u3, u2} R₁ M₁ M₂ M₃ _inst_1 _inst_5 _inst_9 _inst_11 _inst_14 _inst_19 _inst_20 (ContinuousLinearMap.toLinearMap.{u4, u4, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20 f₁) (ContinuousLinearMap.toLinearMap.{u4, u4, u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20 f₂))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_coprod ContinuousLinearMap.coe_coprodₓ'. -/
@[norm_cast, simp]
theorem coe_coprod [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃] (f₁ : M₁ →L[R₁] M₃)
(f₂ : M₂ →L[R₁] M₃) : (f₁.coprod f₂ : M₁ × M₂ →ₗ[R₁] M₃) = LinearMap.coprod f₁ f₂ :=
rfl
#align continuous_linear_map.coe_coprod ContinuousLinearMap.coe_coprod
+/- warning: continuous_linear_map.coprod_apply -> ContinuousLinearMap.coprod_apply is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u4}} [_inst_10 : TopologicalSpace.{u4} M₃] [_inst_11 : AddCommMonoid.{u4} M₃] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u1, u4} R₁ M₃ _inst_1 _inst_11] [_inst_21 : ContinuousAdd.{u4} M₃ _inst_10 (AddZeroClass.toHasAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_11)))] (f₁ : ContinuousLinearMap.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) (f₂ : ContinuousLinearMap.{u1, u1, u3, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20) (x : Prod.{u2, u3} M₁ M₂), Eq.{succ u4} M₃ (coeFn.{max (succ (max u2 u3)) (succ u4), max (succ (max u2 u3)) (succ u4)} (ContinuousLinearMap.{u1, u1, max u2 u3, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) M₃ _inst_10 _inst_11 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) _inst_20) (fun (_x : ContinuousLinearMap.{u1, u1, max u2 u3, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) M₃ _inst_10 _inst_11 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) _inst_20) => (Prod.{u2, u3} M₁ M₂) -> M₃) (ContinuousLinearMap.toFun.{u1, u1, max u2 u3, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (Prod.{u2, u3} M₁ M₂) (Prod.topologicalSpace.{u2, u3} M₁ M₂ _inst_4 _inst_8) (Prod.addCommMonoid.{u2, u3} M₁ M₂ _inst_5 _inst_9) M₃ _inst_10 _inst_11 (Prod.module.{u1, u2, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) _inst_20) (ContinuousLinearMap.coprod.{u1, u2, u3, u4} R₁ _inst_1 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_19 _inst_20 _inst_21 f₁ f₂) x) (HAdd.hAdd.{u4, u4, u4} M₃ M₃ M₃ (instHAdd.{u4} M₃ (AddZeroClass.toHasAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_11)))) (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (ContinuousLinearMap.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) => M₁ -> M₃) (ContinuousLinearMap.toFun.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) f₁ (Prod.fst.{u2, u3} M₁ M₂ x)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u1, u3, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20) (fun (_x : ContinuousLinearMap.{u1, u1, u3, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20) => M₂ -> M₃) (ContinuousLinearMap.toFun.{u1, u1, u3, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20) f₂ (Prod.snd.{u2, u3} M₁ M₂ x)))
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coprod_apply ContinuousLinearMap.coprod_applyₓ'. -/
@[simp]
theorem coprod_apply [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃] (f₁ : M₁ →L[R₁] M₃)
(f₂ : M₂ →L[R₁] M₃) (x) : f₁.coprod f₂ x = f₁ x.1 + f₂ x.2 :=
rfl
#align continuous_linear_map.coprod_apply ContinuousLinearMap.coprod_apply
+/- warning: continuous_linear_map.range_coprod -> ContinuousLinearMap.range_coprod is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M₁] [_inst_5 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u4}} [_inst_10 : TopologicalSpace.{u4} M₃] [_inst_11 : AddCommMonoid.{u4} M₃] [_inst_14 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u1, u4} R₁ M₃ _inst_1 _inst_11] [_inst_21 : ContinuousAdd.{u4} M₃ _inst_10 (AddZeroClass.toHasAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_11)))] (f₁ : ContinuousLinearMap.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) (f₂ : ContinuousLinearMap.{u1, u1, u3, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 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(RingHomSurjective.ids.{u1} R₁ _inst_1) (ContinuousLinearMap.coprod.{u1, u2, u3, u4} R₁ _inst_1 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_19 _inst_20 _inst_21 f₁ f₂)) (Sup.sup.{u4} (Submodule.{u1, u4} R₁ M₃ _inst_1 _inst_11 _inst_20) (SemilatticeSup.toHasSup.{u4} (Submodule.{u1, u4} R₁ M₃ _inst_1 _inst_11 _inst_20) (Lattice.toSemilatticeSup.{u4} (Submodule.{u1, u4} R₁ M₃ _inst_1 _inst_11 _inst_20) (ConditionallyCompleteLattice.toLattice.{u4} (Submodule.{u1, u4} R₁ M₃ _inst_1 _inst_11 _inst_20) (CompleteLattice.toConditionallyCompleteLattice.{u4} (Submodule.{u1, u4} R₁ M₃ _inst_1 _inst_11 _inst_20) (Submodule.completeLattice.{u1, u4} R₁ M₃ _inst_1 _inst_11 _inst_20))))) (LinearMap.range.{u1, u1, u2, u4, max u2 u4} R₁ R₁ M₁ M₃ _inst_1 _inst_1 _inst_5 _inst_11 _inst_14 _inst_20 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (ContinuousLinearMap.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u1, u1, u2, u4} (ContinuousLinearMap.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20)) (RingHomSurjective.ids.{u1} R₁ _inst_1) f₁) (LinearMap.range.{u1, u1, u3, u4, max u3 u4} R₁ R₁ M₂ M₃ _inst_1 _inst_1 _inst_9 _inst_11 _inst_19 _inst_20 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (ContinuousLinearMap.{u1, u1, u3, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u4, u1, u1, u3, u4} (ContinuousLinearMap.{u1, u1, u3, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u3, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20)) (RingHomSurjective.ids.{u1} R₁ _inst_1) f₂))
+but is expected to have type
+ forall {R₁ : Type.{u4}} [_inst_1 : Semiring.{u4} R₁] {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] {M₂ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₂] [_inst_9 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u2}} [_inst_10 : TopologicalSpace.{u2} M₃] [_inst_11 : AddCommMonoid.{u2} M₃] [_inst_14 : Module.{u4, u1} R₁ M₁ _inst_1 _inst_5] [_inst_19 : Module.{u4, u3} R₁ M₂ _inst_1 _inst_9] [_inst_20 : Module.{u4, u2} R₁ M₃ _inst_1 _inst_11] [_inst_21 : ContinuousAdd.{u2} M₃ _inst_10 (AddZeroClass.toAdd.{u2} M₃ (AddMonoid.toAddZeroClass.{u2} M₃ (AddCommMonoid.toAddMonoid.{u2} M₃ _inst_11)))] (f₁ : ContinuousLinearMap.{u4, u4, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) (f₂ : ContinuousLinearMap.{u4, u4, u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20), Eq.{succ u2} (Submodule.{u4, u2} R₁ M₃ _inst_1 _inst_11 _inst_20) (LinearMap.range.{u4, u4, max u1 u3, u2, max (max u1 u2) u3} R₁ R₁ (Prod.{u1, u3} M₁ M₂) M₃ _inst_1 _inst_1 (Prod.instAddCommMonoidSum.{u1, u3} M₁ M₂ _inst_5 _inst_9) _inst_11 (Prod.module.{u4, u1, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) _inst_20 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) (ContinuousLinearMap.{u4, u4, max u3 u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) (Prod.{u1, u3} M₁ M₂) (instTopologicalSpaceProd.{u1, u3} M₁ M₂ _inst_4 _inst_8) (Prod.instAddCommMonoidSum.{u1, u3} M₁ M₂ _inst_5 _inst_9) M₃ _inst_10 _inst_11 (Prod.module.{u4, u1, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) _inst_20) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max (max u1 u3) u2, u4, u4, max u1 u3, u2} (ContinuousLinearMap.{u4, u4, max u3 u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) (Prod.{u1, u3} M₁ M₂) (instTopologicalSpaceProd.{u1, u3} M₁ M₂ _inst_4 _inst_8) (Prod.instAddCommMonoidSum.{u1, u3} M₁ M₂ _inst_5 _inst_9) M₃ _inst_10 _inst_11 (Prod.module.{u4, u1, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) _inst_20) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) (Prod.{u1, u3} M₁ M₂) (instTopologicalSpaceProd.{u1, u3} M₁ M₂ _inst_4 _inst_8) (Prod.instAddCommMonoidSum.{u1, u3} M₁ M₂ _inst_5 _inst_9) M₃ _inst_10 _inst_11 (Prod.module.{u4, u1, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) _inst_20 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, max u1 u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) (Prod.{u1, u3} M₁ M₂) (instTopologicalSpaceProd.{u1, u3} M₁ M₂ _inst_4 _inst_8) (Prod.instAddCommMonoidSum.{u1, u3} M₁ M₂ _inst_5 _inst_9) M₃ _inst_10 _inst_11 (Prod.module.{u4, u1, u3} R₁ M₁ M₂ _inst_1 _inst_5 _inst_9 _inst_14 _inst_19) _inst_20)) (RingHomSurjective.ids.{u4} R₁ _inst_1) (ContinuousLinearMap.coprod.{u4, u1, u3, u2} R₁ _inst_1 M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_14 _inst_19 _inst_20 _inst_21 f₁ f₂)) (Sup.sup.{u2} (Submodule.{u4, u2} R₁ M₃ _inst_1 _inst_11 _inst_20) (SemilatticeSup.toSup.{u2} (Submodule.{u4, u2} R₁ M₃ _inst_1 _inst_11 _inst_20) (Lattice.toSemilatticeSup.{u2} (Submodule.{u4, u2} R₁ M₃ _inst_1 _inst_11 _inst_20) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u4, u2} R₁ M₃ _inst_1 _inst_11 _inst_20) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u4, u2} R₁ M₃ _inst_1 _inst_11 _inst_20) (Submodule.completeLattice.{u4, u2} R₁ M₃ _inst_1 _inst_11 _inst_20))))) (LinearMap.range.{u4, u4, u1, u2, max u1 u2} R₁ R₁ M₁ M₃ _inst_1 _inst_1 _inst_5 _inst_11 _inst_14 _inst_20 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) (ContinuousLinearMap.{u4, u4, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u1 u2, u4, u4, u1, u2} (ContinuousLinearMap.{u4, u4, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_4 _inst_5 M₃ _inst_10 _inst_11 _inst_14 _inst_20)) (RingHomSurjective.ids.{u4} R₁ _inst_1) f₁) (LinearMap.range.{u4, u4, u3, u2, max u3 u2} R₁ R₁ M₂ M₃ _inst_1 _inst_1 _inst_9 _inst_11 _inst_19 _inst_20 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) (ContinuousLinearMap.{u4, u4, u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u2, u4, u4, u3, u2} (ContinuousLinearMap.{u4, u4, u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₂ _inst_8 _inst_9 M₃ _inst_10 _inst_11 _inst_19 _inst_20)) (RingHomSurjective.ids.{u4} R₁ _inst_1) f₂))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.range_coprod ContinuousLinearMap.range_coprodₓ'. -/
theorem range_coprod [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃] (f₁ : M₁ →L[R₁] M₃)
(f₂ : M₂ →L[R₁] M₃) : range (f₁.coprod f₂) = range f₁ ⊔ range f₂ :=
LinearMap.range_coprod _ _
@@ -1232,13 +1967,21 @@ section
variable {R S : Type _} [Semiring R] [Semiring S] [Module R M₁] [Module R M₂] [Module R S]
[Module S M₂] [IsScalarTower R S M₂] [TopologicalSpace S] [ContinuousSMul S M₂]
+#print ContinuousLinearMap.smulRight /-
/-- The linear map `λ x, c x • f`. Associates to a scalar-valued linear map and an element of
`M₂` the `M₂`-valued linear map obtained by multiplying the two (a.k.a. tensoring by `M₂`).
See also `continuous_linear_map.smul_rightₗ` and `continuous_linear_map.smul_rightL`. -/
def smulRight (c : M₁ →L[R] S) (f : M₂) : M₁ →L[R] M₂ :=
{ c.toLinearMap.smul_right f with cont := c.2.smul continuous_const }
#align continuous_linear_map.smul_right ContinuousLinearMap.smulRight
+-/
+/- warning: continuous_linear_map.smul_right_apply -> ContinuousLinearMap.smulRight_apply is a dubious translation:
+lean 3 declaration is
+ forall {M₁ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₁] [_inst_5 : AddCommMonoid.{u1} M₁] {M₂ : Type.{u2}} [_inst_8 : TopologicalSpace.{u2} M₂] [_inst_9 : AddCommMonoid.{u2} M₂] {R : Type.{u3}} {S : Type.{u4}} [_inst_19 : Semiring.{u3} R] [_inst_20 : Semiring.{u4} S] [_inst_21 : Module.{u3, u1} R M₁ _inst_19 _inst_5] [_inst_22 : Module.{u3, u2} R M₂ _inst_19 _inst_9] [_inst_23 : Module.{u3, u4} R S _inst_19 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_20)))] [_inst_24 : Module.{u4, u2} S M₂ _inst_20 _inst_9] [_inst_25 : IsScalarTower.{u3, u4, u2} R S M₂ (SMulZeroClass.toHasSmul.{u3, u4} R S (AddZeroClass.toHasZero.{u4} S (AddMonoid.toAddZeroClass.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_20)))))) (SMulWithZero.toSmulZeroClass.{u3, u4} R S (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_19)))) (AddZeroClass.toHasZero.{u4} S (AddMonoid.toAddZeroClass.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_20)))))) (MulActionWithZero.toSMulWithZero.{u3, u4} R S (Semiring.toMonoidWithZero.{u3} R _inst_19) (AddZeroClass.toHasZero.{u4} S (AddMonoid.toAddZeroClass.{u4} S (AddCommMonoid.toAddMonoid.{u4} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_20)))))) (Module.toMulActionWithZero.{u3, u4} R S _inst_19 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_20))) _inst_23)))) (SMulZeroClass.toHasSmul.{u4, u2} S M₂ (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M₂ (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_20)))) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M₂ (Semiring.toMonoidWithZero.{u4} S _inst_20) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (Module.toMulActionWithZero.{u4, u2} S M₂ _inst_20 _inst_9 _inst_24)))) (SMulZeroClass.toHasSmul.{u3, u2} R M₂ (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M₂ (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_19)))) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M₂ (Semiring.toMonoidWithZero.{u3} R _inst_19) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (Module.toMulActionWithZero.{u3, u2} R M₂ _inst_19 _inst_9 _inst_22))))] [_inst_26 : TopologicalSpace.{u4} S] [_inst_27 : ContinuousSMul.{u4, u2} S M₂ (SMulZeroClass.toHasSmul.{u4, u2} S M₂ (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (SMulWithZero.toSmulZeroClass.{u4, u2} S M₂ (MulZeroClass.toHasZero.{u4} S (MulZeroOneClass.toMulZeroClass.{u4} S (MonoidWithZero.toMulZeroOneClass.{u4} S (Semiring.toMonoidWithZero.{u4} S _inst_20)))) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M₂ (Semiring.toMonoidWithZero.{u4} S _inst_20) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (Module.toMulActionWithZero.{u4, u2} S M₂ _inst_20 _inst_9 _inst_24)))) _inst_26 _inst_8] {c : ContinuousLinearMap.{u3, u3, u1, u4} R R _inst_19 _inst_19 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_19)) M₁ _inst_4 _inst_5 S _inst_26 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_20))) _inst_21 _inst_23} {f : M₂} {x : M₁}, Eq.{succ u2} M₂ (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousLinearMap.{u3, u3, u1, u2} R R _inst_19 _inst_19 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_19)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_21 _inst_22) (fun (_x : ContinuousLinearMap.{u3, u3, u1, u2} R R 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_inst_9))) (MulActionWithZero.toSMulWithZero.{u4, u2} S M₂ (Semiring.toMonoidWithZero.{u4} S _inst_20) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (Module.toMulActionWithZero.{u4, u2} S M₂ _inst_20 _inst_9 _inst_24)))) (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (ContinuousLinearMap.{u3, u3, u1, u4} R R _inst_19 _inst_19 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_19)) M₁ _inst_4 _inst_5 S _inst_26 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_20))) _inst_21 _inst_23) (fun (_x : ContinuousLinearMap.{u3, u3, u1, u4} R R _inst_19 _inst_19 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_19)) M₁ _inst_4 _inst_5 S _inst_26 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_20))) _inst_21 _inst_23) => M₁ -> S) (ContinuousLinearMap.toFun.{u3, u3, u1, u4} R R _inst_19 _inst_19 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_19)) M₁ _inst_4 _inst_5 S _inst_26 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S _inst_20))) _inst_21 _inst_23) c x) f)
+but is expected to have type
+ forall {M₁ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₁] [_inst_5 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] {R : Type.{u4}} {S : Type.{u2}} [_inst_19 : Semiring.{u4} R] [_inst_20 : Semiring.{u2} S] [_inst_21 : Module.{u4, u3} R M₁ _inst_19 _inst_5] [_inst_22 : Module.{u4, u1} R M₂ _inst_19 _inst_9] [_inst_23 : Module.{u4, u2} R S _inst_19 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_20)))] [_inst_24 : Module.{u2, u1} S M₂ _inst_20 _inst_9] [_inst_25 : IsScalarTower.{u4, u2, u1} R S M₂ (SMulZeroClass.toSMul.{u4, u2} R S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_20)) (SMulWithZero.toSMulZeroClass.{u4, u2} R S (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_19)) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_20)) (MulActionWithZero.toSMulWithZero.{u4, u2} R S (Semiring.toMonoidWithZero.{u4} R _inst_19) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_20)) (Module.toMulActionWithZero.{u4, u2} R S _inst_19 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_20))) _inst_23)))) (SMulZeroClass.toSMul.{u2, u1} S M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u2, u1} S M₂ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_20)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u2, u1} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_20) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u2, u1} S M₂ _inst_20 _inst_9 _inst_24)))) (SMulZeroClass.toSMul.{u4, u1} R M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u4, u1} R M₂ (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_19)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u4, u1} R M₂ (Semiring.toMonoidWithZero.{u4} R _inst_19) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u4, u1} R M₂ _inst_19 _inst_9 _inst_22))))] [_inst_26 : TopologicalSpace.{u2} S] [_inst_27 : ContinuousSMul.{u2, u1} S M₂ (SMulZeroClass.toSMul.{u2, u1} S M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u2, u1} S M₂ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_20)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u2, u1} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_20) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u2, u1} S M₂ _inst_20 _inst_9 _inst_24)))) _inst_26 _inst_8] {c : ContinuousLinearMap.{u4, u4, u3, u2} R R _inst_19 _inst_19 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_19)) M₁ _inst_4 _inst_5 S _inst_26 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_20))) _inst_21 _inst_23} {f : M₂} {x : M₁}, Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (ContinuousLinearMap.{u4, u4, u3, u1} R R _inst_19 _inst_19 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_19)) M₁ _inst_4 _inst_5 M₂ _inst_8 _inst_9 _inst_21 _inst_22) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u3 u1, u3, u1} (ContinuousLinearMap.{u4, u4, u3, u1} R R _inst_19 _inst_19 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(x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => S) x) M₂ M₂ (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => S) x) M₂ (SMulZeroClass.toSMul.{u2, u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => S) x) M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => S) x) M₂ (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => S) x) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => S) x) _inst_20)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => S) x) M₂ (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => S) x) _inst_20) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u2, u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => S) x) M₂ _inst_20 _inst_9 _inst_24))))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (ContinuousLinearMap.{u4, u4, u3, u2} R R _inst_19 _inst_19 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_19)) M₁ _inst_4 _inst_5 S _inst_26 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_20))) _inst_21 _inst_23) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => S) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u3, u2} (ContinuousLinearMap.{u4, u4, u3, u2} R R _inst_19 _inst_19 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_19)) M₁ _inst_4 _inst_5 S _inst_26 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_20))) _inst_21 _inst_23) M₁ S _inst_4 _inst_26 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u4, u4, u3, u2} (ContinuousLinearMap.{u4, u4, u3, u2} R R _inst_19 _inst_19 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_19)) M₁ _inst_4 _inst_5 S _inst_26 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_20))) _inst_21 _inst_23) R R _inst_19 _inst_19 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_19)) M₁ _inst_4 _inst_5 S _inst_26 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_20))) _inst_21 _inst_23 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, u2} R R _inst_19 _inst_19 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_19)) M₁ _inst_4 _inst_5 S _inst_26 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_20))) _inst_21 _inst_23))) c x) f)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_right_apply ContinuousLinearMap.smulRight_applyₓ'. -/
@[simp]
theorem smulRight_apply {c : M₁ →L[R] S} {f : M₂} {x : M₁} :
(smulRight c f : M₁ → M₂) x = c x • f :=
@@ -1249,17 +1992,35 @@ end
variable [Module R₁ M₂] [TopologicalSpace R₁] [ContinuousSMul R₁ M₂]
+/- warning: continuous_linear_map.smul_right_one_one -> ContinuousLinearMap.smulRight_one_one is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₂ : Type.{u2}} [_inst_8 : TopologicalSpace.{u2} M₂] [_inst_9 : AddCommMonoid.{u2} M₂] [_inst_19 : Module.{u1, u2} R₁ M₂ _inst_1 _inst_9] [_inst_20 : TopologicalSpace.{u1} R₁] [_inst_21 : ContinuousSMul.{u1, u2} R₁ M₂ (SMulZeroClass.toHasSmul.{u1, u2} R₁ M₂ (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (SMulWithZero.toSmulZeroClass.{u1, u2} R₁ M₂ (MulZeroClass.toHasZero.{u1} R₁ (MulZeroOneClass.toMulZeroClass.{u1} R₁ (MonoidWithZero.toMulZeroOneClass.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)))) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (MulActionWithZero.toSMulWithZero.{u1, u2} R₁ M₂ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (Module.toMulActionWithZero.{u1, u2} R₁ M₂ _inst_1 _inst_9 _inst_19)))) _inst_20 _inst_8] (c : ContinuousLinearMap.{u1, u1, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) M₂ _inst_8 _inst_9 (Semiring.toModule.{u1} R₁ _inst_1) _inst_19), Eq.{max (succ u1) (succ u2)} (ContinuousLinearMap.{u1, u1, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) M₂ _inst_8 _inst_9 (Semiring.toModule.{u1} R₁ _inst_1) _inst_19) (ContinuousLinearMap.smulRight.{u1, u2, u1, u1} R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) 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_inst_1))) (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1)) 1 (OfNat.mk.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1)) 1 (One.one.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1)) (ContinuousLinearMap.one.{u1, u1} R₁ _inst_1 R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousLinearMap.{u1, u1, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) M₂ _inst_8 _inst_9 (Semiring.toModule.{u1} R₁ _inst_1) _inst_19) (fun (_x : ContinuousLinearMap.{u1, u1, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) M₂ _inst_8 _inst_9 (Semiring.toModule.{u1} R₁ _inst_1) _inst_19) => R₁ -> M₂) (ContinuousLinearMap.toFun.{u1, u1, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) M₂ _inst_8 _inst_9 (Semiring.toModule.{u1} R₁ _inst_1) _inst_19) c (OfNat.ofNat.{u1} R₁ 1 (OfNat.mk.{u1} R₁ 1 (One.one.{u1} R₁ (AddMonoidWithOne.toOne.{u1} R₁ (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R₁ (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))))))))) c
+but is expected to have type
+ forall {R₁ : Type.{u2}} [_inst_1 : Semiring.{u2} R₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_19 : Module.{u2, u1} R₁ M₂ _inst_1 _inst_9] [_inst_20 : TopologicalSpace.{u2} R₁] [_inst_21 : ContinuousSMul.{u2, u1} R₁ M₂ (SMulZeroClass.toSMul.{u2, u1} R₁ M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u2, u1} R₁ M₂ (MonoidWithZero.toZero.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ _inst_1)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u2, u1} R₁ M₂ (Semiring.toMonoidWithZero.{u2} R₁ _inst_1) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u2, u1} R₁ M₂ _inst_1 _inst_9 _inst_19)))) _inst_20 _inst_8] (c : ContinuousLinearMap.{u2, u2, u2, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) M₂ _inst_8 _inst_9 (Semiring.toModule.{u2} R₁ _inst_1) _inst_19), Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u2, u2, u2, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R₁) => M₂) (OfNat.ofNat.{u2} R₁ 1 (One.toOfNat1.{u2} R₁ (Semiring.toOne.{u2} R₁ _inst_1)))) _inst_8 _inst_9 (Semiring.toModule.{u2} R₁ _inst_1) _inst_19) (ContinuousLinearMap.smulRight.{u2, u1, u2, u2} R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R₁) => M₂) (OfNat.ofNat.{u2} R₁ 1 (One.toOfNat1.{u2} R₁ (Semiring.toOne.{u2} R₁ _inst_1)))) _inst_8 _inst_9 R₁ R₁ _inst_1 _inst_1 (Semiring.toModule.{u2} R₁ _inst_1) _inst_19 (Semiring.toModule.{u2} R₁ _inst_1) _inst_19 (IsScalarTower.left.{u2, u1} R₁ ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R₁) => M₂) (OfNat.ofNat.{u2} R₁ 1 (One.toOfNat1.{u2} R₁ (Semiring.toOne.{u2} R₁ _inst_1)))) (MonoidWithZero.toMonoid.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R₁ ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R₁) => M₂) (OfNat.ofNat.{u2} R₁ 1 (One.toOfNat1.{u2} R₁ (Semiring.toOne.{u2} R₁ _inst_1)))) (Semiring.toMonoidWithZero.{u2} R₁ _inst_1) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R₁) => M₂) (OfNat.ofNat.{u2} R₁ 1 (One.toOfNat1.{u2} R₁ (Semiring.toOne.{u2} R₁ _inst_1)))) 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(One.toOfNat1.{u2} (ContinuousLinearMap.{u2, u2, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) (Semiring.toModule.{u2} R₁ _inst_1) (Semiring.toModule.{u2} R₁ _inst_1)) (ContinuousLinearMap.one.{u2, u2} R₁ _inst_1 R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) (Semiring.toModule.{u2} R₁ _inst_1)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u2, u2, u2, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) M₂ _inst_8 _inst_9 (Semiring.toModule.{u2} R₁ _inst_1) _inst_19) R₁ (fun (_x : R₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u2, u2, u2, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) M₂ _inst_8 _inst_9 (Semiring.toModule.{u2} R₁ _inst_1) _inst_19) R₁ M₂ _inst_20 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u2, u2, u2, u1} (ContinuousLinearMap.{u2, u2, u2, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) M₂ _inst_8 _inst_9 (Semiring.toModule.{u2} R₁ _inst_1) _inst_19) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) M₂ _inst_8 _inst_9 (Semiring.toModule.{u2} R₁ _inst_1) _inst_19 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u2, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) M₂ _inst_8 _inst_9 (Semiring.toModule.{u2} R₁ _inst_1) _inst_19))) c (OfNat.ofNat.{u2} R₁ 1 (One.toOfNat1.{u2} R₁ (Semiring.toOne.{u2} R₁ _inst_1))))) c
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_right_one_one ContinuousLinearMap.smulRight_one_oneₓ'. -/
@[simp]
theorem smulRight_one_one (c : R₁ →L[R₁] M₂) : smulRight (1 : R₁ →L[R₁] R₁) (c 1) = c := by
ext <;> simp [← ContinuousLinearMap.map_smul_of_tower]
#align continuous_linear_map.smul_right_one_one ContinuousLinearMap.smulRight_one_one
+/- warning: continuous_linear_map.smul_right_one_eq_iff -> ContinuousLinearMap.smulRight_one_eq_iff is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₂ : Type.{u2}} [_inst_8 : TopologicalSpace.{u2} M₂] [_inst_9 : AddCommMonoid.{u2} M₂] [_inst_19 : Module.{u1, u2} R₁ M₂ _inst_1 _inst_9] [_inst_20 : TopologicalSpace.{u1} R₁] [_inst_21 : ContinuousSMul.{u1, u2} R₁ M₂ (SMulZeroClass.toHasSmul.{u1, u2} R₁ M₂ (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (SMulWithZero.toSmulZeroClass.{u1, u2} R₁ M₂ (MulZeroClass.toHasZero.{u1} R₁ (MulZeroOneClass.toMulZeroClass.{u1} R₁ (MonoidWithZero.toMulZeroOneClass.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)))) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (MulActionWithZero.toSMulWithZero.{u1, u2} R₁ M₂ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (Module.toMulActionWithZero.{u1, u2} R₁ M₂ _inst_1 _inst_9 _inst_19)))) _inst_20 _inst_8] {f : M₂} {f' : M₂}, Iff (Eq.{max (succ u1) (succ u2)} (ContinuousLinearMap.{u1, u1, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) M₂ _inst_8 _inst_9 (Semiring.toModule.{u1} R₁ _inst_1) _inst_19) (ContinuousLinearMap.smulRight.{u1, u2, u1, u1} R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) M₂ _inst_8 _inst_9 R₁ R₁ _inst_1 _inst_1 (Semiring.toModule.{u1} R₁ _inst_1) _inst_19 (Semiring.toModule.{u1} R₁ _inst_1) _inst_19 (IsScalarTower.left.{u1, u2} R₁ M₂ (MonoidWithZero.toMonoid.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R₁ M₂ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) 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+but is expected to have type
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_inst_1) (Semiring.toModule.{u2} R₁ _inst_1)) (ContinuousLinearMap.one.{u2, u2} R₁ _inst_1 R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) (Semiring.toModule.{u2} R₁ _inst_1)))) f) (ContinuousLinearMap.smulRight.{u2, u1, u2, u2} R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) M₂ _inst_8 _inst_9 R₁ R₁ _inst_1 _inst_1 (Semiring.toModule.{u2} R₁ _inst_1) _inst_19 (Semiring.toModule.{u2} R₁ _inst_1) _inst_19 (IsScalarTower.left.{u2, u1} R₁ M₂ (MonoidWithZero.toMonoid.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R₁ M₂ (Semiring.toMonoidWithZero.{u2} R₁ _inst_1) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u2, u1} R₁ M₂ _inst_1 _inst_9 _inst_19))) _inst_20 _inst_21 (OfNat.ofNat.{u2} (ContinuousLinearMap.{u2, u2, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) (Semiring.toModule.{u2} R₁ _inst_1) (Semiring.toModule.{u2} R₁ _inst_1)) 1 (One.toOfNat1.{u2} (ContinuousLinearMap.{u2, u2, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) (Semiring.toModule.{u2} R₁ _inst_1) (Semiring.toModule.{u2} R₁ _inst_1)) (ContinuousLinearMap.one.{u2, u2} R₁ _inst_1 R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) (Semiring.toModule.{u2} R₁ _inst_1)))) f')) (Eq.{succ u1} M₂ f f')
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_right_one_eq_iff ContinuousLinearMap.smulRight_one_eq_iffₓ'. -/
@[simp]
theorem smulRight_one_eq_iff {f f' : M₂} :
smulRight (1 : R₁ →L[R₁] R₁) f = smulRight (1 : R₁ →L[R₁] R₁) f' ↔ f = f' := by
simp only [ext_ring_iff, smul_right_apply, one_apply, one_smul]
#align continuous_linear_map.smul_right_one_eq_iff ContinuousLinearMap.smulRight_one_eq_iff
+/- warning: continuous_linear_map.smul_right_comp -> ContinuousLinearMap.smulRight_comp is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₂ : Type.{u2}} [_inst_8 : TopologicalSpace.{u2} M₂] [_inst_9 : AddCommMonoid.{u2} M₂] [_inst_19 : Module.{u1, u2} R₁ M₂ _inst_1 _inst_9] [_inst_20 : TopologicalSpace.{u1} R₁] [_inst_21 : ContinuousSMul.{u1, u2} R₁ M₂ (SMulZeroClass.toHasSmul.{u1, u2} R₁ M₂ (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (SMulWithZero.toSmulZeroClass.{u1, u2} R₁ M₂ (MulZeroClass.toHasZero.{u1} R₁ (MulZeroOneClass.toMulZeroClass.{u1} R₁ (MonoidWithZero.toMulZeroOneClass.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)))) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (MulActionWithZero.toSMulWithZero.{u1, u2} R₁ M₂ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (Module.toMulActionWithZero.{u1, u2} R₁ M₂ _inst_1 _inst_9 _inst_19)))) _inst_20 _inst_8] [_inst_22 : ContinuousMul.{u1} R₁ _inst_20 (Distrib.toHasMul.{u1} R₁ (NonUnitalNonAssocSemiring.toDistrib.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))))] {x : M₂} {c : R₁}, Eq.{max (succ u1) (succ u2)} (ContinuousLinearMap.{u1, u1, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) M₂ _inst_8 _inst_9 (Semiring.toModule.{u1} R₁ _inst_1) _inst_19) (ContinuousLinearMap.comp.{u1, u1, u1, u1, u1, u2} R₁ R₁ R₁ _inst_1 _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) M₂ _inst_8 _inst_9 (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1) _inst_19 (RingHomCompTriple.right_ids.{u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (ContinuousLinearMap.smulRight.{u1, u2, u1, u1} R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) M₂ _inst_8 _inst_9 R₁ R₁ _inst_1 _inst_1 (Semiring.toModule.{u1} R₁ _inst_1) _inst_19 (Semiring.toModule.{u1} R₁ _inst_1) _inst_19 (IsScalarTower.left.{u1, u2} R₁ M₂ (MonoidWithZero.toMonoid.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R₁ M₂ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (Module.toMulActionWithZero.{u1, u2} R₁ M₂ _inst_1 _inst_9 _inst_19))) _inst_20 _inst_21 (OfNat.ofNat.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1)) 1 (OfNat.mk.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1)) 1 (One.one.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1)) (ContinuousLinearMap.one.{u1, u1} R₁ _inst_1 R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1))))) x) (ContinuousLinearMap.smulRight.{u1, u1, u1, u1} R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) R₁ R₁ _inst_1 _inst_1 (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1) (IsScalarTower.left.{u1, u1} R₁ R₁ (MonoidWithZero.toMonoid.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)) (Monoid.toMulAction.{u1} R₁ (MonoidWithZero.toMonoid.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)))) _inst_20 (ContinuousMul.to_continuousSMul.{u1} R₁ _inst_20 (Distrib.toHasMul.{u1} R₁ (NonUnitalNonAssocSemiring.toDistrib.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)))) _inst_22) (OfNat.ofNat.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1)) 1 (OfNat.mk.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1)) 1 (One.one.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1)) (ContinuousLinearMap.one.{u1, u1} R₁ _inst_1 R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1))))) c)) (ContinuousLinearMap.smulRight.{u1, u2, u1, u1} R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) M₂ _inst_8 _inst_9 R₁ R₁ _inst_1 _inst_1 (Semiring.toModule.{u1} R₁ _inst_1) _inst_19 (Semiring.toModule.{u1} R₁ _inst_1) _inst_19 (IsScalarTower.left.{u1, u2} R₁ M₂ (MonoidWithZero.toMonoid.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R₁ M₂ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (Module.toMulActionWithZero.{u1, u2} R₁ M₂ _inst_1 _inst_9 _inst_19))) _inst_20 _inst_21 (OfNat.ofNat.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1)) 1 (OfNat.mk.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1)) 1 (One.one.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1) (Semiring.toModule.{u1} R₁ _inst_1)) (ContinuousLinearMap.one.{u1, u1} R₁ _inst_1 R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1))) (Semiring.toModule.{u1} R₁ _inst_1))))) (SMul.smul.{u1, u2} R₁ M₂ (SMulZeroClass.toHasSmul.{u1, u2} R₁ M₂ (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (SMulWithZero.toSmulZeroClass.{u1, u2} R₁ M₂ (MulZeroClass.toHasZero.{u1} R₁ (MulZeroOneClass.toMulZeroClass.{u1} R₁ (MonoidWithZero.toMulZeroOneClass.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)))) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (MulActionWithZero.toSMulWithZero.{u1, u2} R₁ M₂ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddZeroClass.toHasZero.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_9))) (Module.toMulActionWithZero.{u1, u2} R₁ M₂ _inst_1 _inst_9 _inst_19)))) c x))
+but is expected to have type
+ forall {R₁ : Type.{u2}} [_inst_1 : Semiring.{u2} R₁] {M₂ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₂] [_inst_9 : AddCommMonoid.{u1} M₂] [_inst_19 : Module.{u2, u1} R₁ M₂ _inst_1 _inst_9] [_inst_20 : TopologicalSpace.{u2} R₁] [_inst_21 : ContinuousSMul.{u2, u1} R₁ M₂ (SMulZeroClass.toSMul.{u2, u1} R₁ M₂ (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (SMulWithZero.toSMulZeroClass.{u2, u1} R₁ M₂ (MonoidWithZero.toZero.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ _inst_1)) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (MulActionWithZero.toSMulWithZero.{u2, u1} R₁ M₂ (Semiring.toMonoidWithZero.{u2} R₁ _inst_1) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u2, u1} R₁ M₂ _inst_1 _inst_9 _inst_19)))) _inst_20 _inst_8] [_inst_22 : ContinuousMul.{u2} R₁ _inst_20 (NonUnitalNonAssocSemiring.toMul.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)))] {x : M₂} {c : R₁}, Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u2, u2, u2, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) M₂ _inst_8 _inst_9 (Semiring.toModule.{u2} R₁ _inst_1) _inst_19) (ContinuousLinearMap.comp.{u2, u2, u2, u2, u2, u1} R₁ R₁ R₁ _inst_1 _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) M₂ _inst_8 _inst_9 (Semiring.toModule.{u2} R₁ _inst_1) (Semiring.toModule.{u2} R₁ _inst_1) _inst_19 (RingHomCompTriple.ids.{u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) (ContinuousLinearMap.smulRight.{u2, u1, u2, u2} R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) M₂ _inst_8 _inst_9 R₁ R₁ _inst_1 _inst_1 (Semiring.toModule.{u2} R₁ _inst_1) _inst_19 (Semiring.toModule.{u2} R₁ _inst_1) _inst_19 (IsScalarTower.left.{u2, u1} R₁ M₂ (MonoidWithZero.toMonoid.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R₁ M₂ (Semiring.toMonoidWithZero.{u2} R₁ _inst_1) (AddMonoid.toZero.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_9)) (Module.toMulActionWithZero.{u2, u1} R₁ M₂ _inst_1 _inst_9 _inst_19))) _inst_20 _inst_21 (OfNat.ofNat.{u2} (ContinuousLinearMap.{u2, u2, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) (Semiring.toModule.{u2} R₁ _inst_1) (Semiring.toModule.{u2} R₁ _inst_1)) 1 (One.toOfNat1.{u2} (ContinuousLinearMap.{u2, u2, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) (Semiring.toModule.{u2} R₁ _inst_1) (Semiring.toModule.{u2} R₁ _inst_1)) (ContinuousLinearMap.one.{u2, u2} R₁ _inst_1 R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) (Semiring.toModule.{u2} R₁ _inst_1)))) x) (ContinuousLinearMap.smulRight.{u2, u2, u2, u2} R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) R₁ _inst_20 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) R₁ R₁ _inst_1 _inst_1 (Semiring.toModule.{u2} R₁ _inst_1) (Semiring.toModule.{u2} R₁ _inst_1) (Semiring.toModule.{u2} R₁ _inst_1) (Semiring.toModule.{u2} R₁ _inst_1) (IsScalarTower.left.{u2, u2} R₁ R₁ (MonoidWithZero.toMonoid.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ _inst_1)) 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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_right_comp ContinuousLinearMap.smulRight_compₓ'. -/
theorem smulRight_comp [ContinuousMul R₁] {x : M₂} {c : R₁} :
(smulRight (1 : R₁ →L[R₁] R₁) x).comp (smulRight (1 : R₁ →L[R₁] R₁) c) =
smulRight (1 : R₁ →L[R₁] R₁) (c • x) :=
@@ -1276,64 +2037,128 @@ variable {R : Type _} [Semiring R] {M : Type _} [TopologicalSpace M] [AddCommMon
{M₂ : Type _} [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M₂] {ι : Type _} {φ : ι → Type _}
[∀ i, TopologicalSpace (φ i)] [∀ i, AddCommMonoid (φ i)] [∀ i, Module R (φ i)]
+#print ContinuousLinearMap.pi /-
/-- `pi` construction for continuous linear functions. From a family of continuous linear functions
it produces a continuous linear function into a family of topological modules. -/
def pi (f : ∀ i, M →L[R] φ i) : M →L[R] ∀ i, φ i :=
⟨LinearMap.pi fun i => f i, continuous_pi fun i => (f i).Continuous⟩
#align continuous_linear_map.pi ContinuousLinearMap.pi
+-/
+/- warning: continuous_linear_map.coe_pi' -> ContinuousLinearMap.coe_pi' 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 continuous_linear_map.coe_pi' ContinuousLinearMap.coe_pi'ₓ'. -/
@[simp]
theorem coe_pi' (f : ∀ i, M →L[R] φ i) : ⇑(pi f) = fun c i => f i c :=
rfl
#align continuous_linear_map.coe_pi' ContinuousLinearMap.coe_pi'
+/- warning: continuous_linear_map.coe_pi -> ContinuousLinearMap.coe_pi is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_pi ContinuousLinearMap.coe_piₓ'. -/
@[simp]
theorem coe_pi (f : ∀ i, M →L[R] φ i) : (pi f : M →ₗ[R] ∀ i, φ i) = LinearMap.pi fun i => f i :=
rfl
#align continuous_linear_map.coe_pi ContinuousLinearMap.coe_pi
+/- warning: continuous_linear_map.pi_apply -> ContinuousLinearMap.pi_apply is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.pi_apply ContinuousLinearMap.pi_applyₓ'. -/
theorem pi_apply (f : ∀ i, M →L[R] φ i) (c : M) (i : ι) : pi f c i = f i c :=
rfl
#align continuous_linear_map.pi_apply ContinuousLinearMap.pi_apply
+/- warning: continuous_linear_map.pi_eq_zero -> ContinuousLinearMap.pi_eq_zero 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 continuous_linear_map.pi_eq_zero ContinuousLinearMap.pi_eq_zeroₓ'. -/
theorem pi_eq_zero (f : ∀ i, M →L[R] φ i) : pi f = 0 ↔ ∀ i, f i = 0 :=
by
simp only [ext_iff, pi_apply, Function.funext_iff]
exact forall_swap
#align continuous_linear_map.pi_eq_zero ContinuousLinearMap.pi_eq_zero
+/- warning: continuous_linear_map.pi_zero -> ContinuousLinearMap.pi_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.pi_zero ContinuousLinearMap.pi_zeroₓ'. -/
theorem pi_zero : pi (fun i => 0 : ∀ i, M →L[R] φ i) = 0 :=
ext fun _ => rfl
#align continuous_linear_map.pi_zero ContinuousLinearMap.pi_zero
+/- warning: continuous_linear_map.pi_comp -> ContinuousLinearMap.pi_comp 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 continuous_linear_map.pi_comp ContinuousLinearMap.pi_compₓ'. -/
theorem pi_comp (f : ∀ i, M →L[R] φ i) (g : M₂ →L[R] M) :
(pi f).comp g = pi fun i => (f i).comp g :=
rfl
#align continuous_linear_map.pi_comp ContinuousLinearMap.pi_comp
+#print ContinuousLinearMap.proj /-
/-- The projections from a family of topological modules are continuous linear maps. -/
def proj (i : ι) : (∀ i, φ i) →L[R] φ i :=
⟨LinearMap.proj i, continuous_apply _⟩
#align continuous_linear_map.proj ContinuousLinearMap.proj
+-/
+/- warning: continuous_linear_map.proj_apply -> ContinuousLinearMap.proj_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.proj_apply ContinuousLinearMap.proj_applyₓ'. -/
@[simp]
theorem proj_apply (i : ι) (b : ∀ i, φ i) : (proj i : (∀ i, φ i) →L[R] φ i) b = b i :=
rfl
#align continuous_linear_map.proj_apply ContinuousLinearMap.proj_apply
+/- warning: continuous_linear_map.proj_pi -> ContinuousLinearMap.proj_pi is a dubious translation:
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+ forall {R : Type.{u4}} [_inst_1 : Semiring.{u4} R] {M₂ : Type.{u3}} [_inst_5 : TopologicalSpace.{u3} M₂] [_inst_6 : AddCommMonoid.{u3} M₂] [_inst_7 : Module.{u4, u3} R M₂ _inst_1 _inst_6] {ι : Type.{u1}} {φ : ι -> Type.{u2}} [_inst_8 : forall (i : ι), TopologicalSpace.{u2} (φ i)] [_inst_9 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_10 : forall (i : ι), Module.{u4, u2} R (φ i) _inst_1 (_inst_9 i)] (f : forall (i : ι), ContinuousLinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M₂ _inst_5 _inst_6 (φ i) (_inst_8 i) (_inst_9 i) _inst_7 (_inst_10 i)) (i : ι), Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u4, u4, u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M₂ _inst_5 _inst_6 (φ i) (_inst_8 i) (_inst_9 i) _inst_7 (_inst_10 i)) (ContinuousLinearMap.comp.{u4, u4, u4, u3, max u1 u2, u2} R R R _inst_1 _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) M₂ _inst_5 _inst_6 (forall (i : ι), φ i) (Pi.topologicalSpace.{u1, u2} ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a)) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (φ i) (_inst_8 i) (_inst_9 i) _inst_7 (Pi.module.{u1, u2, u4} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i)) (_inst_10 i) (RingHomCompTriple.ids.{u4, u4} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) (ContinuousLinearMap.proj.{u4, u1, u2} R _inst_1 ι (fun (i : ι) => φ i) (fun (a : ι) => _inst_8 a) (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i) i) (ContinuousLinearMap.pi.{u4, u3, u1, u2} R _inst_1 M₂ _inst_5 _inst_6 _inst_7 ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_8 i) (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i) f)) (f i)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.proj_pi ContinuousLinearMap.proj_piₓ'. -/
theorem proj_pi (f : ∀ i, M₂ →L[R] φ i) (i : ι) : (proj i).comp (pi f) = f i :=
ext fun c => rfl
#align continuous_linear_map.proj_pi ContinuousLinearMap.proj_pi
+/- warning: continuous_linear_map.infi_ker_proj -> ContinuousLinearMap.infᵢ_ker_proj 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 continuous_linear_map.infi_ker_proj ContinuousLinearMap.infᵢ_ker_projₓ'. -/
theorem infᵢ_ker_proj : (⨅ i, ker (proj i : (∀ i, φ i) →L[R] φ i) : Submodule R (∀ i, φ i)) = ⊥ :=
LinearMap.infᵢ_ker_proj
#align continuous_linear_map.infi_ker_proj ContinuousLinearMap.infᵢ_ker_proj
variable (R φ)
+/- warning: continuous_linear_map.infi_ker_proj_equiv -> ContinuousLinearMap.infᵢKerProjEquiv is a dubious translation:
+lean 3 declaration is
+ forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {ι : Type.{u2}} (φ : ι -> Type.{u3}) [_inst_8 : forall (i : ι), TopologicalSpace.{u3} (φ i)] [_inst_9 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_10 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_9 i)] {I : Set.{u2} ι} {J : Set.{u2} ι} [_inst_11 : DecidablePred.{succ u2} ι (fun (i : ι) => Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i I)], (Disjoint.{u2} (Set.{u2} ι) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} ι) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.completeBooleanAlgebra.{u2} ι)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u2} (Set.{u2} ι) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u2} (Set.{u2} ι) (Set.booleanAlgebra.{u2} ι))) I J) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) (Set.univ.{u2} ι) (Union.union.{u2} (Set.{u2} ι) (Set.hasUnion.{u2} ι) I J)) -> (ContinuousLinearEquiv.{u1, u1, max u2 u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (coeSort.{succ (max u2 u3), succ (succ (max u2 u3))} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) Type.{max u2 u3} (SetLike.hasCoeToSort.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_9 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_9 i) (fun (i : ι) => _inst_10 i))) (forall (i : ι), φ i) 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(Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x I) i))))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.infi_ker_proj_equiv ContinuousLinearMap.infᵢKerProjEquivₓ'. -/
/-- If `I` and `J` are complementary index sets, the product of the kernels of the `J`th projections
of `φ` is linearly equivalent to the product over `I`. -/
-def infiKerProjEquiv {I J : Set ι} [DecidablePred fun i => i ∈ I] (hd : Disjoint I J)
+def infᵢKerProjEquiv {I J : Set ι} [DecidablePred fun i => i ∈ I] (hd : Disjoint I J)
(hu : Set.univ ⊆ I ∪ J) :
(⨅ i ∈ J, ker (proj i : (∀ i, φ i) →L[R] φ i) : Submodule R (∀ i, φ i)) ≃L[R] ∀ i : I, φ i
where
@@ -1351,7 +2176,7 @@ def infiKerProjEquiv {I J : Set ι} [DecidablePred fun i => i ∈ I] (hd : Disjo
(continuous_pi fun i => by dsimp;
split_ifs <;> [apply continuous_apply, exact continuous_zero])
_
-#align continuous_linear_map.infi_ker_proj_equiv ContinuousLinearMap.infiKerProjEquiv
+#align continuous_linear_map.infi_ker_proj_equiv ContinuousLinearMap.infᵢKerProjEquiv
end Pi
@@ -1365,14 +2190,32 @@ variable {R : Type _} [Ring R] {R₂ : Type _} [Ring R₂] {R₃ : Type _} [Ring
section
+/- warning: continuous_linear_map.map_neg -> ContinuousLinearMap.map_neg is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_neg ContinuousLinearMap.map_negₓ'. -/
protected theorem map_neg (f : M →SL[σ₁₂] M₂) (x : M) : f (-x) = -f x :=
map_neg _ _
#align continuous_linear_map.map_neg ContinuousLinearMap.map_neg
+/- warning: continuous_linear_map.map_sub -> ContinuousLinearMap.map_sub is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.map_sub ContinuousLinearMap.map_subₓ'. -/
protected theorem map_sub (f : M →SL[σ₁₂] M₂) (x y : M) : f (x - y) = f x - f y :=
map_sub _ _ _
#align continuous_linear_map.map_sub ContinuousLinearMap.map_sub
+/- warning: continuous_linear_map.sub_apply' -> ContinuousLinearMap.sub_apply' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.sub_apply' ContinuousLinearMap.sub_apply'ₓ'. -/
@[simp]
theorem sub_apply' (f g : M →SL[σ₁₂] M₂) (x : M) : ((f : M →ₛₗ[σ₁₂] M₂) - g) x = f x - g x :=
rfl
@@ -1384,16 +2227,34 @@ section
variable [Module R M₂] [Module R M₃] [Module R M₄]
+/- warning: continuous_linear_map.range_prod_eq -> ContinuousLinearMap.range_prod_eq is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] {M₃ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₃] [_inst_9 : AddCommGroup.{u4} M₃] [_inst_12 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_15 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_16 : Module.{u1, u4} R M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)] {f : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15} {g : 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(ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u3, u1, u1, u2, u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15)) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f) M₃ (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16 (LinearMap.range.{u1, u1, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u1, u1, u2, u4} (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16)) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) g)))
+but is expected to have type
+ forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u2}} [_inst_6 : TopologicalSpace.{u2} M₂] [_inst_7 : AddCommGroup.{u2} M₂] {M₃ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₃] [_inst_9 : AddCommGroup.{u1} M₃] [_inst_12 : Module.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_15 : Module.{u4, u2} R M₂ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7)] [_inst_16 : Module.{u4, u1} R M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)] {f : ContinuousLinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15} {g : ContinuousLinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16}, (Eq.{succ u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (Sup.sup.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (SemilatticeSup.toSup.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (Lattice.toSemilatticeSup.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (ConditionallyCompleteLattice.toLattice.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (Submodule.completeLattice.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12))))) (LinearMap.ker.{u4, u4, u3, u2, max u3 u2} R R M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15 (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) (ContinuousLinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u2, u4, u4, u3, u2} (ContinuousLinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15) R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15)) f) (LinearMap.ker.{u4, u4, u3, u1, max u3 u1} R R M M₃ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) (ContinuousLinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u1, u4, u4, u3, u1} (ContinuousLinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16)) g)) (Top.top.{u3} (Submodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12) (Submodule.instTopSubmodule.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12))) -> (Eq.{max (succ u2) (succ u1)} (Submodule.{u4, max u2 u1} R (Prod.{u2, u1} M₂ M₃) (Ring.toSemiring.{u4} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)) (Prod.module.{u4, u2, u1} R M₂ M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_15 _inst_16)) (LinearMap.range.{u4, u4, u3, max u2 u1, max (max u3 u2) u1} R R M (Prod.{u2, u1} M₂ M₃) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (Prod.instAddCommMonoidSum.{u2, u1} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)) _inst_12 (Prod.module.{u4, u2, u1} R M₂ M₃ (Ring.toSemiring.{u4} R _inst_1) 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(AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)) _inst_12 (Prod.module.{u4, u2, u1} R M₂ M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_15 _inst_16) (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, max u2 u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (Prod.{u2, u1} M₂ M₃) (instTopologicalSpaceProd.{u2, u1} M₂ M₃ _inst_6 _inst_8) (Prod.instAddCommMonoidSum.{u2, u1} M₂ M₃ (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9)) _inst_12 (Prod.module.{u4, u2, u1} R M₂ M₃ (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_15 _inst_16))) 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_inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u2, u4, u4, u3, u2} (ContinuousLinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15) R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_15)) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) f) M₃ (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_16 (LinearMap.range.{u4, u4, u3, u1, max u3 u1} R R M M₃ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) (ContinuousLinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u1, u4, u4, u3, u1} (ContinuousLinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_9) _inst_12 _inst_16)) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) g)))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.range_prod_eq ContinuousLinearMap.range_prod_eqₓ'. -/
theorem range_prod_eq {f : M →L[R] M₂} {g : M →L[R] M₃} (h : ker f ⊔ ker g = ⊤) :
range (f.Prod g) = (range f).Prod (range g) :=
LinearMap.range_prod_eq h
#align continuous_linear_map.range_prod_eq ContinuousLinearMap.range_prod_eq
+/- warning: continuous_linear_map.ker_prod_ker_le_ker_coprod -> ContinuousLinearMap.ker_prod_ker_le_ker_coprod is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] {M₃ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₃] [_inst_9 : AddCommGroup.{u4} M₃] [_inst_12 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_15 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_16 : Module.{u1, u4} R M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)] [_inst_18 : ContinuousAdd.{u4} M₃ _inst_8 (AddZeroClass.toHasAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (SubNegMonoid.toAddMonoid.{u4} M₃ (AddGroup.toSubNegMonoid.{u4} M₃ (AddCommGroup.toAddGroup.{u4} M₃ _inst_9)))))] (f : ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R 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(Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max (max u2 u3) u4, u1, u1, max u2 u3, u4} (ContinuousLinearMap.{u1, u1, max u2 u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, max u2 u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16)) (ContinuousLinearMap.coprod.{u1, u2, u3, u4} R (Ring.toSemiring.{u1} R _inst_1) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_15 _inst_16 _inst_18 f g))
+but is expected to have type
+ forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] {M₃ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₃] [_inst_9 : AddCommGroup.{u4} M₃] [_inst_12 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_15 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] [_inst_16 : Module.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)] [_inst_18 : ContinuousAdd.{u4} M₃ _inst_8 (AddZeroClass.toAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (SubNegMonoid.toAddMonoid.{u4} M₃ (AddGroup.toSubNegMonoid.{u4} M₃ (AddCommGroup.toAddGroup.{u4} M₃ _inst_9)))))] (f : ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (g : ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16), LE.le.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (Preorder.toLE.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (PartialOrder.toPreorder.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, 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M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)))))) (Submodule.prod.{u3, u2, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12 (LinearMap.ker.{u3, u3, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u3, u3, u2, u4} (ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16)) f) M₂ (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_15 (LinearMap.ker.{u3, u3, u1, u4, max u1 u4} R R M₂ M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u1 u4, u3, u3, u1, u4} (ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16)) g)) (LinearMap.ker.{u3, u3, max u2 u1, u4, max (max u2 u4) u1} R R (Prod.{u2, u1} M M₂) M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, max u1 u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max (max u2 u1) u4, u3, u3, max u2 u1, u4} (ContinuousLinearMap.{u3, u3, max u1 u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, max u2 u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16)) (ContinuousLinearMap.coprod.{u3, u2, u1, u4} R (Ring.toSemiring.{u3} R _inst_1) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_15 _inst_16 _inst_18 f g))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ker_prod_ker_le_ker_coprod ContinuousLinearMap.ker_prod_ker_le_ker_coprodₓ'. -/
theorem ker_prod_ker_le_ker_coprod [ContinuousAdd M₃] (f : M →L[R] M₃) (g : M₂ →L[R] M₃) :
(LinearMap.ker f).Prod (LinearMap.ker g) ≤ LinearMap.ker (f.coprod g) :=
LinearMap.ker_prod_ker_le_ker_coprod f.toLinearMap g.toLinearMap
#align continuous_linear_map.ker_prod_ker_le_ker_coprod ContinuousLinearMap.ker_prod_ker_le_ker_coprod
+/- warning: continuous_linear_map.ker_coprod_of_disjoint_range -> ContinuousLinearMap.ker_coprod_of_disjoint_range is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] {M₃ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₃] [_inst_9 : AddCommGroup.{u4} M₃] [_inst_12 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_15 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_16 : Module.{u1, u4} R M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)] [_inst_18 : ContinuousAdd.{u4} M₃ _inst_8 (AddZeroClass.toHasAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (SubNegMonoid.toAddMonoid.{u4} M₃ (AddGroup.toSubNegMonoid.{u4} M₃ (AddCommGroup.toAddGroup.{u4} M₃ _inst_9)))))] (f : ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (g : ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16), (Disjoint.{u4} (Submodule.{u1, u4} R M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16) (SetLike.partialOrder.{u4, u4} (Submodule.{u1, u4} R M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16) M₃ (Submodule.setLike.{u1, u4} R M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16)) (Submodule.orderBot.{u1, u4} R M₃ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16) (LinearMap.range.{u1, u1, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u1, u1, u2, u4} (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16)) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f) (LinearMap.range.{u1, u1, u3, u4, max u3 u4} R R M₂ M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u4, u1, u1, u3, u4} (ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16)) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) g)) -> (Eq.{succ (max u2 u3)} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M₂) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15)) (LinearMap.ker.{u1, u1, max u2 u3, u4, max (max u2 u3) u4} R R (Prod.{u2, u3} M M₂) M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, max u2 u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max (max u2 u3) u4, u1, u1, max u2 u3, u4} (ContinuousLinearMap.{u1, u1, max u2 u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, max u2 u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u3} M M₂) (Prod.topologicalSpace.{u2, u3} M M₂ _inst_4 _inst_6) (Prod.addCommMonoid.{u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u1, u2, u3} R M M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_15) _inst_16)) (ContinuousLinearMap.coprod.{u1, u2, u3, u4} R (Ring.toSemiring.{u1} R _inst_1) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_15 _inst_16 _inst_18 f g)) (Submodule.prod.{u1, u2, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12 (LinearMap.ker.{u1, u1, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u1, u1, u2, u4} (ContinuousLinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16)) f) M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_15 (LinearMap.ker.{u1, u1, u3, u4, max u3 u4} R R M₂ M₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u4, u1, u1, u3, u4} (ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16)) g)))
+but is expected to have type
+ forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] {M₃ : Type.{u4}} [_inst_8 : TopologicalSpace.{u4} M₃] [_inst_9 : AddCommGroup.{u4} M₃] [_inst_12 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_15 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] [_inst_16 : Module.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9)] [_inst_18 : ContinuousAdd.{u4} M₃ _inst_8 (AddZeroClass.toAdd.{u4} M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (SubNegMonoid.toAddMonoid.{u4} M₃ (AddGroup.toSubNegMonoid.{u4} M₃ (AddCommGroup.toAddGroup.{u4} M₃ _inst_9)))))] (f : ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (g : ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16), (Disjoint.{u4} (Submodule.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submodule.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submodule.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16) (Submodule.completeLattice.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u3, u4} R M₃ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_16) (LinearMap.range.{u3, u3, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) 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_inst_1)) g)) -> (Eq.{max (succ u2) (succ u1)} (Submodule.{u3, max u2 u1} R (Prod.{u2, u1} M M₂) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15)) (LinearMap.ker.{u3, u3, max u2 u1, u4, max (max u2 u4) u1} R R (Prod.{u2, u1} M M₂) M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, max u1 u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max (max u2 u1) u4, u3, u3, max u2 u1, u4} (ContinuousLinearMap.{u3, u3, max u1 u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, max u2 u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (Prod.{u2, u1} M M₂) (instTopologicalSpaceProd.{u2, u1} M M₂ _inst_4 _inst_6) (Prod.instAddCommMonoidSum.{u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) (Prod.module.{u3, u2, u1} R M M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_15) _inst_16)) (ContinuousLinearMap.coprod.{u3, u2, u1, u4} R (Ring.toSemiring.{u3} R _inst_1) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_15 _inst_16 _inst_18 f g)) (Submodule.prod.{u3, u2, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_12 (LinearMap.ker.{u3, u3, u2, u4, max u2 u4} R R M M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u4, u3, u3, u2, u4} (ContinuousLinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_12 _inst_16)) f) M₂ (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_15 (LinearMap.ker.{u3, u3, u1, u4, max u1 u4} R R M₂ M₃ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u1 u4, u3, u3, u1, u4} (ContinuousLinearMap.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u1, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_9) _inst_15 _inst_16)) g)))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ker_coprod_of_disjoint_range ContinuousLinearMap.ker_coprod_of_disjoint_rangeₓ'. -/
theorem ker_coprod_of_disjoint_range [ContinuousAdd M₃] (f : M →L[R] M₃) (g : M₂ →L[R] M₃)
(hd : Disjoint (range f) (range g)) :
LinearMap.ker (f.coprod g) = (LinearMap.ker f).Prod (LinearMap.ker g) :=
@@ -1409,16 +2270,34 @@ variable [TopologicalAddGroup M₂]
instance : Neg (M →SL[σ₁₂] M₂) :=
⟨fun f => ⟨-f, f.2.neg⟩⟩
+/- warning: continuous_linear_map.neg_apply -> ContinuousLinearMap.neg_apply is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.neg_apply ContinuousLinearMap.neg_applyₓ'. -/
@[simp]
theorem neg_apply (f : M →SL[σ₁₂] M₂) (x : M) : (-f) x = -f x :=
rfl
#align continuous_linear_map.neg_apply ContinuousLinearMap.neg_apply
+/- warning: continuous_linear_map.coe_neg -> ContinuousLinearMap.coe_neg is a dubious translation:
+lean 3 declaration is
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M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13)))) f))
+but is expected to have type
+ forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_13 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2))} [_inst_15 : TopologicalAddGroup.{u1} M₂ _inst_6 (AddCommGroup.toAddGroup.{u1} M₂ _inst_7)] (f : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u2) (succ u1)} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.neg.{u4, u3, u2, u1} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_15) f)) (Neg.neg.{max u2 u1} (LinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (LinearMap.instNegLinearMapToAddCommMonoid.{u4, u3, u2, u1} R R₂ M M₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) _inst_7 _inst_12 _inst_13 σ₁₂) (ContinuousLinearMap.toLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 f))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_neg ContinuousLinearMap.coe_negₓ'. -/
@[simp, norm_cast]
theorem coe_neg (f : M →SL[σ₁₂] M₂) : (↑(-f) : M →ₛₗ[σ₁₂] M₂) = -f :=
rfl
#align continuous_linear_map.coe_neg ContinuousLinearMap.coe_neg
+/- warning: continuous_linear_map.coe_neg' -> ContinuousLinearMap.coe_neg' is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13))) f))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_neg' ContinuousLinearMap.coe_neg'ₓ'. -/
@[norm_cast]
theorem coe_neg' (f : M →SL[σ₁₂] M₂) : ⇑(-f) = -f :=
rfl
@@ -1450,15 +2329,33 @@ instance : AddCommGroup (M →SL[σ₁₂] M₂) := by
ext <;>
apply_rules [zero_add, add_assoc, add_zero, add_left_neg, add_comm, sub_eq_add_neg]
+/- warning: continuous_linear_map.sub_apply -> ContinuousLinearMap.sub_apply is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} [_inst_15 : TopologicalAddGroup.{u4} M₂ _inst_6 (AddCommGroup.toAddGroup.{u4} M₂ _inst_7)] (f : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.sub_apply ContinuousLinearMap.sub_applyₓ'. -/
theorem sub_apply (f g : M →SL[σ₁₂] M₂) (x : M) : (f - g) x = f x - g x :=
rfl
#align continuous_linear_map.sub_apply ContinuousLinearMap.sub_apply
+/- warning: continuous_linear_map.coe_sub -> ContinuousLinearMap.coe_sub is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} [_inst_15 : TopologicalAddGroup.{u4} M₂ _inst_6 (AddCommGroup.toAddGroup.{u4} M₂ _inst_7)] (f : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_sub ContinuousLinearMap.coe_subₓ'. -/
@[simp, norm_cast]
theorem coe_sub (f g : M →SL[σ₁₂] M₂) : (↑(f - g) : M →ₛₗ[σ₁₂] M₂) = f - g :=
rfl
#align continuous_linear_map.coe_sub ContinuousLinearMap.coe_sub
+/- warning: continuous_linear_map.coe_sub' -> ContinuousLinearMap.coe_sub' is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} [_inst_15 : TopologicalAddGroup.{u4} M₂ _inst_6 (AddCommGroup.toAddGroup.{u4} M₂ _inst_7)] (f : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (g : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13), Eq.{succ (max u3 u4)} (M -> M₂) (coeFn.{succ (max u3 u4), succ (max u3 u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) => M -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 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+but is expected to have type
+ forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} M] [_inst_5 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_5)] [_inst_13 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2))} [_inst_15 : TopologicalAddGroup.{u1} M₂ _inst_6 (AddCommGroup.toAddGroup.{u1} M₂ _inst_7)] (f : ContinuousLinearMap.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u2} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) 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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_sub' ContinuousLinearMap.coe_sub'ₓ'. -/
@[simp, norm_cast]
theorem coe_sub' (f g : M →SL[σ₁₂] M₂) : ⇑(f - g) = f - g :=
rfl
@@ -1466,6 +2363,12 @@ theorem coe_sub' (f g : M →SL[σ₁₂] M₂) : ⇑(f - g) = f - g :=
end
+/- warning: continuous_linear_map.comp_neg -> ContinuousLinearMap.comp_neg is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {R₃ : Type.{u3}} [_inst_3 : Ring.{u3} R₃] {M : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} M] [_inst_5 : AddCommGroup.{u4} M] {M₂ : Type.{u5}} [_inst_6 : TopologicalSpace.{u5} M₂] [_inst_7 : AddCommGroup.{u5} M₂] {M₃ : Type.{u6}} [_inst_8 : TopologicalSpace.{u6} M₃] [_inst_9 : AddCommGroup.{u6} M₃] [_inst_12 : Module.{u1, u4} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5)] [_inst_13 : Module.{u2, u5} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7)] [_inst_14 : Module.{u3, u6} R₃ M₃ (Ring.toSemiring.{u3} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₃ : RingHom.{u2, u3} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u3} R₃ (Ring.toNonAssocRing.{u3} R₃ _inst_3))} {σ₁₃ : RingHom.{u1, u3} R R₃ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₃ (Ring.toNonAssocRing.{u3} R₃ _inst_3))} [_inst_15 : RingHomCompTriple.{u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃] [_inst_16 : TopologicalAddGroup.{u5} M₂ _inst_6 (AddCommGroup.toAddGroup.{u5} M₂ _inst_7)] [_inst_17 : TopologicalAddGroup.{u6} M₃ _inst_8 (AddCommGroup.toAddGroup.{u6} M₃ _inst_9)] (g : ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_13 _inst_14) (f : ContinuousLinearMap.{u1, u2, u4, u5} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u4) (succ u6)} (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g (Neg.neg.{max u4 u5} (ContinuousLinearMap.{u1, u2, u4, u5} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.neg.{u1, u2, u4, u5} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_16) f)) (Neg.neg.{max u4 u6} (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.neg.{u1, u3, u4, u6} R _inst_1 R₃ _inst_3 M _inst_4 _inst_5 M₃ _inst_8 _inst_9 _inst_12 _inst_14 σ₁₃ _inst_17) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g f))
+but is expected to have type
+ forall {R : Type.{u6}} [_inst_1 : Ring.{u6} R] {R₂ : Type.{u5}} [_inst_2 : Ring.{u5} R₂] {R₃ : Type.{u4}} [_inst_3 : Ring.{u4} R₃] {M : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M] [_inst_5 : AddCommGroup.{u1} M] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] {M₃ : Type.{u2}} [_inst_8 : TopologicalSpace.{u2} M₃] [_inst_9 : AddCommGroup.{u2} M₃] [_inst_12 : Module.{u6, u1} R M (Ring.toSemiring.{u6} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_5)] [_inst_13 : Module.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_14 : Module.{u4, u2} R₃ M₃ (Ring.toSemiring.{u4} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9)] {σ₁₂ : RingHom.{u6, u5} R R₂ (NonAssocRing.toNonAssocSemiring.{u6} R (Ring.toNonAssocRing.{u6} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u5} R₂ (Ring.toNonAssocRing.{u5} R₂ _inst_2))} {σ₂₃ : RingHom.{u5, u4} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u5} R₂ (Ring.toNonAssocRing.{u5} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u4} R₃ (Ring.toNonAssocRing.{u4} R₃ _inst_3))} {σ₁₃ : RingHom.{u6, u4} R R₃ (NonAssocRing.toNonAssocSemiring.{u6} R (Ring.toNonAssocRing.{u6} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u4} R₃ (Ring.toNonAssocRing.{u4} R₃ _inst_3))} [_inst_15 : RingHomCompTriple.{u6, u5, u4} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃] [_inst_16 : TopologicalAddGroup.{u3} M₂ _inst_6 (AddCommGroup.toAddGroup.{u3} M₂ _inst_7)] [_inst_17 : TopologicalAddGroup.{u2} M₃ _inst_8 (AddCommGroup.toAddGroup.{u2} M₃ _inst_9)] (g : ContinuousLinearMap.{u5, u4, u3, u2} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_13 _inst_14) (f : ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u1) (succ u2)} (ContinuousLinearMap.{u6, u4, u1, u2} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u3, u2} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g (Neg.neg.{max u1 u3} (ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.neg.{u6, u5, u1, u3} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_16) f)) (Neg.neg.{max u1 u2} (ContinuousLinearMap.{u6, u4, u1, u2} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.neg.{u6, u4, u1, u2} R _inst_1 R₃ _inst_3 M _inst_4 _inst_5 M₃ _inst_8 _inst_9 _inst_12 _inst_14 σ₁₃ _inst_17) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u3, u2} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g f))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_neg ContinuousLinearMap.comp_negₓ'. -/
@[simp]
theorem comp_neg [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₂] [TopologicalAddGroup M₃]
(g : M₂ →SL[σ₂₃] M₃) (f : M →SL[σ₁₂] M₂) : g.comp (-f) = -g.comp f :=
@@ -1474,6 +2377,12 @@ theorem comp_neg [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddG
simp
#align continuous_linear_map.comp_neg ContinuousLinearMap.comp_neg
+/- warning: continuous_linear_map.neg_comp -> ContinuousLinearMap.neg_comp is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {R₃ : Type.{u3}} [_inst_3 : Ring.{u3} R₃] {M : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} M] [_inst_5 : AddCommGroup.{u4} M] {M₂ : Type.{u5}} [_inst_6 : TopologicalSpace.{u5} M₂] [_inst_7 : AddCommGroup.{u5} M₂] {M₃ : Type.{u6}} [_inst_8 : TopologicalSpace.{u6} M₃] [_inst_9 : AddCommGroup.{u6} M₃] [_inst_12 : Module.{u1, u4} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5)] [_inst_13 : Module.{u2, u5} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7)] [_inst_14 : Module.{u3, u6} R₃ M₃ (Ring.toSemiring.{u3} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₃ : RingHom.{u2, u3} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u3} R₃ (Ring.toNonAssocRing.{u3} R₃ _inst_3))} {σ₁₃ : RingHom.{u1, u3} R R₃ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₃ (Ring.toNonAssocRing.{u3} R₃ _inst_3))} [_inst_15 : RingHomCompTriple.{u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃] [_inst_16 : TopologicalAddGroup.{u6} M₃ _inst_8 (AddCommGroup.toAddGroup.{u6} M₃ _inst_9)] (g : ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_13 _inst_14) (f : ContinuousLinearMap.{u1, u2, u4, u5} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u4) (succ u6)} (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 (Neg.neg.{max u5 u6} (ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_13 _inst_14) (ContinuousLinearMap.neg.{u2, u3, u5, u6} R₂ _inst_2 R₃ _inst_3 M₂ _inst_6 _inst_7 M₃ _inst_8 _inst_9 _inst_13 _inst_14 σ₂₃ _inst_16) g) f) (Neg.neg.{max u4 u6} (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.neg.{u1, u3, u4, u6} R _inst_1 R₃ _inst_3 M _inst_4 _inst_5 M₃ _inst_8 _inst_9 _inst_12 _inst_14 σ₁₃ _inst_16) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g f))
+but is expected to have type
+ forall {R : Type.{u6}} [_inst_1 : Ring.{u6} R] {R₂ : Type.{u5}} [_inst_2 : Ring.{u5} R₂] {R₃ : Type.{u4}} [_inst_3 : Ring.{u4} R₃] {M : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M] [_inst_5 : AddCommGroup.{u1} M] {M₂ : Type.{u2}} [_inst_6 : TopologicalSpace.{u2} M₂] [_inst_7 : AddCommGroup.{u2} M₂] {M₃ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₃] [_inst_9 : AddCommGroup.{u3} M₃] [_inst_12 : Module.{u6, u1} R M (Ring.toSemiring.{u6} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_5)] [_inst_13 : Module.{u5, u2} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7)] [_inst_14 : Module.{u4, u3} R₃ M₃ (Ring.toSemiring.{u4} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9)] {σ₁₂ : RingHom.{u6, u5} R R₂ (NonAssocRing.toNonAssocSemiring.{u6} R (Ring.toNonAssocRing.{u6} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u5} R₂ (Ring.toNonAssocRing.{u5} R₂ _inst_2))} {σ₂₃ : RingHom.{u5, u4} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u5} R₂ (Ring.toNonAssocRing.{u5} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u4} R₃ (Ring.toNonAssocRing.{u4} R₃ _inst_3))} {σ₁₃ : RingHom.{u6, u4} R R₃ (NonAssocRing.toNonAssocSemiring.{u6} R (Ring.toNonAssocRing.{u6} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u4} R₃ (Ring.toNonAssocRing.{u4} R₃ _inst_3))} [_inst_15 : RingHomCompTriple.{u6, u5, u4} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃] [_inst_16 : TopologicalAddGroup.{u3} M₃ _inst_8 (AddCommGroup.toAddGroup.{u3} M₃ _inst_9)] (g : ContinuousLinearMap.{u5, u4, u2, u3} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_13 _inst_14) (f : ContinuousLinearMap.{u6, u5, u1, u2} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u1) (succ u3)} (ContinuousLinearMap.{u6, u4, u1, u3} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u5, u4, u2, u3} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_13 _inst_14) (ContinuousLinearMap.neg.{u5, u4, u2, u3} R₂ _inst_2 R₃ _inst_3 M₂ _inst_6 _inst_7 M₃ _inst_8 _inst_9 _inst_13 _inst_14 σ₂₃ _inst_16) g) f) (Neg.neg.{max u1 u3} (ContinuousLinearMap.{u6, u4, u1, u3} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.neg.{u6, u4, u1, u3} R _inst_1 R₃ _inst_3 M _inst_4 _inst_5 M₃ _inst_8 _inst_9 _inst_12 _inst_14 σ₁₃ _inst_16) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g f))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.neg_comp ContinuousLinearMap.neg_compₓ'. -/
@[simp]
theorem neg_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₃] (g : M₂ →SL[σ₂₃] M₃)
(f : M →SL[σ₁₂] M₂) : (-g).comp f = -g.comp f :=
@@ -1482,6 +2391,12 @@ theorem neg_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddG
simp
#align continuous_linear_map.neg_comp ContinuousLinearMap.neg_comp
+/- warning: continuous_linear_map.comp_sub -> ContinuousLinearMap.comp_sub is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {R₃ : Type.{u3}} [_inst_3 : Ring.{u3} R₃] {M : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} M] [_inst_5 : AddCommGroup.{u4} M] {M₂ : Type.{u5}} [_inst_6 : TopologicalSpace.{u5} M₂] [_inst_7 : AddCommGroup.{u5} M₂] {M₃ : Type.{u6}} [_inst_8 : TopologicalSpace.{u6} M₃] [_inst_9 : AddCommGroup.{u6} M₃] [_inst_12 : Module.{u1, u4} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5)] [_inst_13 : Module.{u2, u5} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7)] [_inst_14 : Module.{u3, u6} R₃ M₃ (Ring.toSemiring.{u3} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₃ : RingHom.{u2, u3} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u3} R₃ (Ring.toNonAssocRing.{u3} R₃ _inst_3))} {σ₁₃ : RingHom.{u1, u3} R R₃ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₃ (Ring.toNonAssocRing.{u3} R₃ _inst_3))} [_inst_15 : RingHomCompTriple.{u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃] [_inst_16 : TopologicalAddGroup.{u5} M₂ _inst_6 (AddCommGroup.toAddGroup.{u5} M₂ _inst_7)] [_inst_17 : TopologicalAddGroup.{u6} M₃ _inst_8 (AddCommGroup.toAddGroup.{u6} M₃ _inst_9)] (g : ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_13 _inst_14) (f₁ : ContinuousLinearMap.{u1, u2, u4, u5} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) _inst_12 _inst_13) (f₂ : ContinuousLinearMap.{u1, u2, u4, u5} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u4) (succ u6)} (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 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(Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g f₂))
+but is expected to have type
+ forall {R : Type.{u6}} [_inst_1 : Ring.{u6} R] {R₂ : Type.{u5}} [_inst_2 : Ring.{u5} R₂] {R₃ : Type.{u4}} [_inst_3 : Ring.{u4} R₃] {M : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M] [_inst_5 : AddCommGroup.{u1} M] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] {M₃ : Type.{u2}} [_inst_8 : TopologicalSpace.{u2} M₃] [_inst_9 : AddCommGroup.{u2} M₃] [_inst_12 : Module.{u6, u1} R M (Ring.toSemiring.{u6} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_5)] [_inst_13 : Module.{u5, u3} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_14 : Module.{u4, u2} R₃ M₃ (Ring.toSemiring.{u4} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9)] {σ₁₂ : RingHom.{u6, u5} R R₂ (NonAssocRing.toNonAssocSemiring.{u6} R (Ring.toNonAssocRing.{u6} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u5} R₂ (Ring.toNonAssocRing.{u5} R₂ _inst_2))} {σ₂₃ : RingHom.{u5, u4} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u5} R₂ (Ring.toNonAssocRing.{u5} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u4} R₃ (Ring.toNonAssocRing.{u4} R₃ _inst_3))} {σ₁₃ : RingHom.{u6, u4} R R₃ (NonAssocRing.toNonAssocSemiring.{u6} R (Ring.toNonAssocRing.{u6} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u4} R₃ (Ring.toNonAssocRing.{u4} R₃ _inst_3))} [_inst_15 : RingHomCompTriple.{u6, u5, u4} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃] [_inst_16 : TopologicalAddGroup.{u3} M₂ _inst_6 (AddCommGroup.toAddGroup.{u3} M₂ _inst_7)] [_inst_17 : TopologicalAddGroup.{u2} M₃ _inst_8 (AddCommGroup.toAddGroup.{u2} M₃ _inst_9)] (g : ContinuousLinearMap.{u5, u4, u3, u2} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_13 _inst_14) (f₁ : ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13) (f₂ : ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u1) (succ u2)} (ContinuousLinearMap.{u6, u4, u1, u2} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u3, u2} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g (HSub.hSub.{max u1 u3, max u1 u3, max u1 u3} (ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13) (instHSub.{max u1 u3} (ContinuousLinearMap.{u6, u5, u1, u3} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_12 _inst_13) (ContinuousLinearMap.sub.{u6, u5, u1, u3} R _inst_1 R₂ _inst_2 M _inst_4 _inst_5 M₂ _inst_6 _inst_7 _inst_12 _inst_13 σ₁₂ _inst_16)) f₁ f₂)) (HSub.hSub.{max u1 u2, max u1 u2, max u1 u2} (ContinuousLinearMap.{u6, u4, u1, u2} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.{u6, u4, u1, u2} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.{u6, u4, u1, u2} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_14) (instHSub.{max u1 u2} (ContinuousLinearMap.{u6, u4, u1, u2} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.sub.{u6, u4, u1, u2} R _inst_1 R₃ _inst_3 M _inst_4 _inst_5 M₃ _inst_8 _inst_9 _inst_12 _inst_14 σ₁₃ _inst_17)) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u3, u2} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g f₁) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u3, u2} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g f₂))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_sub ContinuousLinearMap.comp_subₓ'. -/
@[simp]
theorem comp_sub [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₂] [TopologicalAddGroup M₃]
(g : M₂ →SL[σ₂₃] M₃) (f₁ f₂ : M →SL[σ₁₂] M₂) : g.comp (f₁ - f₂) = g.comp f₁ - g.comp f₂ :=
@@ -1490,6 +2405,12 @@ theorem comp_sub [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddG
simp
#align continuous_linear_map.comp_sub ContinuousLinearMap.comp_sub
+/- warning: continuous_linear_map.sub_comp -> ContinuousLinearMap.sub_comp is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {R₃ : Type.{u3}} [_inst_3 : Ring.{u3} R₃] {M : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} M] [_inst_5 : AddCommGroup.{u4} M] {M₂ : Type.{u5}} [_inst_6 : TopologicalSpace.{u5} M₂] [_inst_7 : AddCommGroup.{u5} M₂] {M₃ : Type.{u6}} [_inst_8 : TopologicalSpace.{u6} M₃] [_inst_9 : AddCommGroup.{u6} M₃] [_inst_12 : Module.{u1, u4} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5)] [_inst_13 : Module.{u2, u5} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7)] [_inst_14 : Module.{u3, u6} R₃ M₃ (Ring.toSemiring.{u3} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₃ : RingHom.{u2, u3} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u3} R₃ (Ring.toNonAssocRing.{u3} R₃ _inst_3))} {σ₁₃ : RingHom.{u1, u3} R R₃ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₃ (Ring.toNonAssocRing.{u3} R₃ _inst_3))} [_inst_15 : RingHomCompTriple.{u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃] [_inst_16 : TopologicalAddGroup.{u6} M₃ _inst_8 (AddCommGroup.toAddGroup.{u6} M₃ _inst_9)] (g₁ : ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_13 _inst_14) (g₂ : ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_13 _inst_14) (f : ContinuousLinearMap.{u1, u2, u4, u5} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u4) (succ u6)} (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 (HSub.hSub.{max 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(instHSub.{max u4 u6} (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.sub.{u1, u3, u4, u6} R _inst_1 R₃ _inst_3 M _inst_4 _inst_5 M₃ _inst_8 _inst_9 _inst_12 _inst_14 σ₁₃ _inst_16)) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g₁ f) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R R₂ R₃ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u3} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u6} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g₂ f))
+but is expected to have type
+ forall {R : Type.{u6}} [_inst_1 : Ring.{u6} R] {R₂ : Type.{u5}} [_inst_2 : Ring.{u5} R₂] {R₃ : Type.{u4}} [_inst_3 : Ring.{u4} R₃] {M : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M] [_inst_5 : AddCommGroup.{u1} M] {M₂ : Type.{u2}} [_inst_6 : TopologicalSpace.{u2} M₂] [_inst_7 : AddCommGroup.{u2} M₂] {M₃ : Type.{u3}} [_inst_8 : TopologicalSpace.{u3} M₃] [_inst_9 : AddCommGroup.{u3} M₃] [_inst_12 : Module.{u6, u1} R M (Ring.toSemiring.{u6} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_5)] [_inst_13 : Module.{u5, u2} R₂ M₂ (Ring.toSemiring.{u5} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7)] [_inst_14 : Module.{u4, u3} R₃ M₃ (Ring.toSemiring.{u4} R₃ _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9)] {σ₁₂ : RingHom.{u6, u5} R R₂ (NonAssocRing.toNonAssocSemiring.{u6} R (Ring.toNonAssocRing.{u6} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u5} R₂ (Ring.toNonAssocRing.{u5} R₂ _inst_2))} {σ₂₃ : RingHom.{u5, u4} R₂ R₃ (NonAssocRing.toNonAssocSemiring.{u5} R₂ (Ring.toNonAssocRing.{u5} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u4} R₃ (Ring.toNonAssocRing.{u4} R₃ _inst_3))} {σ₁₃ : RingHom.{u6, u4} R R₃ (NonAssocRing.toNonAssocSemiring.{u6} R (Ring.toNonAssocRing.{u6} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u4} R₃ (Ring.toNonAssocRing.{u4} R₃ _inst_3))} [_inst_15 : RingHomCompTriple.{u6, u5, u4} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃] [_inst_16 : TopologicalAddGroup.{u3} M₃ _inst_8 (AddCommGroup.toAddGroup.{u3} M₃ _inst_9)] (g₁ : ContinuousLinearMap.{u5, u4, u2, u3} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_13 _inst_14) (g₂ : ContinuousLinearMap.{u5, u4, u2, u3} R₂ R₃ (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₂₃ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_13 _inst_14) (f : ContinuousLinearMap.{u6, u5, u1, u2} R R₂ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) _inst_12 _inst_13), Eq.{max (succ u1) (succ u3)} (ContinuousLinearMap.{u6, u4, u1, u3} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 (HSub.hSub.{max 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(AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_13 _inst_14) (ContinuousLinearMap.sub.{u5, u4, u2, u3} R₂ _inst_2 R₃ _inst_3 M₂ _inst_6 _inst_7 M₃ _inst_8 _inst_9 _inst_13 _inst_14 σ₂₃ _inst_16)) g₁ g₂) f) (HSub.hSub.{max u1 u3, max u1 u3, max u1 u3} (ContinuousLinearMap.{u6, u4, u1, u3} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.{u6, u4, u1, u3} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.{u6, u4, u1, u3} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_14) (instHSub.{max u1 u3} (ContinuousLinearMap.{u6, u4, u1, u3} R R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_14) (ContinuousLinearMap.sub.{u6, u4, u1, u3} R _inst_1 R₃ _inst_3 M _inst_4 _inst_5 M₃ _inst_8 _inst_9 _inst_12 _inst_14 σ₁₃ _inst_16)) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g₁ f) (ContinuousLinearMap.comp.{u6, u5, u4, u1, u2, u3} R R₂ R₃ (Ring.toSemiring.{u6} R _inst_1) (Ring.toSemiring.{u5} R₂ _inst_2) (Ring.toSemiring.{u4} R₃ _inst_3) σ₁₂ σ₂₃ σ₁₃ M _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_7) M₃ _inst_8 (AddCommGroup.toAddCommMonoid.{u3} M₃ _inst_9) _inst_12 _inst_13 _inst_14 _inst_15 g₂ f))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.sub_comp ContinuousLinearMap.sub_compₓ'. -/
@[simp]
theorem sub_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₃] (g₁ g₂ : M₂ →SL[σ₂₃] M₃)
(f : M →SL[σ₁₂] M₂) : (g₁ - g₂).comp f = g₁.comp f - g₂.comp f :=
@@ -1504,6 +2425,12 @@ instance [TopologicalAddGroup M] : Ring (M →L[R] M) :=
mul := (· * ·)
one := 1 }
+/- warning: continuous_linear_map.smul_right_one_pow -> ContinuousLinearMap.smulRight_one_pow is a dubious translation:
+lean 3 declaration is
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(NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.one.{u1, u1} R (Ring.toSemiring.{u1} R _inst_1) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) c) n) (ContinuousLinearMap.smulRight.{u1, u1, u1, u1} R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (IsScalarTower.left.{u1, u1} R R (Ring.toMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (Ring.toMonoid.{u1} R _inst_1))) _inst_15 (ContinuousMul.to_continuousSMul.{u1} R _inst_15 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1)) (TopologicalSemiring.to_continuousMul.{u1} R _inst_15 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (TopologicalRing.to_topologicalSemiring.{u1} R _inst_15 (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) _inst_16))) (OfNat.ofNat.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) 1 (One.one.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.one.{u1, u1} R (Ring.toSemiring.{u1} R _inst_1) R _inst_15 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R _inst_1))) c n))
+but is expected to have type
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_15 : TopologicalSpace.{u1} R] [_inst_16 : TopologicalRing.{u1} R _inst_15 (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))] (c : R) (n : Nat), Eq.{succ u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (HPow.hPow.{u1, 0, u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) Nat (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (instHPow.{u1, 0} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.monoidWithZero.{u1, u1} R (Ring.toSemiring.{u1} R _inst_1) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (ContinuousLinearMap.smulRight.{u1, u1, u1, u1} R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (IsScalarTower.left.{u1, u1} R R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_15 (ContinuousMul.to_continuousSMul.{u1} R _inst_15 (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (TopologicalSemiring.toContinuousMul.{u1} R _inst_15 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (TopologicalRing.toTopologicalSemiring.{u1} R _inst_15 (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) _inst_16))) (OfNat.ofNat.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.one.{u1, u1} R (Ring.toSemiring.{u1} R _inst_1) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) c) n) (ContinuousLinearMap.smulRight.{u1, u1, u1, u1} R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (IsScalarTower.left.{u1, u1} R R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_15 (ContinuousMul.to_continuousSMul.{u1} R _inst_15 (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (TopologicalSemiring.toContinuousMul.{u1} R _inst_15 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (TopologicalRing.toTopologicalSemiring.{u1} R _inst_15 (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) _inst_16))) (OfNat.ofNat.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) 1 (One.toOfNat1.{u1} (ContinuousLinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearMap.one.{u1, u1} R (Ring.toSemiring.{u1} R _inst_1) R _inst_15 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) c n))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_right_one_pow ContinuousLinearMap.smulRight_one_powₓ'. -/
theorem smulRight_one_pow [TopologicalSpace R] [TopologicalRing R] (c : R) (n : ℕ) :
smulRight (1 : R →L[R] R) c ^ n = smulRight (1 : R →L[R] R) (c ^ n) :=
by
@@ -1517,6 +2444,12 @@ section
variable {σ₂₁ : R₂ →+* R} [RingHomInvPair σ₁₂ σ₂₁]
+/- warning: continuous_linear_map.proj_ker_of_right_inverse -> ContinuousLinearMap.projKerOfRightInverse is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u1} R₂ R (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))} [_inst_15 : RingHomInvPair.{u1, u2} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : TopologicalAddGroup.{u3} M _inst_4 (AddCommGroup.toAddGroup.{u3} M _inst_5)] (f₁ : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (f₂ : ContinuousLinearMap.{u2, u1, u4, u3} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_13 _inst_12), (Function.RightInverse.{succ u3, succ u4} M M₂ (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (ContinuousLinearMap.{u2, u1, u4, u3} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_13 _inst_12) (fun (_x : ContinuousLinearMap.{u2, u1, u4, u3} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_13 _inst_12) => M₂ -> M) (ContinuousLinearMap.toFun.{u2, u1, u4, u3} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_13 _inst_12) f₂) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 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(AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (Submodule.addCommMonoid.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) _inst_12 (LinearMap.ker.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u3 u4, u1, u2, u3, u4} (ContinuousLinearMap.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M _inst_5) M₂ 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+but is expected to have type
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u1} R₂ R (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))} [_inst_15 : RingHomInvPair.{u1, u2} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : 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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.proj_ker_of_right_inverse ContinuousLinearMap.projKerOfRightInverseₓ'. -/
/-- Given a right inverse `f₂ : M₂ →L[R] M` to `f₁ : M →L[R] M₂`,
`proj_ker_of_right_inverse f₁ f₂ h` is the projection `M →L[R] f₁.ker` along `f₂.range`. -/
def projKerOfRightInverse [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂) (f₂ : M₂ →SL[σ₂₁] M)
@@ -1524,6 +2457,12 @@ def projKerOfRightInverse [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂
(id R M - f₂.comp f₁).codRestrict (LinearMap.ker f₁) fun x => by simp [h (f₁ x)]
#align continuous_linear_map.proj_ker_of_right_inverse ContinuousLinearMap.projKerOfRightInverse
+/- warning: continuous_linear_map.coe_proj_ker_of_right_inverse_apply -> ContinuousLinearMap.coe_projKerOfRightInverse_apply is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u1} R₂ R (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))} [_inst_15 : RingHomInvPair.{u1, u2} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : 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+but is expected to have type
+ forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} M] [_inst_5 : AddCommGroup.{u4} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5)] [_inst_13 : Module.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u3, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u3} R₂ R (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))} [_inst_15 : RingHomInvPair.{u3, u2} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : 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(Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ 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_inst_12 _inst_13)) f₁))) _x) (ContinuousMapClass.toFunLike.{u4, u4, u4} (ContinuousLinearMap.{u3, u3, u4, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M 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(ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) M (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) 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_inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) _inst_4 (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) 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(Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) 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(Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (Submodule.addCommMonoid.{u3, u4} R M 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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_proj_ker_of_right_inverse_apply ContinuousLinearMap.coe_projKerOfRightInverse_applyₓ'. -/
@[simp]
theorem coe_projKerOfRightInverse_apply [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂)
(f₂ : M₂ →SL[σ₂₁] M) (h : Function.RightInverse f₂ f₁) (x : M) :
@@ -1531,6 +2470,12 @@ theorem coe_projKerOfRightInverse_apply [TopologicalAddGroup M] (f₁ : M →SL[
rfl
#align continuous_linear_map.coe_proj_ker_of_right_inverse_apply ContinuousLinearMap.coe_projKerOfRightInverse_apply
+/- warning: continuous_linear_map.proj_ker_of_right_inverse_apply_idem -> ContinuousLinearMap.projKerOfRightInverse_apply_idem is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u1} R₂ R (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))} [_inst_15 : RingHomInvPair.{u1, u2} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : 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+but is expected to have type
+ forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} M] [_inst_5 : AddCommGroup.{u4} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5)] [_inst_13 : Module.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u3, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u3} R₂ R (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))} [_inst_15 : RingHomInvPair.{u3, u2} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : 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_inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (Submodule.addCommMonoid.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_12 (Submodule.module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) M (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) _inst_4 (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (ContinuousSemilinearMapClass.toContinuousMapClass.{u4, u3, u3, u4, u4} (ContinuousLinearMap.{u3, u3, u4, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (Submodule.addCommMonoid.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M 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(AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (Submodule.addCommMonoid.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ 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(AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_12 (Submodule.module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u4, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 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_inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) x)) x
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.proj_ker_of_right_inverse_apply_idem ContinuousLinearMap.projKerOfRightInverse_apply_idemₓ'. -/
@[simp]
theorem projKerOfRightInverse_apply_idem [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂)
(f₂ : M₂ →SL[σ₂₁] M) (h : Function.RightInverse f₂ f₁) (x : LinearMap.ker f₁) :
@@ -1538,6 +2483,12 @@ theorem projKerOfRightInverse_apply_idem [TopologicalAddGroup M] (f₁ : M →SL
Subtype.ext_iff_val.2 <| by simp
#align continuous_linear_map.proj_ker_of_right_inverse_apply_idem ContinuousLinearMap.projKerOfRightInverse_apply_idem
+/- warning: continuous_linear_map.proj_ker_of_right_inverse_comp_inv -> ContinuousLinearMap.projKerOfRightInverse_comp_inv is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M] [_inst_5 : AddCommGroup.{u3} M] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_12 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_5)] [_inst_13 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u1} R₂ R (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))} [_inst_15 : RingHomInvPair.{u1, u2} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : 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+but is expected to have type
+ forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u4}} [_inst_4 : TopologicalSpace.{u4} M] [_inst_5 : AddCommGroup.{u4} M] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_12 : Module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5)] [_inst_13 : Module.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u3, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u3} R₂ R (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))} [_inst_15 : RingHomInvPair.{u3, u2} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_16 : 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_inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (Submodule.addCommMonoid.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_12 (Submodule.module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) M (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) _inst_4 (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (ContinuousSemilinearMapClass.toContinuousMapClass.{u4, u3, u3, u4, u4} (ContinuousLinearMap.{u3, u3, u4, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12)) x (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u4 u1, u3, u2, u4, u1} (ContinuousLinearMap.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (Submodule.addCommMonoid.{u3, u4} R M 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(AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) _inst_4) (Submodule.addCommMonoid.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12 (LinearMap.ker.{u3, u2, u4, u1, max u4 u1} R R₂ M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 σ₁₂ 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_inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁)) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u4, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} 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(AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13) R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u2, u4, u1} R R₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ M _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_12 _inst_13)) f₁))) (instTopologicalSpaceSubtype.{u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_5) _inst_12) M (Submodule.setLike.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M 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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.proj_ker_of_right_inverse_comp_inv ContinuousLinearMap.projKerOfRightInverse_comp_invₓ'. -/
@[simp]
theorem projKerOfRightInverse_comp_inv [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂)
(f₂ : M₂ →SL[σ₂₁] M) (h : Function.RightInverse f₂ f₁) (y : M₂) :
@@ -1553,6 +2504,12 @@ section DivisionMonoid
variable {R M : Type _}
+/- warning: continuous_linear_map.is_open_map_of_ne_zero -> ContinuousLinearMap.isOpenMap_of_ne_zero is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} R] [_inst_2 : DivisionRing.{u1} R] [_inst_3 : ContinuousSub.{u1} R _inst_1 (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_2))))))] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : TopologicalSpace.{u2} M] [_inst_6 : ContinuousAdd.{u2} M _inst_5 (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_4)))))] [_inst_7 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_8 : ContinuousSMul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_7)))) _inst_1 _inst_5] (f : ContinuousLinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) R _inst_1 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_2))))) _inst_7 (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))), (Ne.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) R _inst_1 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_2))))) _inst_7 (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) f (OfNat.ofNat.{max u2 u1} (ContinuousLinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) R _inst_1 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_2))))) _inst_7 (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) 0 (OfNat.mk.{max u2 u1} (ContinuousLinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) R _inst_1 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_2))))) _inst_7 (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) 0 (Zero.zero.{max u2 u1} (ContinuousLinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) R _inst_1 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_2))))) _inst_7 (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) (ContinuousLinearMap.zero.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) R _inst_1 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_2))))) _inst_7 (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))))))) -> (IsOpenMap.{u2, u1} M R _inst_5 _inst_1 (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (ContinuousLinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) R _inst_1 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_2))))) _inst_7 (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) R _inst_1 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_2))))) _inst_7 (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) => M -> R) (ContinuousLinearMap.toFun.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) R _inst_1 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R _inst_2))))) _inst_7 (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R _inst_2)))) f))
+but is expected to have type
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} R] [_inst_2 : DivisionRing.{u2} R] [_inst_3 : ContinuousSub.{u2} R _inst_1 (Ring.toSub.{u2} R (DivisionRing.toRing.{u2} R _inst_2))] [_inst_4 : AddCommGroup.{u1} M] [_inst_5 : TopologicalSpace.{u1} M] [_inst_6 : ContinuousAdd.{u1} M _inst_5 (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_4)))))] [_inst_7 : Module.{u2, u1} R M (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4)] [_inst_8 : ContinuousSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_4))))) (Module.toMulActionWithZero.{u2, u1} R M (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_7)))) _inst_1 _inst_5] (f : ContinuousLinearMap.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))), (Ne.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) f (OfNat.ofNat.{max u2 u1} (ContinuousLinearMap.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) 0 (Zero.toOfNat0.{max u2 u1} (ContinuousLinearMap.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) (ContinuousLinearMap.zero.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2))))))) -> (IsOpenMap.{u1, u2} M R _inst_5 _inst_1 (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousLinearMap.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => R) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousLinearMap.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) M R _inst_5 _inst_1 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u2, u2, u1, u2} (ContinuousLinearMap.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))) R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2))) (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u2} R R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2)))) M _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (DivisionRing.toRing.{u2} R _inst_2))))) _inst_7 (Semiring.toModule.{u2} R (DivisionSemiring.toSemiring.{u2} R (DivisionRing.toDivisionSemiring.{u2} R _inst_2)))))) f))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.is_open_map_of_ne_zero ContinuousLinearMap.isOpenMap_of_ne_zeroₓ'. -/
/-- A nonzero continuous linear functional is open. -/
protected theorem isOpenMap_of_ne_zero [TopologicalSpace R] [DivisionRing R] [ContinuousSub R]
[AddCommGroup M] [TopologicalSpace M] [ContinuousAdd M] [Module R M] [ContinuousSMul R M]
@@ -1579,6 +2536,12 @@ variable {R R₂ R₃ S S₃ : Type _} [Semiring R] [Semiring R₂] [Semiring R
include σ₁₃
+/- warning: continuous_linear_map.smul_comp -> ContinuousLinearMap.smul_comp is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {R₂ : Type.{u2}} {R₃ : Type.{u3}} {S₃ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : Semiring.{u3} R₃] [_inst_5 : Monoid.{u4} S₃] {M : Type.{u5}} [_inst_6 : TopologicalSpace.{u5} M] [_inst_7 : AddCommMonoid.{u5} M] [_inst_8 : Module.{u1, u5} R M _inst_1 _inst_7] {M₂ : Type.{u6}} [_inst_9 : TopologicalSpace.{u6} M₂] [_inst_10 : AddCommMonoid.{u6} M₂] [_inst_11 : Module.{u2, u6} R₂ M₂ _inst_2 _inst_10] {M₃ : Type.{u7}} [_inst_12 : TopologicalSpace.{u7} M₃] [_inst_13 : AddCommMonoid.{u7} M₃] [_inst_14 : Module.{u3, u7} R₃ M₃ _inst_3 _inst_13] [_inst_21 : DistribMulAction.{u4, u7} S₃ M₃ _inst_5 (AddCommMonoid.toAddMonoid.{u7} M₃ _inst_13)] [_inst_22 : SMulCommClass.{u3, u4, u7} R₃ S₃ M₃ (SMulZeroClass.toHasSmul.{u3, u7} R₃ M₃ (AddZeroClass.toHasZero.{u7} M₃ (AddMonoid.toAddZeroClass.{u7} M₃ (AddCommMonoid.toAddMonoid.{u7} M₃ _inst_13))) (SMulWithZero.toSmulZeroClass.{u3, u7} R₃ M₃ (MulZeroClass.toHasZero.{u3} R₃ (MulZeroOneClass.toMulZeroClass.{u3} R₃ (MonoidWithZero.toMulZeroOneClass.{u3} R₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3)))) (AddZeroClass.toHasZero.{u7} M₃ (AddMonoid.toAddZeroClass.{u7} M₃ (AddCommMonoid.toAddMonoid.{u7} M₃ _inst_13))) (MulActionWithZero.toSMulWithZero.{u3, u7} R₃ M₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3) (AddZeroClass.toHasZero.{u7} M₃ (AddMonoid.toAddZeroClass.{u7} M₃ (AddCommMonoid.toAddMonoid.{u7} M₃ _inst_13))) (Module.toMulActionWithZero.{u3, u7} R₃ M₃ _inst_3 _inst_13 _inst_14)))) (SMulZeroClass.toHasSmul.{u4, u7} S₃ M₃ (AddZeroClass.toHasZero.{u7} M₃ (AddMonoid.toAddZeroClass.{u7} M₃ (AddCommMonoid.toAddMonoid.{u7} M₃ _inst_13))) (DistribSMul.toSmulZeroClass.{u4, u7} S₃ M₃ (AddMonoid.toAddZeroClass.{u7} M₃ (AddCommMonoid.toAddMonoid.{u7} M₃ _inst_13)) (DistribMulAction.toDistribSMul.{u4, u7} S₃ M₃ _inst_5 (AddCommMonoid.toAddMonoid.{u7} M₃ _inst_13) _inst_21)))] [_inst_23 : ContinuousConstSMul.{u4, u7} S₃ M₃ _inst_12 (SMulZeroClass.toHasSmul.{u4, u7} S₃ M₃ (AddZeroClass.toHasZero.{u7} M₃ (AddMonoid.toAddZeroClass.{u7} M₃ (AddCommMonoid.toAddMonoid.{u7} M₃ _inst_13))) (DistribSMul.toSmulZeroClass.{u4, u7} S₃ M₃ (AddMonoid.toAddZeroClass.{u7} M₃ (AddCommMonoid.toAddMonoid.{u7} M₃ _inst_13)) (DistribMulAction.toDistribSMul.{u4, u7} S₃ M₃ _inst_5 (AddCommMonoid.toAddMonoid.{u7} M₃ _inst_13) _inst_21)))] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₃ : RingHom.{u2, u3} R₂ R₃ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {σ₁₃ : RingHom.{u1, u3} R R₃ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} [_inst_27 : RingHomCompTriple.{u1, u2, u3} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] (c : S₃) (h : ContinuousLinearMap.{u2, u3, u6, u7} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14) (f : ContinuousLinearMap.{u1, u2, u5, u6} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11), Eq.{max (succ u5) (succ u7)} (ContinuousLinearMap.{u1, u3, u5, u7} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (ContinuousLinearMap.comp.{u1, u2, u3, u5, u6, u7} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_8 _inst_11 _inst_14 _inst_27 (SMul.smul.{u4, max u6 u7} S₃ (ContinuousLinearMap.{u2, u3, u6, u7} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14) (MulAction.toHasSmul.{u4, max u6 u7} S₃ (ContinuousLinearMap.{u2, u3, u6, u7} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14) _inst_5 (ContinuousLinearMap.mulAction.{u2, u3, u6, u7, u4} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14 S₃ _inst_5 _inst_21 _inst_22 _inst_23)) c h) f) (SMul.smul.{u4, max u5 u7} S₃ (ContinuousLinearMap.{u1, u3, u5, u7} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (MulAction.toHasSmul.{u4, max u5 u7} S₃ (ContinuousLinearMap.{u1, u3, u5, u7} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) _inst_5 (ContinuousLinearMap.mulAction.{u1, u3, u5, u7, u4} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14 S₃ _inst_5 _inst_21 _inst_22 _inst_23)) c (ContinuousLinearMap.comp.{u1, u2, u3, u5, u6, u7} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_8 _inst_11 _inst_14 _inst_27 h f))
+but is expected to have type
+ forall {R : Type.{u3}} {R₂ : Type.{u7}} {R₃ : Type.{u6}} {S₃ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : Semiring.{u7} R₂] [_inst_3 : Semiring.{u6} R₃] [_inst_5 : Monoid.{u1} S₃] {M : Type.{u2}} [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : AddCommMonoid.{u2} M] [_inst_8 : Module.{u3, u2} R M _inst_1 _inst_7] {M₂ : Type.{u5}} [_inst_9 : TopologicalSpace.{u5} M₂] [_inst_10 : AddCommMonoid.{u5} M₂] [_inst_11 : Module.{u7, u5} R₂ M₂ _inst_2 _inst_10] {M₃ : Type.{u4}} [_inst_12 : TopologicalSpace.{u4} M₃] [_inst_13 : AddCommMonoid.{u4} M₃] [_inst_14 : Module.{u6, u4} R₃ M₃ _inst_3 _inst_13] [_inst_21 : DistribMulAction.{u1, u4} S₃ M₃ _inst_5 (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_13)] [_inst_22 : SMulCommClass.{u6, u1, u4} R₃ S₃ M₃ (SMulZeroClass.toSMul.{u6, u4} R₃ M₃ (AddMonoid.toZero.{u4} M₃ (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_13)) (SMulWithZero.toSMulZeroClass.{u6, u4} R₃ M₃ (MonoidWithZero.toZero.{u6} R₃ (Semiring.toMonoidWithZero.{u6} R₃ _inst_3)) (AddMonoid.toZero.{u4} M₃ (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_13)) (MulActionWithZero.toSMulWithZero.{u6, u4} R₃ M₃ (Semiring.toMonoidWithZero.{u6} R₃ _inst_3) (AddMonoid.toZero.{u4} M₃ (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_13)) (Module.toMulActionWithZero.{u6, u4} R₃ M₃ _inst_3 _inst_13 _inst_14)))) (SMulZeroClass.toSMul.{u1, u4} S₃ M₃ (AddMonoid.toZero.{u4} M₃ (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_13)) (DistribSMul.toSMulZeroClass.{u1, u4} S₃ M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_13)) (DistribMulAction.toDistribSMul.{u1, u4} S₃ M₃ _inst_5 (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_13) _inst_21)))] [_inst_23 : ContinuousConstSMul.{u1, u4} S₃ M₃ _inst_12 (SMulZeroClass.toSMul.{u1, u4} S₃ M₃ (AddMonoid.toZero.{u4} M₃ (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_13)) (DistribSMul.toSMulZeroClass.{u1, u4} S₃ M₃ (AddMonoid.toAddZeroClass.{u4} M₃ (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_13)) (DistribMulAction.toDistribSMul.{u1, u4} S₃ M₃ _inst_5 (AddCommMonoid.toAddMonoid.{u4} M₃ _inst_13) _inst_21)))] {σ₁₂ : RingHom.{u3, u7} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u7} R₂ _inst_2)} {σ₂₃ : RingHom.{u7, u6} R₂ R₃ (Semiring.toNonAssocSemiring.{u7} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u6} R₃ _inst_3)} {σ₁₃ : RingHom.{u3, u6} R R₃ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u6} R₃ _inst_3)} [_inst_27 : RingHomCompTriple.{u3, u7, u6} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] (c : S₃) (h : ContinuousLinearMap.{u7, u6, u5, u4} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14) (f : ContinuousLinearMap.{u3, u7, u2, u5} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11), Eq.{max (succ u2) (succ u4)} (ContinuousLinearMap.{u3, u6, u2, u4} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (ContinuousLinearMap.comp.{u3, u7, u6, u2, u5, u4} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_8 _inst_11 _inst_14 _inst_27 (HSMul.hSMul.{u1, max u4 u5, max u4 u5} S₃ (ContinuousLinearMap.{u7, u6, u5, u4} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14) (ContinuousLinearMap.{u7, u6, u5, u4} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14) (instHSMul.{u1, max u4 u5} S₃ (ContinuousLinearMap.{u7, u6, u5, u4} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14) (MulAction.toSMul.{u1, max u4 u5} S₃ (ContinuousLinearMap.{u7, u6, u5, u4} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14) _inst_5 (ContinuousLinearMap.mulAction.{u7, u6, u5, u4, u1} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14 S₃ _inst_5 _inst_21 _inst_22 _inst_23))) c h) f) (HSMul.hSMul.{u1, max u4 u2, max u4 u2} S₃ (ContinuousLinearMap.{u3, u6, u2, u4} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (ContinuousLinearMap.{u3, u6, u2, u4} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (instHSMul.{u1, max u4 u2} S₃ (ContinuousLinearMap.{u3, u6, u2, u4} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (MulAction.toSMul.{u1, max u4 u2} S₃ (ContinuousLinearMap.{u3, u6, u2, u4} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) _inst_5 (ContinuousLinearMap.mulAction.{u3, u6, u2, u4, u1} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14 S₃ _inst_5 _inst_21 _inst_22 _inst_23))) c (ContinuousLinearMap.comp.{u3, u7, u6, u2, u5, u4} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_8 _inst_11 _inst_14 _inst_27 h f))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_comp ContinuousLinearMap.smul_compₓ'. -/
@[simp]
theorem smul_comp (c : S₃) (h : M₂ →SL[σ₂₃] M₃) (f : M →SL[σ₁₂] M₂) :
(c • h).comp f = c • h.comp f :=
@@ -1591,6 +2554,12 @@ variable [DistribMulAction S₃ M₂] [ContinuousConstSMul S₃ M₂] [SMulCommC
variable [DistribMulAction S N₂] [ContinuousConstSMul S N₂] [SMulCommClass R S N₂]
+/- warning: continuous_linear_map.comp_smul -> ContinuousLinearMap.comp_smul is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_4 : Monoid.{u2} S] {M : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : AddCommMonoid.{u3} M] [_inst_8 : Module.{u1, u3} R M _inst_1 _inst_7] {N₂ : Type.{u4}} [_inst_15 : TopologicalSpace.{u4} N₂] [_inst_16 : AddCommMonoid.{u4} N₂] [_inst_17 : Module.{u1, u4} R N₂ _inst_1 _inst_16] {N₃ : Type.{u5}} [_inst_18 : TopologicalSpace.{u5} N₃] [_inst_19 : AddCommMonoid.{u5} N₃] [_inst_20 : Module.{u1, u5} R N₃ _inst_1 _inst_19] [_inst_24 : DistribMulAction.{u2, u5} S N₃ _inst_4 (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)] [_inst_25 : SMulCommClass.{u1, u2, u5} R S N₃ (SMulZeroClass.toHasSmul.{u1, u5} R N₃ (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (SMulWithZero.toSmulZeroClass.{u1, u5} R N₃ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (MulActionWithZero.toSMulWithZero.{u1, u5} R N₃ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (Module.toMulActionWithZero.{u1, u5} R N₃ _inst_1 _inst_19 _inst_20)))) (SMulZeroClass.toHasSmul.{u2, u5} S N₃ (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (DistribSMul.toSmulZeroClass.{u2, u5} S N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (DistribMulAction.toDistribSMul.{u2, u5} S N₃ _inst_4 (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19) _inst_24)))] [_inst_26 : ContinuousConstSMul.{u2, u5} S N₃ _inst_18 (SMulZeroClass.toHasSmul.{u2, u5} S N₃ (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (DistribSMul.toSmulZeroClass.{u2, u5} S N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (DistribMulAction.toDistribSMul.{u2, u5} S N₃ _inst_4 (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19) _inst_24)))] [_inst_31 : DistribMulAction.{u2, u4} S N₂ _inst_4 (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)] [_inst_32 : ContinuousConstSMul.{u2, u4} S N₂ _inst_15 (SMulZeroClass.toHasSmul.{u2, u4} S N₂ (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (DistribSMul.toSmulZeroClass.{u2, u4} S N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (DistribMulAction.toDistribSMul.{u2, u4} S N₂ _inst_4 (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16) _inst_31)))] [_inst_33 : SMulCommClass.{u1, u2, u4} R S N₂ (SMulZeroClass.toHasSmul.{u1, u4} R N₂ (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (SMulWithZero.toSmulZeroClass.{u1, u4} R N₂ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (MulActionWithZero.toSMulWithZero.{u1, u4} R N₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (Module.toMulActionWithZero.{u1, u4} R N₂ _inst_1 _inst_16 _inst_17)))) (SMulZeroClass.toHasSmul.{u2, u4} S N₂ (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (DistribSMul.toSmulZeroClass.{u2, u4} S N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (DistribMulAction.toDistribSMul.{u2, u4} S N₂ _inst_4 (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16) _inst_31)))] [_inst_34 : LinearMap.CompatibleSMul.{u4, u5, u2, u1} N₂ N₃ _inst_16 _inst_19 S R _inst_1 (SMulZeroClass.toHasSmul.{u2, u4} S N₂ (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (DistribSMul.toSmulZeroClass.{u2, u4} S N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (DistribMulAction.toDistribSMul.{u2, u4} S N₂ _inst_4 (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16) _inst_31))) _inst_17 (SMulZeroClass.toHasSmul.{u2, u5} S N₃ (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (DistribSMul.toSmulZeroClass.{u2, u5} S N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (DistribMulAction.toDistribSMul.{u2, u5} S N₃ _inst_4 (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19) _inst_24))) _inst_20] (hₗ : ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) N₂ _inst_15 _inst_16 N₃ _inst_18 _inst_19 _inst_17 _inst_20) (c : S) (fₗ : ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17), Eq.{max (succ u3) (succ u5)} (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) (ContinuousLinearMap.comp.{u1, u1, u1, u3, u4, u5} R R R _inst_1 _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 N₃ _inst_18 _inst_19 _inst_8 _inst_17 _inst_20 (RingHomCompTriple.right_ids.{u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) hₗ (SMul.smul.{u2, max u3 u4} S (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (MulAction.toHasSmul.{u2, max u3 u4} S (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) _inst_4 (ContinuousLinearMap.mulAction.{u1, u1, u3, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17 S _inst_4 _inst_31 _inst_33 _inst_32)) c fₗ)) (SMul.smul.{u2, max u3 u5} S (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) (MulAction.toHasSmul.{u2, max u3 u5} S (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) _inst_4 (ContinuousLinearMap.mulAction.{u1, u1, u3, u5, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20 S _inst_4 _inst_24 _inst_25 _inst_26)) c (ContinuousLinearMap.comp.{u1, u1, u1, u3, u4, u5} R R R _inst_1 _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 N₃ _inst_18 _inst_19 _inst_8 _inst_17 _inst_20 (RingHomCompTriple.right_ids.{u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) hₗ fₗ))
+but is expected to have type
+ forall {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : Semiring.{u2} R] [_inst_4 : Monoid.{u3} S] {M : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M] [_inst_7 : AddCommMonoid.{u1} M] [_inst_8 : Module.{u2, u1} R M _inst_1 _inst_7] {N₂ : Type.{u5}} [_inst_15 : TopologicalSpace.{u5} N₂] [_inst_16 : AddCommMonoid.{u5} N₂] [_inst_17 : Module.{u2, u5} R N₂ _inst_1 _inst_16] {N₃ : Type.{u4}} [_inst_18 : TopologicalSpace.{u4} N₃] [_inst_19 : AddCommMonoid.{u4} N₃] [_inst_20 : Module.{u2, u4} R N₃ _inst_1 _inst_19] [_inst_24 : DistribMulAction.{u3, u4} S N₃ _inst_4 (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)] [_inst_25 : SMulCommClass.{u2, u3, u4} R S N₃ (SMulZeroClass.toSMul.{u2, u4} R N₃ (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (SMulWithZero.toSMulZeroClass.{u2, u4} R N₃ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (MulActionWithZero.toSMulWithZero.{u2, u4} R N₃ (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (Module.toMulActionWithZero.{u2, u4} R N₃ _inst_1 _inst_19 _inst_20)))) (SMulZeroClass.toSMul.{u3, u4} S N₃ (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (DistribSMul.toSMulZeroClass.{u3, u4} S N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (DistribMulAction.toDistribSMul.{u3, u4} S N₃ _inst_4 (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19) _inst_24)))] [_inst_26 : ContinuousConstSMul.{u3, u4} S N₃ _inst_18 (SMulZeroClass.toSMul.{u3, u4} S N₃ (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (DistribSMul.toSMulZeroClass.{u3, u4} S N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (DistribMulAction.toDistribSMul.{u3, u4} S N₃ _inst_4 (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19) _inst_24)))] [_inst_31 : DistribMulAction.{u3, u5} S N₂ _inst_4 (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16)] [_inst_32 : ContinuousConstSMul.{u3, u5} S N₂ _inst_15 (SMulZeroClass.toSMul.{u3, u5} S N₂ (AddMonoid.toZero.{u5} N₂ (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16)) (DistribSMul.toSMulZeroClass.{u3, u5} S N₂ (AddMonoid.toAddZeroClass.{u5} N₂ (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16)) (DistribMulAction.toDistribSMul.{u3, u5} S N₂ _inst_4 (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16) _inst_31)))] [_inst_33 : SMulCommClass.{u2, u3, u5} R S N₂ (SMulZeroClass.toSMul.{u2, u5} R N₂ (AddMonoid.toZero.{u5} N₂ (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16)) (SMulWithZero.toSMulZeroClass.{u2, u5} R N₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddMonoid.toZero.{u5} N₂ (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16)) (MulActionWithZero.toSMulWithZero.{u2, u5} R N₂ (Semiring.toMonoidWithZero.{u2} R _inst_1) (AddMonoid.toZero.{u5} N₂ (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16)) (Module.toMulActionWithZero.{u2, u5} R N₂ _inst_1 _inst_16 _inst_17)))) (SMulZeroClass.toSMul.{u3, u5} S N₂ (AddMonoid.toZero.{u5} N₂ (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16)) (DistribSMul.toSMulZeroClass.{u3, u5} S N₂ (AddMonoid.toAddZeroClass.{u5} N₂ (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16)) (DistribMulAction.toDistribSMul.{u3, u5} S N₂ _inst_4 (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16) _inst_31)))] [_inst_34 : LinearMap.CompatibleSMul.{u5, u4, u3, u2} N₂ N₃ _inst_16 _inst_19 S R _inst_1 (SMulZeroClass.toSMul.{u3, u5} S N₂ (AddMonoid.toZero.{u5} N₂ (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16)) (DistribSMul.toSMulZeroClass.{u3, u5} S N₂ (AddMonoid.toAddZeroClass.{u5} N₂ (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16)) (DistribMulAction.toDistribSMul.{u3, u5} S N₂ _inst_4 (AddCommMonoid.toAddMonoid.{u5} N₂ _inst_16) _inst_31))) _inst_17 (SMulZeroClass.toSMul.{u3, u4} S N₃ (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (DistribSMul.toSMulZeroClass.{u3, u4} S N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (DistribMulAction.toDistribSMul.{u3, u4} S N₃ _inst_4 (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19) _inst_24))) _inst_20] (hₗ : ContinuousLinearMap.{u2, u2, u5, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) N₂ _inst_15 _inst_16 N₃ _inst_18 _inst_19 _inst_17 _inst_20) (c : S) (fₗ : ContinuousLinearMap.{u2, u2, u1, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17), Eq.{max (succ u1) (succ u4)} (ContinuousLinearMap.{u2, u2, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) (ContinuousLinearMap.comp.{u2, u2, u2, u1, u5, u4} R R R _inst_1 _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 N₃ _inst_18 _inst_19 _inst_8 _inst_17 _inst_20 (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) hₗ (HSMul.hSMul.{u3, max u5 u1, max u5 u1} S (ContinuousLinearMap.{u2, u2, u1, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u2, u2, u1, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (instHSMul.{u3, max u5 u1} S (ContinuousLinearMap.{u2, u2, u1, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (MulAction.toSMul.{u3, max u5 u1} S (ContinuousLinearMap.{u2, u2, u1, u5} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) _inst_4 (ContinuousLinearMap.mulAction.{u2, u2, u1, u5, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17 S _inst_4 _inst_31 _inst_33 _inst_32))) c fₗ)) (HSMul.hSMul.{u3, max u4 u1, max u4 u1} S (ContinuousLinearMap.{u2, u2, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) (ContinuousLinearMap.{u2, u2, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) (instHSMul.{u3, max u4 u1} S (ContinuousLinearMap.{u2, u2, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) (MulAction.toSMul.{u3, max u4 u1} S (ContinuousLinearMap.{u2, u2, u1, u4} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) _inst_4 (ContinuousLinearMap.mulAction.{u2, u2, u1, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20 S _inst_4 _inst_24 _inst_25 _inst_26))) c (ContinuousLinearMap.comp.{u2, u2, u2, u1, u5, u4} R R R _inst_1 _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 N₃ _inst_18 _inst_19 _inst_8 _inst_17 _inst_20 (RingHomCompTriple.ids.{u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) hₗ fₗ))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_smul ContinuousLinearMap.comp_smulₓ'. -/
@[simp]
theorem comp_smul [LinearMap.CompatibleSMul N₂ N₃ S R] (hₗ : N₂ →L[R] N₃) (c : S)
(fₗ : M →L[R] N₂) : hₗ.comp (c • fₗ) = c • hₗ.comp fₗ :=
@@ -1601,6 +2570,12 @@ theorem comp_smul [LinearMap.CompatibleSMul N₂ N₃ S R] (hₗ : N₂ →L[R]
include σ₁₃
+/- warning: continuous_linear_map.comp_smulₛₗ -> ContinuousLinearMap.comp_smulₛₗ is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {R₂ : Type.{u2}} {R₃ : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : Semiring.{u3} R₃] {M : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M] [_inst_7 : AddCommMonoid.{u4} M] [_inst_8 : Module.{u1, u4} R M _inst_1 _inst_7] {M₂ : Type.{u5}} [_inst_9 : TopologicalSpace.{u5} M₂] [_inst_10 : AddCommMonoid.{u5} M₂] [_inst_11 : Module.{u2, u5} R₂ M₂ _inst_2 _inst_10] {M₃ : Type.{u6}} [_inst_12 : TopologicalSpace.{u6} M₃] [_inst_13 : AddCommMonoid.{u6} M₃] [_inst_14 : Module.{u3, u6} R₃ M₃ _inst_3 _inst_13] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₃ : RingHom.{u2, u3} R₂ R₃ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {σ₁₃ : RingHom.{u1, u3} R R₃ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} [_inst_27 : RingHomCompTriple.{u1, u2, u3} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] [_inst_34 : SMulCommClass.{u2, u2, u5} R₂ R₂ M₂ (SMulZeroClass.toHasSmul.{u2, u5} R₂ M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (SMulWithZero.toSmulZeroClass.{u2, u5} R₂ M₂ (MulZeroClass.toHasZero.{u2} R₂ (MulZeroOneClass.toMulZeroClass.{u2} R₂ (MonoidWithZero.toMulZeroOneClass.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (MulActionWithZero.toSMulWithZero.{u2, u5} R₂ M₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (Module.toMulActionWithZero.{u2, u5} R₂ M₂ _inst_2 _inst_10 _inst_11)))) (SMulZeroClass.toHasSmul.{u2, u5} R₂ M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (SMulWithZero.toSmulZeroClass.{u2, u5} R₂ M₂ (MulZeroClass.toHasZero.{u2} R₂ (MulZeroOneClass.toMulZeroClass.{u2} R₂ (MonoidWithZero.toMulZeroOneClass.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (MulActionWithZero.toSMulWithZero.{u2, u5} R₂ M₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (Module.toMulActionWithZero.{u2, u5} R₂ M₂ _inst_2 _inst_10 _inst_11))))] [_inst_35 : SMulCommClass.{u3, u3, u6} R₃ R₃ M₃ (SMulZeroClass.toHasSmul.{u3, u6} R₃ M₃ (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (SMulWithZero.toSmulZeroClass.{u3, u6} R₃ M₃ (MulZeroClass.toHasZero.{u3} R₃ (MulZeroOneClass.toMulZeroClass.{u3} R₃ (MonoidWithZero.toMulZeroOneClass.{u3} R₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3)))) (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (MulActionWithZero.toSMulWithZero.{u3, u6} R₃ M₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3) (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (Module.toMulActionWithZero.{u3, u6} R₃ M₃ _inst_3 _inst_13 _inst_14)))) (SMulZeroClass.toHasSmul.{u3, u6} R₃ M₃ (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (SMulWithZero.toSmulZeroClass.{u3, u6} R₃ M₃ (MulZeroClass.toHasZero.{u3} R₃ (MulZeroOneClass.toMulZeroClass.{u3} R₃ (MonoidWithZero.toMulZeroOneClass.{u3} R₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3)))) (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (MulActionWithZero.toSMulWithZero.{u3, u6} R₃ M₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3) (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (Module.toMulActionWithZero.{u3, u6} R₃ M₃ _inst_3 _inst_13 _inst_14))))] [_inst_36 : ContinuousConstSMul.{u2, u5} R₂ M₂ _inst_9 (SMulZeroClass.toHasSmul.{u2, u5} R₂ M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (SMulWithZero.toSmulZeroClass.{u2, u5} R₂ M₂ (MulZeroClass.toHasZero.{u2} R₂ (MulZeroOneClass.toMulZeroClass.{u2} R₂ (MonoidWithZero.toMulZeroOneClass.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (MulActionWithZero.toSMulWithZero.{u2, u5} R₂ M₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10))) (Module.toMulActionWithZero.{u2, u5} R₂ M₂ _inst_2 _inst_10 _inst_11))))] [_inst_37 : ContinuousConstSMul.{u3, u6} R₃ M₃ _inst_12 (SMulZeroClass.toHasSmul.{u3, u6} R₃ M₃ (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (SMulWithZero.toSmulZeroClass.{u3, u6} R₃ M₃ (MulZeroClass.toHasZero.{u3} R₃ (MulZeroOneClass.toMulZeroClass.{u3} R₃ (MonoidWithZero.toMulZeroOneClass.{u3} R₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3)))) (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (MulActionWithZero.toSMulWithZero.{u3, u6} R₃ M₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3) (AddZeroClass.toHasZero.{u6} M₃ (AddMonoid.toAddZeroClass.{u6} M₃ (AddCommMonoid.toAddMonoid.{u6} M₃ _inst_13))) (Module.toMulActionWithZero.{u3, u6} R₃ M₃ _inst_3 _inst_13 _inst_14))))] (h : ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14) (c : R₂) (f : ContinuousLinearMap.{u1, u2, u4, u5} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11), Eq.{max (succ u4) (succ u6)} (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_8 _inst_11 _inst_14 _inst_27 h (SMul.smul.{u2, max u4 u5} R₂ (ContinuousLinearMap.{u1, u2, u4, u5} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11) (MulAction.toHasSmul.{u2, max u4 u5} R₂ (ContinuousLinearMap.{u1, u2, u4, u5} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11) (MonoidWithZero.toMonoid.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)) (ContinuousLinearMap.mulAction.{u1, u2, u4, u5, u2} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11 R₂ (MonoidWithZero.toMonoid.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)) (Module.toDistribMulAction.{u2, u5} R₂ M₂ _inst_2 _inst_10 _inst_11) _inst_34 _inst_36)) c f)) (SMul.smul.{u3, max u4 u6} R₃ (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (MulAction.toHasSmul.{u3, max u4 u6} R₃ (ContinuousLinearMap.{u1, u3, u4, u6} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (MonoidWithZero.toMonoid.{u3} R₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3)) (ContinuousLinearMap.mulAction.{u1, u3, u4, u6, u3} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14 R₃ (MonoidWithZero.toMonoid.{u3} R₃ (Semiring.toMonoidWithZero.{u3} R₃ _inst_3)) (Module.toDistribMulAction.{u3, u6} R₃ M₃ _inst_3 _inst_13 _inst_14) _inst_35 _inst_37)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} R₂ R₃ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)) (fun (_x : RingHom.{u2, u3} R₂ R₃ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)) => R₂ -> R₃) (RingHom.hasCoeToFun.{u2, u3} R₂ R₃ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)) σ₂₃ c) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_8 _inst_11 _inst_14 _inst_27 h f))
+but is expected to have type
+ forall {R : Type.{u2}} {R₂ : Type.{u6}} {R₃ : Type.{u4}} [_inst_1 : Semiring.{u2} R] [_inst_2 : Semiring.{u6} R₂] [_inst_3 : Semiring.{u4} R₃] {M : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M] [_inst_7 : AddCommMonoid.{u1} M] [_inst_8 : Module.{u2, u1} R M _inst_1 _inst_7] {M₂ : Type.{u5}} [_inst_9 : TopologicalSpace.{u5} M₂] [_inst_10 : AddCommMonoid.{u5} M₂] [_inst_11 : Module.{u6, u5} R₂ M₂ _inst_2 _inst_10] {M₃ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₃] [_inst_13 : AddCommMonoid.{u3} M₃] [_inst_14 : Module.{u4, u3} R₃ M₃ _inst_3 _inst_13] {σ₁₂ : RingHom.{u2, u6} R R₂ (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2)} {σ₂₃ : RingHom.{u6, u4} R₂ R₃ (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3)} {σ₁₃ : RingHom.{u2, u4} R R₃ (Semiring.toNonAssocSemiring.{u2} R _inst_1) (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3)} [_inst_27 : RingHomCompTriple.{u2, u6, u4} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] [_inst_34 : SMulCommClass.{u6, u6, u5} R₂ R₂ M₂ (SMulZeroClass.toSMul.{u6, u5} R₂ M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (SMulWithZero.toSMulZeroClass.{u6, u5} R₂ M₂ (MonoidWithZero.toZero.{u6} R₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (MulActionWithZero.toSMulWithZero.{u6, u5} R₂ M₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (Module.toMulActionWithZero.{u6, u5} R₂ M₂ _inst_2 _inst_10 _inst_11)))) (SMulZeroClass.toSMul.{u6, u5} R₂ M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (SMulWithZero.toSMulZeroClass.{u6, u5} R₂ M₂ (MonoidWithZero.toZero.{u6} R₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (MulActionWithZero.toSMulWithZero.{u6, u5} R₂ M₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (Module.toMulActionWithZero.{u6, u5} R₂ M₂ _inst_2 _inst_10 _inst_11))))] [_inst_35 : SMulCommClass.{u4, u4, u3} R₃ R₃ M₃ (SMulZeroClass.toSMul.{u4, u3} R₃ M₃ (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (SMulWithZero.toSMulZeroClass.{u4, u3} R₃ M₃ (MonoidWithZero.toZero.{u4} R₃ (Semiring.toMonoidWithZero.{u4} R₃ _inst_3)) (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (MulActionWithZero.toSMulWithZero.{u4, u3} R₃ M₃ (Semiring.toMonoidWithZero.{u4} R₃ _inst_3) (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (Module.toMulActionWithZero.{u4, u3} R₃ M₃ _inst_3 _inst_13 _inst_14)))) (SMulZeroClass.toSMul.{u4, u3} R₃ M₃ (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (SMulWithZero.toSMulZeroClass.{u4, u3} R₃ M₃ (MonoidWithZero.toZero.{u4} R₃ (Semiring.toMonoidWithZero.{u4} R₃ _inst_3)) (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (MulActionWithZero.toSMulWithZero.{u4, u3} R₃ M₃ (Semiring.toMonoidWithZero.{u4} R₃ _inst_3) (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (Module.toMulActionWithZero.{u4, u3} R₃ M₃ _inst_3 _inst_13 _inst_14))))] [_inst_36 : ContinuousConstSMul.{u6, u5} R₂ M₂ _inst_9 (SMulZeroClass.toSMul.{u6, u5} R₂ M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (SMulWithZero.toSMulZeroClass.{u6, u5} R₂ M₂ (MonoidWithZero.toZero.{u6} R₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (MulActionWithZero.toSMulWithZero.{u6, u5} R₂ M₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_10)) (Module.toMulActionWithZero.{u6, u5} R₂ M₂ _inst_2 _inst_10 _inst_11))))] [_inst_37 : ContinuousConstSMul.{u4, u3} R₃ M₃ _inst_12 (SMulZeroClass.toSMul.{u4, u3} R₃ M₃ (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (SMulWithZero.toSMulZeroClass.{u4, u3} R₃ M₃ (MonoidWithZero.toZero.{u4} R₃ (Semiring.toMonoidWithZero.{u4} R₃ _inst_3)) (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (MulActionWithZero.toSMulWithZero.{u4, u3} R₃ M₃ (Semiring.toMonoidWithZero.{u4} R₃ _inst_3) (AddMonoid.toZero.{u3} M₃ (AddCommMonoid.toAddMonoid.{u3} M₃ _inst_13)) (Module.toMulActionWithZero.{u4, u3} R₃ M₃ _inst_3 _inst_13 _inst_14))))] (h : ContinuousLinearMap.{u6, u4, u5, u3} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_11 _inst_14) (c : R₂) (f : ContinuousLinearMap.{u2, u6, u1, u5} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11), Eq.{max (succ u1) (succ u3)} (ContinuousLinearMap.{u2, u4, u1, u3} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (ContinuousLinearMap.comp.{u2, u6, u4, u1, u5, u3} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_8 _inst_11 _inst_14 _inst_27 h (HSMul.hSMul.{u6, max u5 u1, max u5 u1} R₂ (ContinuousLinearMap.{u2, u6, u1, u5} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11) (ContinuousLinearMap.{u2, u6, u1, u5} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11) (instHSMul.{u6, max u5 u1} R₂ (ContinuousLinearMap.{u2, u6, u1, u5} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11) (MulAction.toSMul.{u6, max u5 u1} R₂ (ContinuousLinearMap.{u2, u6, u1, u5} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11) (MonoidWithZero.toMonoid.{u6} R₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2)) (ContinuousLinearMap.mulAction.{u2, u6, u1, u5, u6} R R₂ _inst_1 _inst_2 σ₁₂ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 _inst_8 _inst_11 R₂ (MonoidWithZero.toMonoid.{u6} R₂ (Semiring.toMonoidWithZero.{u6} R₂ _inst_2)) (Module.toDistribMulAction.{u6, u5} R₂ M₂ 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(Semiring.toNonAssocSemiring.{u6} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₃ _inst_3))))) σ₂₃ c) (ContinuousLinearMap.comp.{u2, u6, u4, u1, u5, u3} R R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M _inst_6 _inst_7 M₂ _inst_9 _inst_10 M₃ _inst_12 _inst_13 _inst_8 _inst_11 _inst_14 _inst_27 h f))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_smulₛₗ ContinuousLinearMap.comp_smulₛₗₓ'. -/
@[simp]
theorem comp_smulₛₗ [SMulCommClass R₂ R₂ M₂] [SMulCommClass R₃ R₃ M₃] [ContinuousConstSMul R₂ M₂]
[ContinuousConstSMul R₃ M₃] (h : M₂ →SL[σ₂₃] M₃) (c : R₂) (f : M →SL[σ₁₂] M₂) :
@@ -1632,6 +2607,12 @@ variable {R R₂ R₃ S S₃ : Type _} [Semiring R] [Semiring R₂] [Semiring R
{σ₁₂ : R →+* R₂} {σ₂₃ : R₂ →+* R₃} {σ₁₃ : R →+* R₃} [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] (c : S)
(h : M₂ →SL[σ₂₃] M₃) (f g : M →SL[σ₁₂] M₂) (x y z : M)
+/- warning: continuous_linear_map.prod_equiv -> ContinuousLinearMap.prodEquiv is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : AddCommMonoid.{u2} M] [_inst_8 : Module.{u1, u2} R M _inst_1 _inst_7] {N₂ : Type.{u3}} [_inst_15 : TopologicalSpace.{u3} N₂] [_inst_16 : AddCommMonoid.{u3} N₂] [_inst_17 : Module.{u1, u3} R N₂ _inst_1 _inst_16] {N₃ : Type.{u4}} [_inst_18 : TopologicalSpace.{u4} N₃] [_inst_19 : AddCommMonoid.{u4} N₃] [_inst_20 : Module.{u1, u4} R N₃ _inst_1 _inst_19], Equiv.{max (succ (max u2 u3)) (succ (max u2 u4)), max (succ u2) (succ (max u3 u4))} (Prod.{max u2 u3, max u2 u4} (ContinuousLinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u1, u1, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20)) (ContinuousLinearMap.{u1, u1, u2, max u3 u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 (Prod.{u3, u4} N₂ N₃) (Prod.topologicalSpace.{u3, u4} N₂ N₃ _inst_15 _inst_18) (Prod.addCommMonoid.{u3, u4} N₂ N₃ _inst_16 _inst_19) _inst_8 (Prod.module.{u1, u3, u4} R N₂ N₃ _inst_1 _inst_16 _inst_19 _inst_17 _inst_20))
+but is expected to have type
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : AddCommMonoid.{u2} M] [_inst_8 : Module.{u1, u2} R M _inst_1 _inst_7] {N₂ : Type.{u3}} [_inst_15 : TopologicalSpace.{u3} N₂] [_inst_16 : AddCommMonoid.{u3} N₂] [_inst_17 : Module.{u1, u3} R N₂ _inst_1 _inst_16] {N₃ : Type.{u4}} [_inst_18 : TopologicalSpace.{u4} N₃] [_inst_19 : AddCommMonoid.{u4} N₃] [_inst_20 : Module.{u1, u4} R N₃ _inst_1 _inst_19], Equiv.{max (succ (max u4 u2)) (succ (max u3 u2)), max (succ (max u4 u3)) (succ u2)} (Prod.{max u3 u2, max u4 u2} (ContinuousLinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u1, u1, u2, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20)) (ContinuousLinearMap.{u1, u1, u2, max u4 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 (Prod.{u3, u4} N₂ N₃) (instTopologicalSpaceProd.{u3, u4} N₂ N₃ _inst_15 _inst_18) (Prod.instAddCommMonoidSum.{u3, u4} N₂ N₃ _inst_16 _inst_19) _inst_8 (Prod.module.{u1, u3, u4} R N₂ N₃ _inst_1 _inst_16 _inst_19 _inst_17 _inst_20))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.prod_equiv ContinuousLinearMap.prodEquivₓ'. -/
/-- `continuous_linear_map.prod` as an `equiv`. -/
@[simps apply]
def prodEquiv : (M →L[R] N₂) × (M →L[R] N₃) ≃ (M →L[R] N₂ × N₃)
@@ -1642,6 +2623,12 @@ def prodEquiv : (M →L[R] N₂) × (M →L[R] N₃) ≃ (M →L[R] N₂ × N₃
right_inv f := by ext <;> rfl
#align continuous_linear_map.prod_equiv ContinuousLinearMap.prodEquiv
+/- warning: continuous_linear_map.prod_ext_iff -> ContinuousLinearMap.prod_ext_iff is a dubious translation:
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+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : AddCommMonoid.{u2} M] [_inst_8 : Module.{u1, u2} R M _inst_1 _inst_7] {N₂ : Type.{u3}} [_inst_15 : TopologicalSpace.{u3} N₂] [_inst_16 : AddCommMonoid.{u3} N₂] [_inst_17 : Module.{u1, u3} R N₂ _inst_1 _inst_16] {N₃ : Type.{u4}} [_inst_18 : TopologicalSpace.{u4} N₃] [_inst_19 : AddCommMonoid.{u4} N₃] [_inst_20 : Module.{u1, u4} R N₃ _inst_1 _inst_19] {f : ContinuousLinearMap.{u1, u1, max u2 u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Prod.{u2, u3} M N₂) (Prod.topologicalSpace.{u2, u3} M N₂ _inst_6 _inst_15) (Prod.addCommMonoid.{u2, u3} M N₂ _inst_7 _inst_16) N₃ _inst_18 _inst_19 (Prod.module.{u1, u2, u3} R M N₂ _inst_1 _inst_7 _inst_16 _inst_8 _inst_17) _inst_20} {g : ContinuousLinearMap.{u1, u1, max u2 u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Prod.{u2, u3} M N₂) 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.prod_ext_iff ContinuousLinearMap.prod_ext_iffₓ'. -/
theorem prod_ext_iff {f g : M × N₂ →L[R] N₃} :
f = g ↔ f.comp (inl _ _ _) = g.comp (inl _ _ _) ∧ f.comp (inr _ _ _) = g.comp (inr _ _ _) :=
by
@@ -1649,6 +2636,12 @@ theorem prod_ext_iff {f g : M × N₂ →L[R] N₃} :
rfl
#align continuous_linear_map.prod_ext_iff ContinuousLinearMap.prod_ext_iff
+/- warning: continuous_linear_map.prod_ext -> ContinuousLinearMap.prod_ext is a dubious translation:
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_inst_17))) -> (Eq.{max (succ u3) (succ u1)} (ContinuousLinearMap.{u4, u4, u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) N₂ _inst_15 _inst_16 N₃ _inst_18 _inst_19 _inst_17 _inst_20) (ContinuousLinearMap.comp.{u4, u4, u4, u3, max u2 u3, u1} R R R _inst_1 _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) N₂ _inst_15 _inst_16 (Prod.{u2, u3} M N₂) (instTopologicalSpaceProd.{u2, u3} M N₂ _inst_6 _inst_15) (Prod.instAddCommMonoidSum.{u2, u3} M N₂ _inst_7 _inst_16) N₃ _inst_18 _inst_19 _inst_17 (Prod.module.{u4, u2, u3} R M N₂ _inst_1 _inst_7 _inst_16 _inst_8 _inst_17) _inst_20 (RingHomCompTriple.ids.{u4, u4} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) f (ContinuousLinearMap.inr.{u4, u2, u3} R _inst_1 M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17)) (ContinuousLinearMap.comp.{u4, u4, u4, u3, max u2 u3, u1} R R R _inst_1 _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) N₂ _inst_15 _inst_16 (Prod.{u2, u3} M N₂) (instTopologicalSpaceProd.{u2, u3} M N₂ _inst_6 _inst_15) (Prod.instAddCommMonoidSum.{u2, u3} M N₂ _inst_7 _inst_16) N₃ _inst_18 _inst_19 _inst_17 (Prod.module.{u4, u2, u3} R M N₂ _inst_1 _inst_7 _inst_16 _inst_8 _inst_17) _inst_20 (RingHomCompTriple.ids.{u4, u4} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1))) g (ContinuousLinearMap.inr.{u4, u2, u3} R _inst_1 M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17))) -> (Eq.{max (max (succ u2) (succ u3)) (succ u1)} (ContinuousLinearMap.{u4, u4, max u3 u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R _inst_1)) (Prod.{u2, u3} M N₂) (instTopologicalSpaceProd.{u2, u3} M N₂ _inst_6 _inst_15) (Prod.instAddCommMonoidSum.{u2, u3} M N₂ _inst_7 _inst_16) N₃ _inst_18 _inst_19 (Prod.module.{u4, u2, u3} R M N₂ _inst_1 _inst_7 _inst_16 _inst_8 _inst_17) _inst_20) f g)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.prod_ext ContinuousLinearMap.prod_extₓ'. -/
@[ext]
theorem prod_ext {f g : M × N₂ →L[R] N₃} (hl : f.comp (inl _ _ _) = g.comp (inl _ _ _))
(hr : f.comp (inr _ _ _) = g.comp (inr _ _ _)) : f = g :=
@@ -1667,6 +2660,12 @@ instance [Module S₃ᵐᵒᵖ M₃] [IsCentralScalar S₃ M₃] : IsCentralScal
variable (S) [ContinuousAdd N₃]
+/- warning: continuous_linear_map.prodₗ -> ContinuousLinearMap.prodₗ is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} (S : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_4 : Semiring.{u2} S] {M : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : AddCommMonoid.{u3} M] [_inst_8 : Module.{u1, u3} R M _inst_1 _inst_7] {N₂ : Type.{u4}} [_inst_15 : TopologicalSpace.{u4} N₂] [_inst_16 : AddCommMonoid.{u4} N₂] [_inst_17 : Module.{u1, u4} R N₂ _inst_1 _inst_16] {N₃ : Type.{u5}} [_inst_18 : TopologicalSpace.{u5} N₃] [_inst_19 : AddCommMonoid.{u5} N₃] [_inst_20 : Module.{u1, u5} R N₃ _inst_1 _inst_19] [_inst_24 : Module.{u2, u4} S N₂ _inst_4 _inst_16] [_inst_25 : ContinuousConstSMul.{u2, u4} S N₂ _inst_15 (SMulZeroClass.toHasSmul.{u2, u4} S N₂ (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (SMulWithZero.toSmulZeroClass.{u2, u4} S N₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)))) (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (MulActionWithZero.toSMulWithZero.{u2, u4} S N₂ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (Module.toMulActionWithZero.{u2, u4} S N₂ _inst_4 _inst_16 _inst_24))))] [_inst_26 : SMulCommClass.{u1, u2, u4} R S N₂ (SMulZeroClass.toHasSmul.{u1, u4} R N₂ (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (SMulWithZero.toSmulZeroClass.{u1, u4} R N₂ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (MulActionWithZero.toSMulWithZero.{u1, u4} R N₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (Module.toMulActionWithZero.{u1, u4} R N₂ _inst_1 _inst_16 _inst_17)))) (SMulZeroClass.toHasSmul.{u2, u4} S N₂ (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (SMulWithZero.toSmulZeroClass.{u2, u4} S N₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)))) (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (MulActionWithZero.toSMulWithZero.{u2, u4} S N₂ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddZeroClass.toHasZero.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) (Module.toMulActionWithZero.{u2, u4} S N₂ _inst_4 _inst_16 _inst_24))))] [_inst_27 : Module.{u2, u5} S N₃ _inst_4 _inst_19] [_inst_28 : SMulCommClass.{u1, u2, u5} R S N₃ (SMulZeroClass.toHasSmul.{u1, u5} R N₃ (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (SMulWithZero.toSmulZeroClass.{u1, u5} R N₃ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (MulActionWithZero.toSMulWithZero.{u1, u5} R N₃ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (Module.toMulActionWithZero.{u1, u5} R N₃ _inst_1 _inst_19 _inst_20)))) (SMulZeroClass.toHasSmul.{u2, u5} S N₃ (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (SMulWithZero.toSmulZeroClass.{u2, u5} S N₃ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)))) (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (MulActionWithZero.toSMulWithZero.{u2, u5} S N₃ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (Module.toMulActionWithZero.{u2, u5} S N₃ _inst_4 _inst_19 _inst_27))))] [_inst_29 : ContinuousConstSMul.{u2, u5} S N₃ _inst_18 (SMulZeroClass.toHasSmul.{u2, u5} S N₃ (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (SMulWithZero.toSmulZeroClass.{u2, u5} S N₃ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)))) (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (MulActionWithZero.toSMulWithZero.{u2, u5} S N₃ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddZeroClass.toHasZero.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) (Module.toMulActionWithZero.{u2, u5} S N₃ _inst_4 _inst_19 _inst_27))))] [_inst_33 : ContinuousAdd.{u4} N₂ _inst_15 (AddZeroClass.toHasAdd.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)))] [_inst_34 : ContinuousAdd.{u5} N₃ _inst_18 (AddZeroClass.toHasAdd.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)))], LinearEquiv.{u2, u2, max (max u3 u4) u3 u5, max u3 u4 u5} S S _inst_4 _inst_4 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_4)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_4)) (RingHomInvPair.ids.{u2} S _inst_4) (RingHomInvPair.ids.{u2} S _inst_4) (Prod.{max u3 u4, max u3 u5} (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20)) (ContinuousLinearMap.{u1, u1, u3, max u4 u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 (Prod.{u4, u5} N₂ N₃) (Prod.topologicalSpace.{u4, u5} N₂ N₃ _inst_15 _inst_18) (Prod.addCommMonoid.{u4, u5} N₂ N₃ _inst_16 _inst_19) _inst_8 (Prod.module.{u1, u4, u5} R N₂ N₃ _inst_1 _inst_16 _inst_19 _inst_17 _inst_20)) (Prod.addCommMonoid.{max u3 u4, max u3 u5} (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17 _inst_33) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20 _inst_34)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, max u4 u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 (Prod.{u4, u5} N₂ N₃) (Prod.topologicalSpace.{u4, u5} N₂ N₃ _inst_15 _inst_18) (Prod.addCommMonoid.{u4, u5} N₂ N₃ _inst_16 _inst_19) _inst_8 (Prod.module.{u1, u4, u5} R N₂ N₃ _inst_1 _inst_16 _inst_19 _inst_17 _inst_20) (ContinuousLinearMap.prodₗ._proof_1.{u5, u4} N₂ _inst_15 _inst_16 N₃ _inst_18 _inst_19 _inst_33 _inst_34)) (Prod.module.{u2, max u3 u4, max u3 u5} S (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) _inst_4 (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17 _inst_33) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20 _inst_34) (ContinuousLinearMap.module.{u1, u1, u2, u3, u4} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 N₂ _inst_15 _inst_16 _inst_17 _inst_24 _inst_26 _inst_25 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_33) (ContinuousLinearMap.module.{u1, u1, u2, u3, u5} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 N₃ _inst_18 _inst_19 _inst_20 _inst_27 _inst_28 _inst_29 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_34)) (ContinuousLinearMap.module.{u1, u1, u2, u3, max u4 u5} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 (Prod.{u4, u5} N₂ N₃) (Prod.topologicalSpace.{u4, u5} N₂ N₃ _inst_15 _inst_18) (Prod.addCommMonoid.{u4, u5} N₂ N₃ _inst_16 _inst_19) (Prod.module.{u1, u4, u5} R N₂ N₃ _inst_1 _inst_16 _inst_19 _inst_17 _inst_20) (Prod.module.{u2, u4, u5} S N₂ N₃ _inst_4 _inst_16 _inst_19 _inst_24 _inst_27) (ContinuousLinearMap.prodₗ._proof_2.{u1, u5, u2, u4} R S _inst_1 _inst_4 N₂ _inst_16 _inst_17 N₃ _inst_19 _inst_20 _inst_24 _inst_26 _inst_27 _inst_28) (ContinuousLinearMap.prodₗ._proof_3.{u5, u2, u4} S _inst_4 N₂ _inst_15 _inst_16 N₃ _inst_18 _inst_19 _inst_24 _inst_25 _inst_27 _inst_29) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (ContinuousLinearMap.prodₗ._proof_4.{u5, u4} N₂ _inst_15 _inst_16 N₃ _inst_18 _inst_19 _inst_33 _inst_34))
+but is expected to have type
+ forall {R : Type.{u1}} (S : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_4 : Semiring.{u2} S] {M : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : AddCommMonoid.{u3} M] [_inst_8 : Module.{u1, u3} R M _inst_1 _inst_7] {N₂ : Type.{u4}} [_inst_15 : TopologicalSpace.{u4} N₂] [_inst_16 : AddCommMonoid.{u4} N₂] [_inst_17 : Module.{u1, u4} R N₂ _inst_1 _inst_16] {N₃ : Type.{u5}} [_inst_18 : TopologicalSpace.{u5} N₃] [_inst_19 : AddCommMonoid.{u5} N₃] [_inst_20 : Module.{u1, u5} R N₃ _inst_1 _inst_19] [_inst_24 : Module.{u2, u4} S N₂ _inst_4 _inst_16] [_inst_25 : ContinuousConstSMul.{u2, u4} S N₂ _inst_15 (SMulZeroClass.toSMul.{u2, u4} S N₂ (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (SMulWithZero.toSMulZeroClass.{u2, u4} S N₂ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (MulActionWithZero.toSMulWithZero.{u2, u4} S N₂ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (Module.toMulActionWithZero.{u2, u4} S N₂ _inst_4 _inst_16 _inst_24))))] [_inst_26 : SMulCommClass.{u1, u2, u4} R S N₂ (SMulZeroClass.toSMul.{u1, u4} R N₂ (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (SMulWithZero.toSMulZeroClass.{u1, u4} R N₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (MulActionWithZero.toSMulWithZero.{u1, u4} R N₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (Module.toMulActionWithZero.{u1, u4} R N₂ _inst_1 _inst_16 _inst_17)))) (SMulZeroClass.toSMul.{u2, u4} S N₂ (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (SMulWithZero.toSMulZeroClass.{u2, u4} S N₂ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (MulActionWithZero.toSMulWithZero.{u2, u4} S N₂ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddMonoid.toZero.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)) (Module.toMulActionWithZero.{u2, u4} S N₂ _inst_4 _inst_16 _inst_24))))] [_inst_27 : Module.{u2, u5} S N₃ _inst_4 _inst_19] [_inst_28 : SMulCommClass.{u1, u2, u5} R S N₃ (SMulZeroClass.toSMul.{u1, u5} R N₃ (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (SMulWithZero.toSMulZeroClass.{u1, u5} R N₃ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (MulActionWithZero.toSMulWithZero.{u1, u5} R N₃ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (Module.toMulActionWithZero.{u1, u5} R N₃ _inst_1 _inst_19 _inst_20)))) (SMulZeroClass.toSMul.{u2, u5} S N₃ (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (SMulWithZero.toSMulZeroClass.{u2, u5} S N₃ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (MulActionWithZero.toSMulWithZero.{u2, u5} S N₃ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (Module.toMulActionWithZero.{u2, u5} S N₃ _inst_4 _inst_19 _inst_27))))] [_inst_29 : ContinuousConstSMul.{u2, u5} S N₃ _inst_18 (SMulZeroClass.toSMul.{u2, u5} S N₃ (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (SMulWithZero.toSMulZeroClass.{u2, u5} S N₃ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (MulActionWithZero.toSMulWithZero.{u2, u5} S N₃ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddMonoid.toZero.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)) (Module.toMulActionWithZero.{u2, u5} S N₃ _inst_4 _inst_19 _inst_27))))] [_inst_33 : ContinuousAdd.{u4} N₂ _inst_15 (AddZeroClass.toAdd.{u4} N₂ (AddMonoid.toAddZeroClass.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16)))] [_inst_34 : ContinuousAdd.{u5} N₃ _inst_18 (AddZeroClass.toAdd.{u5} N₃ (AddMonoid.toAddZeroClass.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19)))], LinearEquiv.{u2, u2, max (max u5 u3) u4 u3, max (max u5 u4) u3} S S _inst_4 _inst_4 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_4)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_4)) (RingHomInvPair.ids.{u2} S _inst_4) (RingHomInvPair.ids.{u2} S _inst_4) (Prod.{max u4 u3, max u5 u3} (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20)) (ContinuousLinearMap.{u1, u1, u3, max u5 u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 (Prod.{u4, u5} N₂ N₃) (instTopologicalSpaceProd.{u4, u5} N₂ N₃ _inst_15 _inst_18) (Prod.instAddCommMonoidSum.{u4, u5} N₂ N₃ _inst_16 _inst_19) _inst_8 (Prod.module.{u1, u4, u5} R N₂ N₃ _inst_1 _inst_16 _inst_19 _inst_17 _inst_20)) (Prod.instAddCommMonoidSum.{max u3 u4, max u3 u5} (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17 _inst_33) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20 _inst_34)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, max u4 u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 (Prod.{u4, u5} N₂ N₃) (instTopologicalSpaceProd.{u4, u5} N₂ N₃ _inst_15 _inst_18) (Prod.instAddCommMonoidSum.{u4, u5} N₂ N₃ _inst_16 _inst_19) _inst_8 (Prod.module.{u1, u4, u5} R N₂ N₃ _inst_1 _inst_16 _inst_19 _inst_17 _inst_20) (instContinuousAddSumInstTopologicalSpaceSumInstAddSum.{u4, u5} N₂ N₃ _inst_15 (AddSemigroup.toAdd.{u4} N₂ (AddMonoid.toAddSemigroup.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) _inst_33 _inst_18 (AddSemigroup.toAdd.{u5} N₃ (AddMonoid.toAddSemigroup.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) _inst_34)) (Prod.module.{u2, max u3 u4, max u3 u5} S (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17) (ContinuousLinearMap.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) _inst_4 (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₂ _inst_15 _inst_16 _inst_8 _inst_17 _inst_33) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20 _inst_34) (ContinuousLinearMap.module.{u1, u1, u2, u3, u4} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 N₂ _inst_15 _inst_16 _inst_17 _inst_24 _inst_26 _inst_25 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_33) (ContinuousLinearMap.module.{u1, u1, u2, u3, u5} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 N₃ _inst_18 _inst_19 _inst_20 _inst_27 _inst_28 _inst_29 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_34)) (ContinuousLinearMap.module.{u1, u1, u2, u3, max u4 u5} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 (Prod.{u4, u5} N₂ N₃) (instTopologicalSpaceProd.{u4, u5} N₂ N₃ _inst_15 _inst_18) (Prod.instAddCommMonoidSum.{u4, u5} N₂ N₃ _inst_16 _inst_19) (Prod.module.{u1, u4, u5} R N₂ N₃ _inst_1 _inst_16 _inst_19 _inst_17 _inst_20) (Prod.module.{u2, u4, u5} S N₂ N₃ _inst_4 _inst_16 _inst_19 _inst_24 _inst_27) (Prod.smulCommClass.{u1, u2, u4, u5} R S N₂ N₃ (MulAction.toSMul.{u1, u4} R N₂ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (DistribMulAction.toMulAction.{u1, u4} R N₂ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16) (Module.toDistribMulAction.{u1, u4} R N₂ _inst_1 _inst_16 _inst_17))) (MulAction.toSMul.{u1, u5} R N₃ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (DistribMulAction.toMulAction.{u1, u5} R N₃ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19) (Module.toDistribMulAction.{u1, u5} R N₃ _inst_1 _inst_19 _inst_20))) (MulAction.toSMul.{u2, u4} S N₂ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (DistribMulAction.toMulAction.{u2, u4} S N₂ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16) (Module.toDistribMulAction.{u2, u4} S N₂ _inst_4 _inst_16 _inst_24))) (MulAction.toSMul.{u2, u5} S N₃ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (DistribMulAction.toMulAction.{u2, u5} S N₃ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19) (Module.toDistribMulAction.{u2, u5} S N₃ _inst_4 _inst_19 _inst_27))) _inst_26 _inst_28) (instContinuousConstSMulProdInstTopologicalSpaceProdSmul.{u2, u4, u5} S N₂ N₃ _inst_15 (MulAction.toSMul.{u2, u4} S N₂ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (DistribMulAction.toMulAction.{u2, u4} S N₂ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16) (Module.toDistribMulAction.{u2, u4} S N₂ _inst_4 _inst_16 _inst_24))) _inst_25 _inst_18 (MulAction.toSMul.{u2, u5} S N₃ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (DistribMulAction.toMulAction.{u2, u5} S N₃ (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19) (Module.toDistribMulAction.{u2, u5} S N₃ _inst_4 _inst_19 _inst_27))) _inst_29) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (instContinuousAddSumInstTopologicalSpaceSumInstAddSum.{u4, u5} N₂ N₃ _inst_15 (AddSemigroup.toAdd.{u4} N₂ (AddMonoid.toAddSemigroup.{u4} N₂ (AddCommMonoid.toAddMonoid.{u4} N₂ _inst_16))) _inst_33 _inst_18 (AddSemigroup.toAdd.{u5} N₃ (AddMonoid.toAddSemigroup.{u5} N₃ (AddCommMonoid.toAddMonoid.{u5} N₃ _inst_19))) _inst_34))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.prodₗ ContinuousLinearMap.prodₗₓ'. -/
/-- `continuous_linear_map.prod` as a `linear_equiv`. -/
@[simps apply]
def prodₗ : ((M →L[R] N₂) × (M →L[R] N₃)) ≃ₗ[S] M →L[R] N₂ × N₃ :=
@@ -1675,25 +2674,37 @@ def prodₗ : ((M →L[R] N₂) × (M →L[R] N₃)) ≃ₗ[S] M →L[R] N₂ ×
map_smul' := fun c f => rfl }
#align continuous_linear_map.prodₗ ContinuousLinearMap.prodₗ
+/- warning: continuous_linear_map.coe_lm -> ContinuousLinearMap.coeLM is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} (S : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_4 : Semiring.{u2} S] {M : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : AddCommMonoid.{u3} M] [_inst_8 : Module.{u1, u3} R M _inst_1 _inst_7] {N₃ : Type.{u4}} [_inst_18 : TopologicalSpace.{u4} N₃] [_inst_19 : AddCommMonoid.{u4} N₃] [_inst_20 : Module.{u1, u4} R N₃ _inst_1 _inst_19] [_inst_27 : Module.{u2, u4} S N₃ _inst_4 _inst_19] [_inst_28 : SMulCommClass.{u1, u2, u4} R S N₃ (SMulZeroClass.toHasSmul.{u1, u4} R N₃ (AddZeroClass.toHasZero.{u4} N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19))) (SMulWithZero.toSmulZeroClass.{u1, u4} R N₃ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u4} N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19))) (MulActionWithZero.toSMulWithZero.{u1, u4} R N₃ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u4} N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19))) (Module.toMulActionWithZero.{u1, u4} R N₃ _inst_1 _inst_19 _inst_20)))) (SMulZeroClass.toHasSmul.{u2, u4} S N₃ (AddZeroClass.toHasZero.{u4} N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19))) (SMulWithZero.toSmulZeroClass.{u2, u4} S N₃ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)))) (AddZeroClass.toHasZero.{u4} N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19))) (MulActionWithZero.toSMulWithZero.{u2, u4} S N₃ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddZeroClass.toHasZero.{u4} N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19))) (Module.toMulActionWithZero.{u2, u4} S N₃ _inst_4 _inst_19 _inst_27))))] [_inst_29 : ContinuousConstSMul.{u2, u4} S N₃ _inst_18 (SMulZeroClass.toHasSmul.{u2, u4} S N₃ (AddZeroClass.toHasZero.{u4} N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19))) (SMulWithZero.toSmulZeroClass.{u2, u4} S N₃ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)))) (AddZeroClass.toHasZero.{u4} N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19))) (MulActionWithZero.toSMulWithZero.{u2, u4} S N₃ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddZeroClass.toHasZero.{u4} N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19))) (Module.toMulActionWithZero.{u2, u4} S N₃ _inst_4 _inst_19 _inst_27))))] [_inst_34 : ContinuousAdd.{u4} N₃ _inst_18 (AddZeroClass.toHasAdd.{u4} N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)))], LinearMap.{u2, u2, max u3 u4, max u3 u4} S S _inst_4 _inst_4 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_4)) (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) (LinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N₃ _inst_7 _inst_19 _inst_8 _inst_20) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20 _inst_34) (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R M N₃ _inst_1 _inst_1 _inst_7 _inst_19 _inst_8 _inst_20 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (ContinuousLinearMap.module.{u1, u1, u2, u3, u4} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 N₃ _inst_18 _inst_19 _inst_20 _inst_27 _inst_28 _inst_29 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_34) (LinearMap.module.{u1, u1, u2, u3, u4} R R S M N₃ _inst_1 _inst_1 _inst_7 _inst_19 _inst_8 _inst_20 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_4 _inst_27 _inst_28)
+but is expected to have type
+ forall {R : Type.{u1}} (S : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_4 : Semiring.{u2} S] {M : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : AddCommMonoid.{u3} M] [_inst_8 : Module.{u1, u3} R M _inst_1 _inst_7] {N₃ : Type.{u4}} [_inst_18 : TopologicalSpace.{u4} N₃] [_inst_19 : AddCommMonoid.{u4} N₃] [_inst_20 : Module.{u1, u4} R N₃ _inst_1 _inst_19] [_inst_27 : Module.{u2, u4} S N₃ _inst_4 _inst_19] [_inst_28 : SMulCommClass.{u1, u2, u4} R S N₃ (SMulZeroClass.toSMul.{u1, u4} R N₃ (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (SMulWithZero.toSMulZeroClass.{u1, u4} R N₃ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (MulActionWithZero.toSMulWithZero.{u1, u4} R N₃ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (Module.toMulActionWithZero.{u1, u4} R N₃ _inst_1 _inst_19 _inst_20)))) (SMulZeroClass.toSMul.{u2, u4} S N₃ (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (SMulWithZero.toSMulZeroClass.{u2, u4} S N₃ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (MulActionWithZero.toSMulWithZero.{u2, u4} S N₃ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (Module.toMulActionWithZero.{u2, u4} S N₃ _inst_4 _inst_19 _inst_27))))] [_inst_29 : ContinuousConstSMul.{u2, u4} S N₃ _inst_18 (SMulZeroClass.toSMul.{u2, u4} S N₃ (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (SMulWithZero.toSMulZeroClass.{u2, u4} S N₃ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_4)) (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (MulActionWithZero.toSMulWithZero.{u2, u4} S N₃ (Semiring.toMonoidWithZero.{u2} S _inst_4) (AddMonoid.toZero.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)) (Module.toMulActionWithZero.{u2, u4} S N₃ _inst_4 _inst_19 _inst_27))))] [_inst_34 : ContinuousAdd.{u4} N₃ _inst_18 (AddZeroClass.toAdd.{u4} N₃ (AddMonoid.toAddZeroClass.{u4} N₃ (AddCommMonoid.toAddMonoid.{u4} N₃ _inst_19)))], LinearMap.{u2, u2, max u4 u3, max u4 u3} S S _inst_4 _inst_4 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_4)) (ContinuousLinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20) (LinearMap.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N₃ _inst_7 _inst_19 _inst_8 _inst_20) (ContinuousLinearMap.addCommMonoid.{u1, u1, u3, u4} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_6 _inst_7 N₃ _inst_18 _inst_19 _inst_8 _inst_20 _inst_34) (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R M N₃ _inst_1 _inst_1 _inst_7 _inst_19 _inst_8 _inst_20 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (ContinuousLinearMap.module.{u1, u1, u2, u3, u4} R R S _inst_1 _inst_1 _inst_4 M _inst_6 _inst_7 _inst_8 N₃ _inst_18 _inst_19 _inst_20 _inst_27 _inst_28 _inst_29 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_34) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u2, u3, u4} R R S M N₃ _inst_1 _inst_1 _inst_7 _inst_19 _inst_8 _inst_20 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_4 _inst_27 _inst_28)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_lm ContinuousLinearMap.coeLMₓ'. -/
/-- The coercion from `M →L[R] M₂` to `M →ₗ[R] M₂`, as a linear map. -/
@[simps]
-def coeLm : (M →L[R] N₃) →ₗ[S] M →ₗ[R] N₃
+def coeLM : (M →L[R] N₃) →ₗ[S] M →ₗ[R] N₃
where
toFun := coe
map_add' f g := coe_add f g
map_smul' c f := coe_smul c f
-#align continuous_linear_map.coe_lm ContinuousLinearMap.coeLm
+#align continuous_linear_map.coe_lm ContinuousLinearMap.coeLM
variable {S} (σ₁₃)
+/- warning: continuous_linear_map.coe_lmₛₗ -> ContinuousLinearMap.coeLMₛₗ is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {R₃ : Type.{u2}} {S₃ : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_3 : Semiring.{u2} R₃] [_inst_5 : Semiring.{u3} S₃] {M : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M] [_inst_7 : AddCommMonoid.{u4} M] [_inst_8 : Module.{u1, u4} R M _inst_1 _inst_7] {M₃ : Type.{u5}} [_inst_12 : TopologicalSpace.{u5} M₃] [_inst_13 : AddCommMonoid.{u5} M₃] [_inst_14 : Module.{u2, u5} R₃ M₃ _inst_3 _inst_13] [_inst_21 : Module.{u3, u5} S₃ M₃ _inst_5 _inst_13] [_inst_22 : SMulCommClass.{u2, u3, u5} R₃ S₃ M₃ (SMulZeroClass.toHasSmul.{u2, u5} R₃ M₃ (AddZeroClass.toHasZero.{u5} M₃ (AddMonoid.toAddZeroClass.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13))) (SMulWithZero.toSmulZeroClass.{u2, u5} R₃ M₃ (MulZeroClass.toHasZero.{u2} R₃ (MulZeroOneClass.toMulZeroClass.{u2} R₃ (MonoidWithZero.toMulZeroOneClass.{u2} R₃ (Semiring.toMonoidWithZero.{u2} R₃ _inst_3)))) (AddZeroClass.toHasZero.{u5} M₃ (AddMonoid.toAddZeroClass.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13))) (MulActionWithZero.toSMulWithZero.{u2, u5} R₃ M₃ (Semiring.toMonoidWithZero.{u2} R₃ _inst_3) (AddZeroClass.toHasZero.{u5} M₃ (AddMonoid.toAddZeroClass.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13))) (Module.toMulActionWithZero.{u2, u5} R₃ M₃ _inst_3 _inst_13 _inst_14)))) (SMulZeroClass.toHasSmul.{u3, u5} S₃ M₃ (AddZeroClass.toHasZero.{u5} M₃ (AddMonoid.toAddZeroClass.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13))) (SMulWithZero.toSmulZeroClass.{u3, u5} S₃ M₃ (MulZeroClass.toHasZero.{u3} S₃ (MulZeroOneClass.toMulZeroClass.{u3} S₃ (MonoidWithZero.toMulZeroOneClass.{u3} S₃ (Semiring.toMonoidWithZero.{u3} S₃ _inst_5)))) (AddZeroClass.toHasZero.{u5} M₃ (AddMonoid.toAddZeroClass.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13))) (MulActionWithZero.toSMulWithZero.{u3, u5} S₃ M₃ (Semiring.toMonoidWithZero.{u3} S₃ _inst_5) (AddZeroClass.toHasZero.{u5} M₃ (AddMonoid.toAddZeroClass.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13))) (Module.toMulActionWithZero.{u3, u5} S₃ M₃ _inst_5 _inst_13 _inst_21))))] [_inst_23 : ContinuousConstSMul.{u3, u5} S₃ M₃ _inst_12 (SMulZeroClass.toHasSmul.{u3, u5} S₃ M₃ (AddZeroClass.toHasZero.{u5} M₃ (AddMonoid.toAddZeroClass.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13))) (SMulWithZero.toSmulZeroClass.{u3, u5} S₃ M₃ (MulZeroClass.toHasZero.{u3} S₃ (MulZeroOneClass.toMulZeroClass.{u3} S₃ (MonoidWithZero.toMulZeroOneClass.{u3} S₃ (Semiring.toMonoidWithZero.{u3} S₃ _inst_5)))) (AddZeroClass.toHasZero.{u5} M₃ (AddMonoid.toAddZeroClass.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13))) (MulActionWithZero.toSMulWithZero.{u3, u5} S₃ M₃ (Semiring.toMonoidWithZero.{u3} S₃ _inst_5) (AddZeroClass.toHasZero.{u5} M₃ (AddMonoid.toAddZeroClass.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13))) (Module.toMulActionWithZero.{u3, u5} S₃ M₃ _inst_5 _inst_13 _inst_21))))] (σ₁₃ : RingHom.{u1, u2} R R₃ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₃ _inst_3)) [_inst_32 : ContinuousAdd.{u5} M₃ _inst_12 (AddZeroClass.toHasAdd.{u5} M₃ (AddMonoid.toAddZeroClass.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13)))], LinearMap.{u3, u3, max u4 u5, max u4 u5} S₃ S₃ _inst_5 _inst_5 (RingHom.id.{u3} S₃ (Semiring.toNonAssocSemiring.{u3} S₃ _inst_5)) (ContinuousLinearMap.{u1, u2, u4, u5} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (LinearMap.{u1, u2, u4, u5} R R₃ _inst_1 _inst_3 σ₁₃ M M₃ _inst_7 _inst_13 _inst_8 _inst_14) (ContinuousLinearMap.addCommMonoid.{u1, u2, u4, u5} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14 _inst_32) (LinearMap.addCommMonoid.{u1, u2, u4, u5} R R₃ M M₃ _inst_1 _inst_3 _inst_7 _inst_13 _inst_8 _inst_14 σ₁₃) (ContinuousLinearMap.module.{u1, u2, u3, u4, u5} R R₃ S₃ _inst_1 _inst_3 _inst_5 M _inst_6 _inst_7 _inst_8 M₃ _inst_12 _inst_13 _inst_14 _inst_21 _inst_22 _inst_23 σ₁₃ _inst_32) (LinearMap.module.{u1, u2, u3, u4, u5} R R₃ S₃ M M₃ _inst_1 _inst_3 _inst_7 _inst_13 _inst_8 _inst_14 σ₁₃ _inst_5 _inst_21 _inst_22)
+but is expected to have type
+ forall {R : Type.{u1}} {R₃ : Type.{u2}} {S₃ : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_3 : Semiring.{u2} R₃] [_inst_5 : Semiring.{u3} S₃] {M : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M] [_inst_7 : AddCommMonoid.{u4} M] [_inst_8 : Module.{u1, u4} R M _inst_1 _inst_7] {M₃ : Type.{u5}} [_inst_12 : TopologicalSpace.{u5} M₃] [_inst_13 : AddCommMonoid.{u5} M₃] [_inst_14 : Module.{u2, u5} R₃ M₃ _inst_3 _inst_13] [_inst_21 : Module.{u3, u5} S₃ M₃ _inst_5 _inst_13] [_inst_22 : SMulCommClass.{u2, u3, u5} R₃ S₃ M₃ (SMulZeroClass.toSMul.{u2, u5} R₃ M₃ (AddMonoid.toZero.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13)) (SMulWithZero.toSMulZeroClass.{u2, u5} R₃ M₃ (MonoidWithZero.toZero.{u2} R₃ (Semiring.toMonoidWithZero.{u2} R₃ _inst_3)) (AddMonoid.toZero.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13)) (MulActionWithZero.toSMulWithZero.{u2, u5} R₃ M₃ (Semiring.toMonoidWithZero.{u2} R₃ _inst_3) (AddMonoid.toZero.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13)) (Module.toMulActionWithZero.{u2, u5} R₃ M₃ _inst_3 _inst_13 _inst_14)))) (SMulZeroClass.toSMul.{u3, u5} S₃ M₃ (AddMonoid.toZero.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13)) (SMulWithZero.toSMulZeroClass.{u3, u5} S₃ M₃ (MonoidWithZero.toZero.{u3} S₃ (Semiring.toMonoidWithZero.{u3} S₃ _inst_5)) (AddMonoid.toZero.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13)) (MulActionWithZero.toSMulWithZero.{u3, u5} S₃ M₃ (Semiring.toMonoidWithZero.{u3} S₃ _inst_5) (AddMonoid.toZero.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13)) (Module.toMulActionWithZero.{u3, u5} S₃ M₃ _inst_5 _inst_13 _inst_21))))] [_inst_23 : ContinuousConstSMul.{u3, u5} S₃ M₃ _inst_12 (SMulZeroClass.toSMul.{u3, u5} S₃ M₃ (AddMonoid.toZero.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13)) (SMulWithZero.toSMulZeroClass.{u3, u5} S₃ M₃ (MonoidWithZero.toZero.{u3} S₃ (Semiring.toMonoidWithZero.{u3} S₃ _inst_5)) (AddMonoid.toZero.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13)) (MulActionWithZero.toSMulWithZero.{u3, u5} S₃ M₃ (Semiring.toMonoidWithZero.{u3} S₃ _inst_5) (AddMonoid.toZero.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13)) (Module.toMulActionWithZero.{u3, u5} S₃ M₃ _inst_5 _inst_13 _inst_21))))] (σ₁₃ : RingHom.{u1, u2} R R₃ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₃ _inst_3)) [_inst_32 : ContinuousAdd.{u5} M₃ _inst_12 (AddZeroClass.toAdd.{u5} M₃ (AddMonoid.toAddZeroClass.{u5} M₃ (AddCommMonoid.toAddMonoid.{u5} M₃ _inst_13)))], LinearMap.{u3, u3, max u5 u4, max u5 u4} S₃ S₃ _inst_5 _inst_5 (RingHom.id.{u3} S₃ (Semiring.toNonAssocSemiring.{u3} S₃ _inst_5)) (ContinuousLinearMap.{u1, u2, u4, u5} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14) (LinearMap.{u1, u2, u4, u5} R R₃ _inst_1 _inst_3 σ₁₃ M M₃ _inst_7 _inst_13 _inst_8 _inst_14) (ContinuousLinearMap.addCommMonoid.{u1, u2, u4, u5} R R₃ _inst_1 _inst_3 σ₁₃ M _inst_6 _inst_7 M₃ _inst_12 _inst_13 _inst_8 _inst_14 _inst_32) (LinearMap.addCommMonoid.{u1, u2, u4, u5} R R₃ M M₃ _inst_1 _inst_3 _inst_7 _inst_13 _inst_8 _inst_14 σ₁₃) (ContinuousLinearMap.module.{u1, u2, u3, u4, u5} R R₃ S₃ _inst_1 _inst_3 _inst_5 M _inst_6 _inst_7 _inst_8 M₃ _inst_12 _inst_13 _inst_14 _inst_21 _inst_22 _inst_23 σ₁₃ _inst_32) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u2, u3, u4, u5} R R₃ S₃ M M₃ _inst_1 _inst_3 _inst_7 _inst_13 _inst_8 _inst_14 σ₁₃ _inst_5 _inst_21 _inst_22)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_lmₛₗ ContinuousLinearMap.coeLMₛₗₓ'. -/
/-- The coercion from `M →SL[σ] M₂` to `M →ₛₗ[σ] M₂`, as a linear map. -/
@[simps]
-def coeLmₛₗ : (M →SL[σ₁₃] M₃) →ₗ[S₃] M →ₛₗ[σ₁₃] M₃
+def coeLMₛₗ : (M →SL[σ₁₃] M₃) →ₗ[S₃] M →ₛₗ[σ₁₃] M₃
where
toFun := coe
map_add' f g := coe_add f g
map_smul' c f := coe_smul c f
-#align continuous_linear_map.coe_lmₛₗ ContinuousLinearMap.coeLmₛₗ
+#align continuous_linear_map.coe_lmₛₗ ContinuousLinearMap.coeLMₛₗ
variable {σ₁₃}
@@ -1707,6 +2718,12 @@ variable {R S T M M₂ : Type _} [Semiring R] [Semiring S] [Semiring T] [Module
[ContinuousAdd M₂] [Module T M₂] [ContinuousConstSMul T M₂] [SMulCommClass R T M₂]
[SMulCommClass S T M₂]
+/- warning: continuous_linear_map.smul_rightₗ -> ContinuousLinearMap.smulRightₗ is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} {M : Type.{u4}} {M₂ : Type.{u5}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : Semiring.{u3} T] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : AddCommMonoid.{u5} M₂] [_inst_6 : Module.{u1, u5} R M₂ _inst_1 _inst_5] [_inst_7 : Module.{u2, u5} S M₂ _inst_2 _inst_5] [_inst_8 : IsScalarTower.{u1, u2, u5} R S M₂ (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u5} S M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u2, u5} S M₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u5} R M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u1, u5} R M₂ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u1, u5} R M₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u1, u5} R M₂ _inst_1 _inst_5 _inst_6))))] [_inst_9 : TopologicalSpace.{u2} S] [_inst_10 : TopologicalSpace.{u5} M₂] [_inst_11 : ContinuousSMul.{u2, u5} S M₂ (SMulZeroClass.toHasSmul.{u2, u5} S M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u2, u5} S M₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) _inst_9 _inst_10] [_inst_12 : TopologicalSpace.{u4} M] [_inst_13 : AddCommMonoid.{u4} M] [_inst_14 : Module.{u1, u4} R M _inst_1 _inst_13] [_inst_15 : ContinuousAdd.{u5} M₂ _inst_10 (AddZeroClass.toHasAdd.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)))] [_inst_16 : Module.{u3, u5} T M₂ _inst_3 _inst_5] [_inst_17 : ContinuousConstSMul.{u3, u5} T M₂ _inst_10 (SMulZeroClass.toHasSmul.{u3, u5} T M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u3, u5} T M₂ (MulZeroClass.toHasZero.{u3} T (MulZeroOneClass.toMulZeroClass.{u3} T (MonoidWithZero.toMulZeroOneClass.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_18 : SMulCommClass.{u1, u3, u5} R T M₂ (SMulZeroClass.toHasSmul.{u1, u5} R M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u1, u5} R M₂ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u1, u5} R M₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u1, u5} R M₂ _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u3, u5} T M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u3, u5} T M₂ (MulZeroClass.toHasZero.{u3} T (MulZeroOneClass.toMulZeroClass.{u3} T (MonoidWithZero.toMulZeroOneClass.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_19 : SMulCommClass.{u2, u3, u5} S T M₂ (SMulZeroClass.toHasSmul.{u2, u5} S M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u2, u5} S M₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toHasSmul.{u3, u5} T M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u3, u5} T M₂ (MulZeroClass.toHasZero.{u3} T (MulZeroOneClass.toMulZeroClass.{u3} T (MonoidWithZero.toMulZeroOneClass.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))], (ContinuousLinearMap.{u1, u1, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 S _inst_9 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_14 _inst_4) -> (LinearMap.{u3, u3, u5, max u4 u5} T T _inst_3 _inst_3 (RingHom.id.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3)) M₂ (ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_5 (ContinuousLinearMap.addCommMonoid.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u1, u1, u3, u4, u5} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_15))
+but is expected to have type
+ forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} {M : Type.{u4}} {M₂ : Type.{u5}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : Semiring.{u3} T] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : AddCommMonoid.{u5} M₂] [_inst_6 : Module.{u1, u5} R M₂ _inst_1 _inst_5] [_inst_7 : Module.{u2, u5} S M₂ _inst_2 _inst_5] [_inst_8 : IsScalarTower.{u1, u2, u5} R S M₂ (SMulZeroClass.toSMul.{u1, u2} R S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R S (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toSMul.{u2, u5} S M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u2, u5} S M₂ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toSMul.{u1, u5} R M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u5} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u5} R M₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (Module.toMulActionWithZero.{u1, u5} R M₂ _inst_1 _inst_5 _inst_6))))] [_inst_9 : TopologicalSpace.{u2} S] [_inst_10 : TopologicalSpace.{u5} M₂] [_inst_11 : ContinuousSMul.{u2, u5} S M₂ (SMulZeroClass.toSMul.{u2, u5} S M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u2, u5} S M₂ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) _inst_9 _inst_10] [_inst_12 : TopologicalSpace.{u4} M] [_inst_13 : AddCommMonoid.{u4} M] [_inst_14 : Module.{u1, u4} R M _inst_1 _inst_13] [_inst_15 : ContinuousAdd.{u5} M₂ _inst_10 (AddZeroClass.toAdd.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)))] [_inst_16 : Module.{u3, u5} T M₂ _inst_3 _inst_5] [_inst_17 : ContinuousConstSMul.{u3, u5} T M₂ _inst_10 (SMulZeroClass.toSMul.{u3, u5} T M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u5} T M₂ (MonoidWithZero.toZero.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_18 : SMulCommClass.{u1, u3, u5} R T M₂ (SMulZeroClass.toSMul.{u1, u5} R M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u5} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u5} R M₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (Module.toMulActionWithZero.{u1, u5} R M₂ _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u3, u5} T M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u5} T M₂ (MonoidWithZero.toZero.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_19 : SMulCommClass.{u2, u3, u5} S T M₂ (SMulZeroClass.toSMul.{u2, u5} S M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u2, u5} S M₂ (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toSMul.{u3, u5} T M₂ (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u5} T M₂ (MonoidWithZero.toZero.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddMonoid.toZero.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))], (ContinuousLinearMap.{u1, u1, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 S _inst_9 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_14 _inst_4) -> (LinearMap.{u3, u3, u5, max u5 u4} T T _inst_3 _inst_3 (RingHom.id.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3)) M₂ (ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_5 (ContinuousLinearMap.addCommMonoid.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u1, u1, u3, u4, u5} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_15))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.smul_rightₗ ContinuousLinearMap.smulRightₗₓ'. -/
/-- Given `c : E →L[𝕜] 𝕜`, `c.smul_rightₗ` is the linear map from `F` to `E →L[𝕜] F`
sending `f` to `λ e, c e • f`. See also `continuous_linear_map.smul_rightL`. -/
def smulRightₗ (c : M →L[R] S) : M₂ →ₗ[T] M →L[R] M₂
@@ -1721,6 +2738,12 @@ def smulRightₗ (c : M →L[R] S) : M₂ →ₗ[T] M →L[R] M₂
apply smul_comm
#align continuous_linear_map.smul_rightₗ ContinuousLinearMap.smulRightₗ
+/- warning: continuous_linear_map.coe_smul_rightₗ -> ContinuousLinearMap.coe_smulRightₗ is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} {M : Type.{u4}} {M₂ : Type.{u5}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : Semiring.{u3} T] [_inst_4 : Module.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))] [_inst_5 : AddCommMonoid.{u5} M₂] [_inst_6 : Module.{u1, u5} R M₂ _inst_1 _inst_5] [_inst_7 : Module.{u2, u5} S M₂ _inst_2 _inst_5] [_inst_8 : IsScalarTower.{u1, u2, u5} R S M₂ (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_4)))) (SMulZeroClass.toHasSmul.{u2, u5} S M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u2, u5} S M₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u5} R M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u1, u5} R M₂ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u1, u5} R M₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u1, u5} R M₂ _inst_1 _inst_5 _inst_6))))] [_inst_9 : TopologicalSpace.{u2} S] [_inst_10 : TopologicalSpace.{u5} M₂] [_inst_11 : ContinuousSMul.{u2, u5} S M₂ (SMulZeroClass.toHasSmul.{u2, u5} S M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u2, u5} S M₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) _inst_9 _inst_10] [_inst_12 : TopologicalSpace.{u4} M] [_inst_13 : AddCommMonoid.{u4} M] [_inst_14 : Module.{u1, u4} R M _inst_1 _inst_13] [_inst_15 : ContinuousAdd.{u5} M₂ _inst_10 (AddZeroClass.toHasAdd.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5)))] [_inst_16 : Module.{u3, u5} T M₂ _inst_3 _inst_5] [_inst_17 : ContinuousConstSMul.{u3, u5} T M₂ _inst_10 (SMulZeroClass.toHasSmul.{u3, u5} T M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u3, u5} T M₂ (MulZeroClass.toHasZero.{u3} T (MulZeroOneClass.toMulZeroClass.{u3} T (MonoidWithZero.toMulZeroOneClass.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_18 : SMulCommClass.{u1, u3, u5} R T M₂ (SMulZeroClass.toHasSmul.{u1, u5} R M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u1, u5} R M₂ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u1, u5} R M₂ (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u1, u5} R M₂ _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toHasSmul.{u3, u5} T M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u3, u5} T M₂ (MulZeroClass.toHasZero.{u3} T (MulZeroOneClass.toMulZeroClass.{u3} T (MonoidWithZero.toMulZeroOneClass.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_19 : SMulCommClass.{u2, u3, u5} S T M₂ (SMulZeroClass.toHasSmul.{u2, u5} S M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u2, u5} S M₂ (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u2, u5} S M₂ (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u2, u5} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toHasSmul.{u3, u5} T M₂ (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (SMulWithZero.toSmulZeroClass.{u3, u5} T M₂ (MulZeroClass.toHasZero.{u3} T (MulZeroOneClass.toMulZeroClass.{u3} T (MonoidWithZero.toMulZeroOneClass.{u3} T (Semiring.toMonoidWithZero.{u3} T _inst_3)))) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (MulActionWithZero.toSMulWithZero.{u3, u5} T M₂ (Semiring.toMonoidWithZero.{u3} T _inst_3) (AddZeroClass.toHasZero.{u5} M₂ (AddMonoid.toAddZeroClass.{u5} M₂ (AddCommMonoid.toAddMonoid.{u5} M₂ _inst_5))) (Module.toMulActionWithZero.{u3, u5} T M₂ _inst_3 _inst_5 _inst_16))))] (c : ContinuousLinearMap.{u1, u1, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 S _inst_9 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) _inst_14 _inst_4), Eq.{max (succ u5) (succ (max u4 u5))} (M₂ -> (ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6)) (coeFn.{max (succ u5) (succ (max u4 u5)), max (succ u5) (succ (max u4 u5))} (LinearMap.{u3, u3, u5, max u4 u5} T T _inst_3 _inst_3 (RingHom.id.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3)) M₂ (ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_5 (ContinuousLinearMap.addCommMonoid.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u1, u1, u3, u4, u5} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_15)) (fun (_x : LinearMap.{u3, u3, u5, max u4 u5} T T _inst_3 _inst_3 (RingHom.id.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3)) M₂ (ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_5 (ContinuousLinearMap.addCommMonoid.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u1, u1, u3, u4, u5} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_15)) => M₂ -> (ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6)) (LinearMap.hasCoeToFun.{u3, u3, u5, max u4 u5} T T M₂ (ContinuousLinearMap.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_3 _inst_3 _inst_5 (ContinuousLinearMap.addCommMonoid.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u1, u1, u3, u4, u5} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) _inst_15) (RingHom.id.{u3} T (Semiring.toNonAssocSemiring.{u3} T _inst_3))) (ContinuousLinearMap.smulRightₗ.{u1, u2, u3, u4, u5} R S T M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 _inst_19 c)) (ContinuousLinearMap.smulRight.{u4, u5, u1, u2} M _inst_12 _inst_13 M₂ _inst_10 _inst_5 R S _inst_1 _inst_2 _inst_14 _inst_6 _inst_4 _inst_7 _inst_8 _inst_9 _inst_11 c)
+but is expected to have type
+ forall {R : Type.{u5}} {S : Type.{u3}} {T : Type.{u1}} {M : Type.{u4}} {M₂ : Type.{u2}} [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u3} S] [_inst_3 : Semiring.{u1} T] [_inst_4 : Module.{u5, u3} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2)))] [_inst_5 : AddCommMonoid.{u2} M₂] [_inst_6 : Module.{u5, u2} R M₂ _inst_1 _inst_5] [_inst_7 : Module.{u3, u2} S M₂ _inst_2 _inst_5] [_inst_8 : IsScalarTower.{u5, u3, u2} R S M₂ (SMulZeroClass.toSMul.{u5, u3} R S (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (SMulWithZero.toSMulZeroClass.{u5, u3} R S (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (MulActionWithZero.toSMulWithZero.{u5, u3} R S (Semiring.toMonoidWithZero.{u5} R _inst_1) (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (Module.toMulActionWithZero.{u5, u3} R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2))) _inst_4)))) (SMulZeroClass.toSMul.{u3, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u2} S M₂ (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u2} S M₂ (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u2} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toSMul.{u5, u2} R M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R M₂ (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R M₂ (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u5, u2} R M₂ _inst_1 _inst_5 _inst_6))))] [_inst_9 : TopologicalSpace.{u3} S] [_inst_10 : TopologicalSpace.{u2} M₂] [_inst_11 : ContinuousSMul.{u3, u2} S M₂ (SMulZeroClass.toSMul.{u3, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u2} S M₂ (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u2} S M₂ (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u2} S M₂ _inst_2 _inst_5 _inst_7)))) _inst_9 _inst_10] [_inst_12 : TopologicalSpace.{u4} M] [_inst_13 : AddCommMonoid.{u4} M] [_inst_14 : Module.{u5, u4} R M _inst_1 _inst_13] [_inst_15 : ContinuousAdd.{u2} M₂ _inst_10 (AddZeroClass.toAdd.{u2} M₂ (AddMonoid.toAddZeroClass.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)))] [_inst_16 : Module.{u1, u2} T M₂ _inst_3 _inst_5] [_inst_17 : ContinuousConstSMul.{u1, u2} T M₂ _inst_10 (SMulZeroClass.toSMul.{u1, u2} T M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} T M₂ (MonoidWithZero.toZero.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} T M₂ (Semiring.toMonoidWithZero.{u1} T _inst_3) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u1, u2} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_18 : SMulCommClass.{u5, u1, u2} R T M₂ (SMulZeroClass.toSMul.{u5, u2} R M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u5, u2} R M₂ (MonoidWithZero.toZero.{u5} R (Semiring.toMonoidWithZero.{u5} R _inst_1)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u5, u2} R M₂ (Semiring.toMonoidWithZero.{u5} R _inst_1) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u5, u2} R M₂ _inst_1 _inst_5 _inst_6)))) (SMulZeroClass.toSMul.{u1, u2} T M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} T M₂ (MonoidWithZero.toZero.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} T M₂ (Semiring.toMonoidWithZero.{u1} T _inst_3) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u1, u2} T M₂ _inst_3 _inst_5 _inst_16))))] [_inst_19 : SMulCommClass.{u3, u1, u2} S T M₂ (SMulZeroClass.toSMul.{u3, u2} S M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u2} S M₂ (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_2)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u2} S M₂ (Semiring.toMonoidWithZero.{u3} S _inst_2) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u3, u2} S M₂ _inst_2 _inst_5 _inst_7)))) (SMulZeroClass.toSMul.{u1, u2} T M₂ (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u2} T M₂ (MonoidWithZero.toZero.{u1} T (Semiring.toMonoidWithZero.{u1} T _inst_3)) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u2} T M₂ (Semiring.toMonoidWithZero.{u1} T _inst_3) (AddMonoid.toZero.{u2} M₂ (AddCommMonoid.toAddMonoid.{u2} M₂ _inst_5)) (Module.toMulActionWithZero.{u1, u2} T M₂ _inst_3 _inst_5 _inst_16))))] (c : ContinuousLinearMap.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 S _inst_9 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S _inst_2))) _inst_14 _inst_4), Eq.{max (succ u4) (succ u2)} (forall (ᾰ : M₂), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₂) => ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) ᾰ) (FunLike.coe.{max (succ u4) (succ u2), succ u2, max (succ u4) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u4} T T _inst_3 _inst_3 (RingHom.id.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3)) M₂ (ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_5 (ContinuousLinearMap.addCommMonoid.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u5, u5, u1, u4, u2} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_15)) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M₂) => ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u4 u2} T T M₂ (ContinuousLinearMap.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6) _inst_3 _inst_3 _inst_5 (ContinuousLinearMap.addCommMonoid.{u5, u5, u4, u2} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) M _inst_12 _inst_13 M₂ _inst_10 _inst_5 _inst_14 _inst_6 _inst_15) _inst_16 (ContinuousLinearMap.module.{u5, u5, u1, u4, u2} R R T _inst_1 _inst_1 _inst_3 M _inst_12 _inst_13 _inst_14 M₂ _inst_10 _inst_5 _inst_6 _inst_16 _inst_18 _inst_17 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) _inst_15) (RingHom.id.{u1} T (Semiring.toNonAssocSemiring.{u1} T _inst_3))) (ContinuousLinearMap.smulRightₗ.{u5, u3, u1, u4, u2} R S T M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17 _inst_18 _inst_19 c)) (ContinuousLinearMap.smulRight.{u4, u2, u5, u3} M _inst_12 _inst_13 M₂ _inst_10 _inst_5 R S _inst_1 _inst_2 _inst_14 _inst_6 _inst_4 _inst_7 _inst_8 _inst_9 _inst_11 c)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_smul_rightₗ ContinuousLinearMap.coe_smulRightₗₓ'. -/
@[simp]
theorem coe_smulRightₗ (c : M →L[R] S) : ⇑(smulRightₗ c : M₂ →ₗ[T] M →L[R] M₂) = c.smul_right :=
rfl
@@ -1747,26 +2770,46 @@ variable {A M M₂ : Type _} [Ring A] [AddCommGroup M] [AddCommGroup M₂] [Modu
[TopologicalSpace M] [TopologicalSpace M₂] (R : Type _) [Ring R] [Module R M] [Module R M₂]
[LinearMap.CompatibleSMul M M₂ R A]
+#print ContinuousLinearMap.restrictScalars /-
/-- If `A` is an `R`-algebra, then a continuous `A`-linear map can be interpreted as a continuous
`R`-linear map. We assume `linear_map.compatible_smul M M₂ R A` to match assumptions of
`linear_map.map_smul_of_tower`. -/
def restrictScalars (f : M →L[A] M₂) : M →L[R] M₂ :=
⟨(f : M →ₗ[A] M₂).restrictScalars R, f.Continuous⟩
#align continuous_linear_map.restrict_scalars ContinuousLinearMap.restrictScalars
+-/
variable {R}
+/- warning: continuous_linear_map.coe_restrict_scalars -> ContinuousLinearMap.coe_restrictScalars is a dubious translation:
+lean 3 declaration is
+ forall {A : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u4}} [_inst_8 : Ring.{u4} R] [_inst_9 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_10 : Module.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u2, u3, u4, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toHasSmul.{u4, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u4, u2} R M (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u4, u2} R M (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5] (f : ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A 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+but is expected to have type
+ forall {A : Type.{u4}} {M : Type.{u3}} {M₂ : Type.{u2}} [_inst_1 : Ring.{u4} A] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u2} M₂] [_inst_4 : Module.{u4, u3} A M (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_5 : Module.{u4, u2} A M₂ (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : TopologicalSpace.{u2} M₂] {R : Type.{u1}} [_inst_8 : Ring.{u1} R] [_inst_9 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_10 : Module.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u3, u2, u1, u4} M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) R A (Ring.toSemiring.{u4} A _inst_1) (SMulZeroClass.toSMul.{u1, u3} R M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (Module.toMulActionWithZero.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u1, u2} R M₂ (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_10)))) _inst_5] (f : ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u3) (succ u2)} (LinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.toLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10 (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f)) (LinearMap.restrictScalars.{u1, u4, u3, u2} R A M M₂ (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10 _inst_4 _inst_5 _inst_11 (ContinuousLinearMap.toLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5 f))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_restrict_scalars ContinuousLinearMap.coe_restrictScalarsₓ'. -/
@[simp, norm_cast]
theorem coe_restrictScalars (f : M →L[A] M₂) :
(f.restrictScalars R : M →ₗ[R] M₂) = (f : M →ₗ[A] M₂).restrictScalars R :=
rfl
#align continuous_linear_map.coe_restrict_scalars ContinuousLinearMap.coe_restrictScalars
+/- warning: continuous_linear_map.coe_restrict_scalars' -> ContinuousLinearMap.coe_restrictScalars' is a dubious translation:
+lean 3 declaration is
+ forall {A : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u4}} [_inst_8 : Ring.{u4} R] [_inst_9 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_10 : Module.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u2, u3, u4, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toHasSmul.{u4, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M 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+but is expected to have type
+ forall {A : Type.{u4}} {M : Type.{u3}} {M₂ : Type.{u2}} [_inst_1 : Ring.{u4} A] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u2} M₂] [_inst_4 : Module.{u4, u3} A M (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_5 : Module.{u4, u2} A M₂ (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : TopologicalSpace.{u2} M₂] {R : Type.{u1}} [_inst_8 : Ring.{u1} R] [_inst_9 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_10 : Module.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u3, u2, u1, u4} M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) R A (Ring.toSemiring.{u4} A _inst_1) (SMulZeroClass.toSMul.{u1, u3} R M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (Module.toMulActionWithZero.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u1, u2} R M₂ (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_10)))) _inst_5] (f : ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u3) (succ u2)} (forall (ᾰ : M), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 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_inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10))) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u3, u2} (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) M M₂ _inst_6 _inst_7 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u4, u4, u3, u2} (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5))) f)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_restrict_scalars' ContinuousLinearMap.coe_restrictScalars'ₓ'. -/
@[simp]
-theorem coe_restrict_scalars' (f : M →L[A] M₂) : ⇑(f.restrictScalars R) = f :=
+theorem coe_restrictScalars' (f : M →L[A] M₂) : ⇑(f.restrictScalars R) = f :=
rfl
-#align continuous_linear_map.coe_restrict_scalars' ContinuousLinearMap.coe_restrict_scalars'
-
+#align continuous_linear_map.coe_restrict_scalars' ContinuousLinearMap.coe_restrictScalars'
+
+/- warning: continuous_linear_map.restrict_scalars_zero -> ContinuousLinearMap.restrictScalars_zero is a dubious translation:
+lean 3 declaration is
+ forall {A : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u4}} [_inst_8 : Ring.{u4} R] [_inst_9 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_10 : Module.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u2, u3, u4, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toHasSmul.{u4, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u4, u2} R M (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u4, u2} R M (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ 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(AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) 0 (Zero.zero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.zero.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5))))) (OfNat.ofNat.{max u2 u3} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) 0 (OfNat.mk.{max u2 u3} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) 0 (Zero.zero.{max u2 u3} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.zero.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10))))
+but is expected to have type
+ forall {A : Type.{u1}} {M : Type.{u4}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u4} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u4} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u4} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u2}} [_inst_8 : Ring.{u2} R] [_inst_9 : Module.{u2, u4} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] [_inst_10 : Module.{u2, u3} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u4, u3, u2, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toSMul.{u2, u4} R M (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (Module.toMulActionWithZero.{u2, u4} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u2, u3} R M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u3} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u3} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5], Eq.{max (succ u4) (succ u3)} (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u1, u4, u3, u2} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (OfNat.ofNat.{max u4 u3} (ContinuousLinearMap.{u1, u1, u4, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) 0 (Zero.toOfNat0.{max u4 u3} (ContinuousLinearMap.{u1, u1, u4, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.zero.{u1, u1, u4, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5)))) (OfNat.ofNat.{max u4 u3} (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) 0 (Zero.toOfNat0.{max u4 u3} (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.zero.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10)))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.restrict_scalars_zero ContinuousLinearMap.restrictScalars_zeroₓ'. -/
@[simp]
theorem restrictScalars_zero : (0 : M →L[A] M₂).restrictScalars R = 0 :=
rfl
@@ -1776,12 +2819,24 @@ section
variable [TopologicalAddGroup M₂]
+/- warning: continuous_linear_map.restrict_scalars_add -> ContinuousLinearMap.restrictScalars_add is a dubious translation:
+lean 3 declaration is
+ forall {A : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u4}} [_inst_8 : Ring.{u4} R] [_inst_9 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_10 : Module.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u2, u3, u4, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toHasSmul.{u4, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u4, u2} R M (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u4, u2} R M (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5] [_inst_12 : TopologicalAddGroup.{u3} M₂ _inst_7 (AddCommGroup.toAddGroup.{u3} M₂ _inst_3)] (f : ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (g : ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.add.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5 (TopologicalAddGroup.to_continuousAdd.{u3} M₂ _inst_7 (AddCommGroup.toAddGroup.{u3} M₂ _inst_3) _inst_12))) f g)) (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.add.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10 (TopologicalAddGroup.to_continuousAdd.{u3} M₂ _inst_7 (AddCommGroup.toAddGroup.{u3} M₂ _inst_3) _inst_12))) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 g))
+but is expected to have type
+ forall {A : Type.{u4}} {M : Type.{u3}} {M₂ : Type.{u2}} [_inst_1 : Ring.{u4} A] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u2} M₂] [_inst_4 : Module.{u4, u3} A M (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_5 : Module.{u4, u2} A M₂ (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : TopologicalSpace.{u2} M₂] {R : Type.{u1}} [_inst_8 : Ring.{u1} R] [_inst_9 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_10 : Module.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u3, u2, u1, u4} M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) R A (Ring.toSemiring.{u4} A _inst_1) (SMulZeroClass.toSMul.{u1, u3} R M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (Module.toMulActionWithZero.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u1, u2} R M₂ (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_10)))) _inst_5] [_inst_12 : TopologicalAddGroup.{u2} M₂ _inst_7 (AddCommGroup.toAddGroup.{u2} M₂ _inst_3)] (f : ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) (g : ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (HAdd.hAdd.{max u3 u2, max u3 u2, max u3 u2} (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) (instHAdd.{max u3 u2} (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.add.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5 (TopologicalAddGroup.toContinuousAdd.{u2} M₂ _inst_7 (AddCommGroup.toAddGroup.{u2} M₂ _inst_3) _inst_12))) f g)) (HAdd.hAdd.{max u3 u2, max u3 u2, max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (instHAdd.{max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.add.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10 (TopologicalAddGroup.toContinuousAdd.{u2} M₂ _inst_7 (AddCommGroup.toAddGroup.{u2} M₂ _inst_3) _inst_12))) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 g))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.restrict_scalars_add ContinuousLinearMap.restrictScalars_addₓ'. -/
@[simp]
theorem restrictScalars_add (f g : M →L[A] M₂) :
(f + g).restrictScalars R = f.restrictScalars R + g.restrictScalars R :=
rfl
#align continuous_linear_map.restrict_scalars_add ContinuousLinearMap.restrictScalars_add
+/- warning: continuous_linear_map.restrict_scalars_neg -> ContinuousLinearMap.restrictScalars_neg is a dubious translation:
+lean 3 declaration is
+ forall {A : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u4}} [_inst_8 : Ring.{u4} R] [_inst_9 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_10 : Module.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u2, u3, u4, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toHasSmul.{u4, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u4, u2} R M (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u4, u2} R M (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5] [_inst_12 : TopologicalAddGroup.{u3} M₂ _inst_7 (AddCommGroup.toAddGroup.{u3} M₂ _inst_3)] (f : ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.neg.{u1, u1, u2, u3} A _inst_1 A _inst_1 M _inst_6 _inst_2 M₂ _inst_7 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) _inst_12) f)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.neg.{u4, u4, u2, u3} R _inst_8 R _inst_8 M _inst_6 _inst_2 M₂ _inst_7 _inst_3 _inst_9 _inst_10 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) _inst_12) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f))
+but is expected to have type
+ forall {A : Type.{u4}} {M : Type.{u3}} {M₂ : Type.{u2}} [_inst_1 : Ring.{u4} A] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u2} M₂] [_inst_4 : Module.{u4, u3} A M (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_5 : Module.{u4, u2} A M₂ (Ring.toSemiring.{u4} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u3} M] [_inst_7 : TopologicalSpace.{u2} M₂] {R : Type.{u1}} [_inst_8 : Ring.{u1} R] [_inst_9 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_10 : Module.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u3, u2, u1, u4} M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) R A (Ring.toSemiring.{u4} A _inst_1) (SMulZeroClass.toSMul.{u1, u3} R M (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u3} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (Module.toMulActionWithZero.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u1, u2} R M₂ (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M₂ (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8))) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M₂ (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_8)) (NegZeroClass.toZero.{u2} M₂ (SubNegZeroMonoid.toNegZeroClass.{u2} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u2} R M₂ (Ring.toSemiring.{u1} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_10)))) _inst_5] [_inst_12 : TopologicalAddGroup.{u2} M₂ _inst_7 (AddCommGroup.toAddGroup.{u2} M₂ _inst_3)] (f : ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (Neg.neg.{max u3 u2} (ContinuousLinearMap.{u4, u4, u3, u2} A A (Ring.toSemiring.{u4} A _inst_1) (Ring.toSemiring.{u4} A _inst_1) (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.neg.{u4, u4, u3, u2} A _inst_1 A _inst_1 M _inst_6 _inst_2 M₂ _inst_7 _inst_3 _inst_4 _inst_5 (RingHom.id.{u4} A (NonAssocRing.toNonAssocSemiring.{u4} A (Ring.toNonAssocRing.{u4} A _inst_1))) _inst_12) f)) (Neg.neg.{max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_8) (Ring.toSemiring.{u1} R _inst_8) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.neg.{u1, u1, u3, u2} R _inst_8 R _inst_8 M _inst_6 _inst_2 M₂ _inst_7 _inst_3 _inst_9 _inst_10 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_8))) _inst_12) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.restrict_scalars_neg ContinuousLinearMap.restrictScalars_negₓ'. -/
@[simp]
theorem restrictScalars_neg (f : M →L[A] M₂) : (-f).restrictScalars R = -f.restrictScalars R :=
rfl
@@ -1792,6 +2847,12 @@ end
variable {S : Type _} [Ring S] [Module S M₂] [ContinuousConstSMul S M₂] [SMulCommClass A S M₂]
[SMulCommClass R S M₂]
+/- warning: continuous_linear_map.restrict_scalars_smul -> ContinuousLinearMap.restrictScalars_smul is a dubious translation:
+lean 3 declaration is
+ forall {A : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u4}} [_inst_8 : Ring.{u4} R] [_inst_9 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_10 : Module.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u2, u3, u4, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toHasSmul.{u4, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u4, u2} R M (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u4, u2} R M (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5] {S : Type.{u5}} [_inst_12 : Ring.{u5} S] [_inst_13 : Module.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_14 : ContinuousConstSMul.{u5, u3} S M₂ _inst_7 (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_15 : SMulCommClass.{u1, u5, u3} A S M₂ (SMulZeroClass.toHasSmul.{u1, u3} A M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u1, u3} A M₂ (MulZeroClass.toHasZero.{u1} A (MulZeroOneClass.toMulZeroClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A _inst_1))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u1, u3} A M₂ (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A _inst_1)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_16 : SMulCommClass.{u4, u5, u3} R S M₂ (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] (c : S) (f : ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (SMul.smul.{u5, max u2 u3} S (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (MulAction.toHasSmul.{u5, max u2 u3} S (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (Ring.toMonoid.{u5} S _inst_12) (ContinuousLinearMap.mulAction.{u1, u1, u2, u3, u5} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5 S (Ring.toMonoid.{u5} S _inst_12) (Module.toDistribMulAction.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13) _inst_15 _inst_14)) c f)) (SMul.smul.{u5, max u2 u3} S (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (MulAction.toHasSmul.{u5, max u2 u3} S (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (Ring.toMonoid.{u5} S _inst_12) (ContinuousLinearMap.mulAction.{u4, u4, u2, u3, u5} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10 S (Ring.toMonoid.{u5} S _inst_12) (Module.toDistribMulAction.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13) _inst_16 _inst_14)) c (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f))
+but is expected to have type
+ forall {A : Type.{u5}} {M : Type.{u4}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u5} A] [_inst_2 : AddCommGroup.{u4} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u5, u4} A M (Ring.toSemiring.{u5} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] [_inst_5 : Module.{u5, u3} A M₂ (Ring.toSemiring.{u5} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u4} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u2}} [_inst_8 : Ring.{u2} R] [_inst_9 : Module.{u2, u4} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2)] [_inst_10 : Module.{u2, u3} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u4, u3, u2, u5} M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u5} A _inst_1) (SMulZeroClass.toSMul.{u2, u4} R M (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M (SubNegZeroMonoid.toNegZeroClass.{u4} M (SubtractionMonoid.toSubNegZeroMonoid.{u4} M (SubtractionCommMonoid.toSubtractionMonoid.{u4} M (AddCommGroup.toDivisionAddCommMonoid.{u4} M _inst_2))))) (Module.toMulActionWithZero.{u2, u4} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u2, u3} R M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u3} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u3} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5] {S : Type.{u1}} [_inst_12 : Ring.{u1} S] [_inst_13 : Module.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_14 : ContinuousConstSMul.{u1, u3} S M₂ _inst_7 (SMulZeroClass.toSMul.{u1, u3} S M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u3} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_15 : SMulCommClass.{u5, u1, u3} A S M₂ (SMulZeroClass.toSMul.{u5, u3} A M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u5, u3} A M₂ (MonoidWithZero.toZero.{u5} A (Semiring.toMonoidWithZero.{u5} A (Ring.toSemiring.{u5} A _inst_1))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u5, u3} A M₂ (Semiring.toMonoidWithZero.{u5} A (Ring.toSemiring.{u5} A _inst_1)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u5, u3} A M₂ (Ring.toSemiring.{u5} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} S M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u3} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_16 : SMulCommClass.{u2, u1, u3} R S M₂ (SMulZeroClass.toSMul.{u2, u3} R M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u3} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u3} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) (SMulZeroClass.toSMul.{u1, u3} S M₂ (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u3} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] (c : S) (f : ContinuousLinearMap.{u5, u5, u4, u3} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (NonAssocRing.toNonAssocSemiring.{u5} A (Ring.toNonAssocRing.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5), Eq.{max (succ u4) (succ u3)} (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.restrictScalars.{u5, u4, u3, u2} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 (HSMul.hSMul.{u1, max u3 u4, max u3 u4} S (ContinuousLinearMap.{u5, u5, u4, u3} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (NonAssocRing.toNonAssocSemiring.{u5} A (Ring.toNonAssocRing.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u5, u5, u4, u3} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (NonAssocRing.toNonAssocSemiring.{u5} A (Ring.toNonAssocRing.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (instHSMul.{u1, max u3 u4} S (ContinuousLinearMap.{u5, u5, u4, u3} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (NonAssocRing.toNonAssocSemiring.{u5} A (Ring.toNonAssocRing.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (MulAction.toSMul.{u1, max u3 u4} S (ContinuousLinearMap.{u5, u5, u4, u3} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (NonAssocRing.toNonAssocSemiring.{u5} A (Ring.toNonAssocRing.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (ContinuousLinearMap.mulAction.{u5, u5, u4, u3, u1} A A (Ring.toSemiring.{u5} A _inst_1) (Ring.toSemiring.{u5} A _inst_1) (RingHom.id.{u5} A (NonAssocRing.toNonAssocSemiring.{u5} A (Ring.toNonAssocRing.{u5} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5 S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (Module.toDistribMulAction.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13) _inst_15 _inst_14))) c f)) (HSMul.hSMul.{u1, max u3 u4, max u3 u4} S (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (instHSMul.{u1, max u3 u4} S (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (MulAction.toSMul.{u1, max u3 u4} S (ContinuousLinearMap.{u2, u2, u4, u3} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (ContinuousLinearMap.mulAction.{u2, u2, u4, u3, u1} R R (Ring.toSemiring.{u2} R _inst_8) (Ring.toSemiring.{u2} R _inst_8) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10 S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (Module.toDistribMulAction.{u1, u3} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13) _inst_16 _inst_14))) c (ContinuousLinearMap.restrictScalars.{u5, u4, u3, u2} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 f))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.restrict_scalars_smul ContinuousLinearMap.restrictScalars_smulₓ'. -/
@[simp]
theorem restrictScalars_smul (c : S) (f : M →L[A] M₂) :
(c • f).restrictScalars R = c • f.restrictScalars R :=
@@ -1800,6 +2861,7 @@ theorem restrictScalars_smul (c : S) (f : M →L[A] M₂) :
variable (A M M₂ R S) [TopologicalAddGroup M₂]
+#print ContinuousLinearMap.restrictScalarsₗ /-
/-- `continuous_linear_map.restrict_scalars` as a `linear_map`. See also
`continuous_linear_map.restrict_scalarsL`. -/
def restrictScalarsₗ : (M →L[A] M₂) →ₗ[S] M →L[R] M₂
@@ -1808,9 +2870,16 @@ def restrictScalarsₗ : (M →L[A] M₂) →ₗ[S] M →L[R] M₂
map_add' := restrictScalars_add
map_smul' := restrictScalars_smul
#align continuous_linear_map.restrict_scalarsₗ ContinuousLinearMap.restrictScalarsₗ
+-/
variable {A M M₂ R S}
+/- warning: continuous_linear_map.coe_restrict_scalarsₗ -> ContinuousLinearMap.coe_restrictScalarsₗ is a dubious translation:
+lean 3 declaration is
+ forall {A : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : Ring.{u1} A] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} A M (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u2} M] [_inst_7 : TopologicalSpace.{u3} M₂] {R : Type.{u4}} [_inst_8 : Ring.{u4} R] [_inst_9 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_10 : Module.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u2, u3, u4, u1} M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R A (Ring.toSemiring.{u1} A _inst_1) (SMulZeroClass.toHasSmul.{u4, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u4, u2} R M (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u4, u2} R M (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) _inst_5] {S : Type.{u5}} [_inst_12 : Ring.{u5} S] [_inst_13 : Module.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_14 : ContinuousConstSMul.{u5, u3} S M₂ _inst_7 (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_15 : SMulCommClass.{u1, u5, u3} A S M₂ (SMulZeroClass.toHasSmul.{u1, u3} A M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u1, u3} A M₂ (MulZeroClass.toHasZero.{u1} A (MulZeroOneClass.toMulZeroClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A _inst_1))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u1, u3} A M₂ (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A _inst_1)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u1, u3} A M₂ (Ring.toSemiring.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_16 : SMulCommClass.{u4, u5, u3} R S M₂ (SMulZeroClass.toHasSmul.{u4, u3} R M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u4, u3} R M₂ (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u4, u3} R M₂ (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_8)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u4, u3} R M₂ (Ring.toSemiring.{u4} R _inst_8) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10)))) (SMulZeroClass.toHasSmul.{u5, u3} S M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (SMulWithZero.toSmulZeroClass.{u5, u3} S M₂ (MulZeroClass.toHasZero.{u5} S (MulZeroOneClass.toMulZeroClass.{u5} S (MonoidWithZero.toMulZeroOneClass.{u5} S (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12))))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (MulActionWithZero.toSMulWithZero.{u5, u3} S M₂ (Semiring.toMonoidWithZero.{u5} S (Ring.toSemiring.{u5} S _inst_12)) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u5, u3} S M₂ (Ring.toSemiring.{u5} S _inst_12) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_13))))] [_inst_17 : TopologicalAddGroup.{u3} M₂ _inst_7 (AddCommGroup.toAddGroup.{u3} M₂ _inst_3)], Eq.{succ (max u2 u3)} ((ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) -> (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10)) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (LinearMap.{u5, u5, max u2 u3, max u2 u3} S S (Ring.toSemiring.{u5} S _inst_12) (Ring.toSemiring.{u5} S 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(Ring.toSemiring.{u1} A _inst_1))) (ContinuousLinearMap.restrictScalarsₗ._proof_3.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.module.{u4, u4, u5, u2, u3} R R S (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u5} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10 _inst_13 _inst_16 _inst_14 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) (ContinuousLinearMap.restrictScalarsₗ._proof_4.{u3} M₂ _inst_3 _inst_7 _inst_17))) (fun (_x : LinearMap.{u5, u5, max u2 u3, max u2 u3} S S (Ring.toSemiring.{u5} S _inst_12) (Ring.toSemiring.{u5} S _inst_12) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S (Ring.toSemiring.{u5} S _inst_12))) (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5 (ContinuousLinearMap.restrictScalarsₗ._proof_1.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.addCommMonoid.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10 (ContinuousLinearMap.restrictScalarsₗ._proof_2.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.module.{u1, u1, u5, u2, u3} A A S (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u5} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5 _inst_13 _inst_15 _inst_14 (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) (ContinuousLinearMap.restrictScalarsₗ._proof_3.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.module.{u4, u4, u5, u2, u3} R R S (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u5} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10 _inst_13 _inst_16 _inst_14 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) (ContinuousLinearMap.restrictScalarsₗ._proof_4.{u3} M₂ _inst_3 _inst_7 _inst_17))) => (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) -> (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10)) (LinearMap.hasCoeToFun.{u5, u5, max u2 u3, max u2 u3} S S (ContinuousLinearMap.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5) (ContinuousLinearMap.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10) (Ring.toSemiring.{u5} S _inst_12) (Ring.toSemiring.{u5} S _inst_12) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} A A (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4 _inst_5 (ContinuousLinearMap.restrictScalarsₗ._proof_1.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.addCommMonoid.{u4, u4, u2, u3} R R (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_9 _inst_10 (ContinuousLinearMap.restrictScalarsₗ._proof_2.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.module.{u1, u1, u5, u2, u3} A A S (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u1} A _inst_1) (Ring.toSemiring.{u5} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5 _inst_13 _inst_15 _inst_14 (RingHom.id.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) (ContinuousLinearMap.restrictScalarsₗ._proof_3.{u3} M₂ _inst_3 _inst_7 _inst_17)) (ContinuousLinearMap.module.{u4, u4, u5, u2, u3} R R S (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u4} R _inst_8) (Ring.toSemiring.{u5} S _inst_12) M _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_9 M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_10 _inst_13 _inst_16 _inst_14 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_8))) (ContinuousLinearMap.restrictScalarsₗ._proof_4.{u3} M₂ _inst_3 _inst_7 _inst_17)) (RingHom.id.{u5} S (Semiring.toNonAssocSemiring.{u5} S (Ring.toSemiring.{u5} S _inst_12)))) (ContinuousLinearMap.restrictScalarsₗ.{u1, u2, u3, u4, u5} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11 S _inst_12 _inst_13 _inst_14 _inst_15 _inst_16 _inst_17)) (ContinuousLinearMap.restrictScalars.{u1, u2, u3, u4} A M M₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 R _inst_8 _inst_9 _inst_10 _inst_11)
+but is expected to have type
+ forall {A : Type.{u3}} {M : Type.{u5}} {M₂ : Type.{u4}} [_inst_1 : Ring.{u3} A] [_inst_2 : AddCommGroup.{u5} M] [_inst_3 : AddCommGroup.{u4} M₂] [_inst_4 : Module.{u3, u5} A M (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2)] [_inst_5 : Module.{u3, u4} A M₂ (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_6 : TopologicalSpace.{u5} M] [_inst_7 : TopologicalSpace.{u4} M₂] {R : Type.{u2}} [_inst_8 : Ring.{u2} R] [_inst_9 : Module.{u2, u5} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2)] [_inst_10 : Module.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_11 : LinearMap.CompatibleSMul.{u5, u4, u2, u3} M M₂ (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) R A (Ring.toSemiring.{u3} A _inst_1) (SMulZeroClass.toSMul.{u2, u5} R M (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u5} R M (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u5} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u5} M (SubNegZeroMonoid.toNegZeroClass.{u5} M (SubtractionMonoid.toSubNegZeroMonoid.{u5} M (SubtractionCommMonoid.toSubtractionMonoid.{u5} M (AddCommGroup.toDivisionAddCommMonoid.{u5} M _inst_2))))) (Module.toMulActionWithZero.{u2, u5} R M (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) _inst_9)))) _inst_4 (SMulZeroClass.toSMul.{u2, u4} R M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10)))) _inst_5] {S : Type.{u1}} [_inst_12 : Ring.{u1} S] [_inst_13 : Module.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3)] [_inst_14 : ContinuousConstSMul.{u1, u4} S M₂ _inst_7 (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_15 : SMulCommClass.{u3, u1, u4} A S M₂ (SMulZeroClass.toSMul.{u3, u4} A M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u3, u4} A M₂ (MonoidWithZero.toZero.{u3} A (Semiring.toMonoidWithZero.{u3} A (Ring.toSemiring.{u3} A _inst_1))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A M₂ (Semiring.toMonoidWithZero.{u3} A (Ring.toSemiring.{u3} A _inst_1)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u3, u4} A M₂ (Ring.toSemiring.{u3} A _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_16 : SMulCommClass.{u2, u1, u4} R S M₂ (SMulZeroClass.toSMul.{u2, u4} R M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u4} R M₂ (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u4} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_8)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u4} R M₂ (Ring.toSemiring.{u2} R _inst_8) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_10)))) (SMulZeroClass.toSMul.{u1, u4} S M₂ (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u4} S M₂ (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12))) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u4} S M₂ (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S _inst_12)) (NegZeroClass.toZero.{u4} M₂ (SubNegZeroMonoid.toNegZeroClass.{u4} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u4} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u4} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u4} M₂ _inst_3))))) (Module.toMulActionWithZero.{u1, u4} S M₂ (Ring.toSemiring.{u1} S _inst_12) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_13))))] [_inst_17 : TopologicalAddGroup.{u4} M₂ _inst_7 (AddCommGroup.toAddGroup.{u4} M₂ _inst_3)], Eq.{max (succ u5) (succ u4)} (forall (ᾰ : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ContinuousLinearMap.{u3, u3, u5, u4} A A (Ring.toSemiring.{u3} A _inst_1) (Ring.toSemiring.{u3} A _inst_1) (RingHom.id.{u3} A (NonAssocRing.toNonAssocSemiring.{u3} A (Ring.toNonAssocRing.{u3} A _inst_1))) M _inst_6 (AddCommGroup.toAddCommMonoid.{u5} M _inst_2) M₂ _inst_7 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_3) _inst_4 _inst_5) => ContinuousLinearMap.{u2, u2, u5, u4} R R (Ring.toSemiring.{u2} R _inst_8) 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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.coe_restrict_scalarsₗ ContinuousLinearMap.coe_restrictScalarsₗₓ'. -/
@[simp]
theorem coe_restrictScalarsₗ : ⇑(restrictScalarsₗ A M M₂ R S) = restrictScalars R :=
rfl
@@ -1836,10 +2905,12 @@ variable {R₁ : Type _} {R₂ : Type _} {R₃ : Type _} [Semiring R₁] [Semiri
include σ₂₁
+#print ContinuousLinearEquiv.toContinuousLinearMap /-
/-- A continuous linear equivalence induces a continuous linear map. -/
def toContinuousLinearMap (e : M₁ ≃SL[σ₁₂] M₂) : M₁ →SL[σ₁₂] M₂ :=
{ e.toLinearEquiv.toLinearMap with cont := e.continuous_toFun }
#align continuous_linear_equiv.to_continuous_linear_map ContinuousLinearEquiv.toContinuousLinearMap
+-/
/-- Coerce continuous linear equivs to continuous linear maps. -/
instance : Coe (M₁ ≃SL[σ₁₂] M₂) (M₁ →SL[σ₁₂] M₂) :=
@@ -1867,82 +2938,181 @@ instance : ContinuousSemilinearEquivClass (M₁ ≃SL[σ₁₂] M₂) σ₁₂ M
instance : CoeFun (M₁ ≃SL[σ₁₂] M₂) fun _ => M₁ → M₂ :=
⟨fun f => f⟩
+/- warning: continuous_linear_equiv.coe_def_rev clashes with [anonymous] -> [anonymous]
+warning: continuous_linear_equiv.coe_def_rev -> [anonymous] is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+ forall {R₁ : Type.{u}} {R₂ : Type.{v}}, (Nat -> R₁ -> R₂) -> Nat -> (List.{u} R₁) -> (List.{v} R₂)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_def_rev [anonymous]ₓ'. -/
@[simp]
-theorem coe_def_rev (e : M₁ ≃SL[σ₁₂] M₂) : e.toContinuousLinearMap = e :=
+theorem [anonymous] (e : M₁ ≃SL[σ₁₂] M₂) : e.toContinuousLinearMap = e :=
rfl
-#align continuous_linear_equiv.coe_def_rev ContinuousLinearEquiv.coe_def_rev
-
+#align continuous_linear_equiv.coe_def_rev [anonymous]
+
+/- warning: continuous_linear_equiv.coe_apply -> ContinuousLinearEquiv.coe_apply 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 continuous_linear_equiv.coe_apply ContinuousLinearEquiv.coe_applyₓ'. -/
theorem coe_apply (e : M₁ ≃SL[σ₁₂] M₂) (b : M₁) : (e : M₁ →SL[σ₁₂] M₂) b = e b :=
rfl
#align continuous_linear_equiv.coe_apply ContinuousLinearEquiv.coe_apply
+/- warning: continuous_linear_equiv.coe_to_linear_equiv -> ContinuousLinearEquiv.coe_toLinearEquiv is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (f : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24), Eq.{max (succ u3) (succ u4)} (M₁ -> M₂) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ M₂ _inst_13 _inst_17 _inst_22 _inst_24) (fun (_x : LinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ M₂ _inst_13 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (LinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_13 _inst_17 _inst_22 _inst_24 σ₁₂ σ₂₁ _inst_4 _inst_5) (ContinuousLinearEquiv.toLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 f)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) f)
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (f : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : M₁), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : M₁) => M₂) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ M₂ _inst_13 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : M₁) => M₂) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (LinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ M₂ _inst_13 _inst_17 _inst_22 _inst_24) M₁ M₂ (EquivLike.toEmbeddingLike.{max (succ u2) (succ u1), succ u2, succ u1} (LinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ M₂ _inst_13 _inst_17 _inst_22 _inst_24) M₁ M₂ (AddEquivClass.toEquivLike.{max u2 u1, u2, u1} (LinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ M₂ _inst_13 _inst_17 _inst_22 _inst_24) M₁ M₂ (AddZeroClass.toAdd.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_13))) (AddZeroClass.toAdd.{u1} M₂ (AddMonoid.toAddZeroClass.{u1} M₂ (AddCommMonoid.toAddMonoid.{u1} M₂ _inst_17))) (SemilinearEquivClass.toAddEquivClass.{max u2 u1, u4, u3, u2, u1} (LinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ M₂ _inst_13 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ M₂ _inst_13 _inst_17 _inst_22 _inst_24 (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_13 _inst_17 _inst_22 _inst_24 σ₁₂ σ₂₁ _inst_4 _inst_5))))) (ContinuousLinearEquiv.toLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 f)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) f)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_to_linear_equiv ContinuousLinearEquiv.coe_toLinearEquivₓ'. -/
@[simp]
theorem coe_toLinearEquiv (f : M₁ ≃SL[σ₁₂] M₂) : ⇑f.toLinearEquiv = f :=
rfl
#align continuous_linear_equiv.coe_to_linear_equiv ContinuousLinearEquiv.coe_toLinearEquiv
+/- warning: continuous_linear_equiv.coe_coe -> ContinuousLinearEquiv.coe_coe 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 continuous_linear_equiv.coe_coe ContinuousLinearEquiv.coe_coeₓ'. -/
@[simp, norm_cast]
theorem coe_coe (e : M₁ ≃SL[σ₁₂] M₂) : ⇑(e : M₁ →SL[σ₁₂] M₂) = e :=
rfl
#align continuous_linear_equiv.coe_coe ContinuousLinearEquiv.coe_coe
+/- warning: continuous_linear_equiv.to_linear_equiv_injective -> ContinuousLinearEquiv.toLinearEquiv_injective is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17], Function.Injective.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (LinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ M₂ _inst_13 _inst_17 _inst_22 _inst_24) (ContinuousLinearEquiv.toLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)
+but is expected to have type
+ forall {R₁ : Type.{u2}} {R₂ : Type.{u1}} [_inst_1 : Semiring.{u2} R₁] [_inst_2 : Semiring.{u1} R₂] {σ₁₂ : RingHom.{u2, u1} R₁ R₂ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u1} R₂ _inst_2)} {σ₂₁ : RingHom.{u1, u2} R₂ R₁ (Semiring.toNonAssocSemiring.{u1} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u4}} [_inst_12 : TopologicalSpace.{u4} M₁] [_inst_13 : AddCommMonoid.{u4} M₁] {M₂ : Type.{u3}} [_inst_16 : TopologicalSpace.{u3} M₂] [_inst_17 : AddCommMonoid.{u3} M₂] [_inst_22 : Module.{u2, u4} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u1, u3} R₂ M₂ _inst_2 _inst_17], Function.Injective.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (ContinuousLinearEquiv.{u2, u1, u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (LinearEquiv.{u2, u1, u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ M₂ _inst_13 _inst_17 _inst_22 _inst_24) (ContinuousLinearEquiv.toLinearEquiv.{u2, u1, u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.to_linear_equiv_injective ContinuousLinearEquiv.toLinearEquiv_injectiveₓ'. -/
theorem toLinearEquiv_injective :
Function.Injective (toLinearEquiv : (M₁ ≃SL[σ₁₂] M₂) → M₁ ≃ₛₗ[σ₁₂] M₂)
| ⟨e, _, _⟩, ⟨e', _, _⟩, rfl => rfl
#align continuous_linear_equiv.to_linear_equiv_injective ContinuousLinearEquiv.toLinearEquiv_injective
+/- warning: continuous_linear_equiv.ext -> ContinuousLinearEquiv.ext is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] {f : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24} {g : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24}, (Eq.{max (succ u3) (succ u4)} ((fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) g)) -> (Eq.{max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) f g)
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] {f : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24} {g : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24}, (Eq.{max (succ u2) (succ u1)} (forall (a : M₁), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) g)) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) f g)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.ext ContinuousLinearEquiv.extₓ'. -/
@[ext]
theorem ext {f g : M₁ ≃SL[σ₁₂] M₂} (h : (f : M₁ → M₂) = g) : f = g :=
toLinearEquiv_injective <| LinearEquiv.ext <| congr_fun h
#align continuous_linear_equiv.ext ContinuousLinearEquiv.ext
+/- warning: continuous_linear_equiv.coe_injective -> ContinuousLinearEquiv.coe_injective is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17], Function.Injective.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) ((fun (a : Sort.{max (succ u3) (succ u4)}) (b : Sort.{max (succ u3) (succ u4)}) [self : HasLiftT.{max (succ u3) (succ u4), max (succ u3) (succ u4)} a b] => self.0) (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (HasLiftT.mk.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (CoeTCₓ.coe.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (coeBase.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))))
+but is expected to have type
+ forall {R₁ : Type.{u2}} {R₂ : Type.{u1}} [_inst_1 : Semiring.{u2} R₁] [_inst_2 : Semiring.{u1} R₂] {σ₁₂ : RingHom.{u2, u1} R₁ R₂ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u1} R₂ _inst_2)} {σ₂₁ : RingHom.{u1, u2} R₂ R₁ (Semiring.toNonAssocSemiring.{u1} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u4}} [_inst_12 : TopologicalSpace.{u4} M₁] [_inst_13 : AddCommMonoid.{u4} M₁] {M₂ : Type.{u3}} [_inst_16 : TopologicalSpace.{u3} M₂] [_inst_17 : AddCommMonoid.{u3} M₂] [_inst_22 : Module.{u2, u4} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u1, u3} R₂ M₂ _inst_2 _inst_17], Function.Injective.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (ContinuousLinearEquiv.{u2, u1, u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (ContinuousLinearMap.{u2, u1, u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (ContinuousLinearEquiv.toContinuousLinearMap.{u2, u1, u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_injective ContinuousLinearEquiv.coe_injectiveₓ'. -/
theorem coe_injective : Function.Injective (coe : (M₁ ≃SL[σ₁₂] M₂) → M₁ →SL[σ₁₂] M₂) :=
fun e e' h => ext <| funext <| ContinuousLinearMap.ext_iff.1 h
#align continuous_linear_equiv.coe_injective ContinuousLinearEquiv.coe_injective
+/- warning: continuous_linear_equiv.coe_inj -> ContinuousLinearEquiv.coe_inj is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_inj ContinuousLinearEquiv.coe_injₓ'. -/
@[simp, norm_cast]
theorem coe_inj {e e' : M₁ ≃SL[σ₁₂] M₂} : (e : M₁ →SL[σ₁₂] M₂) = e' ↔ e = e' :=
coe_injective.eq_iff
#align continuous_linear_equiv.coe_inj ContinuousLinearEquiv.coe_inj
+#print ContinuousLinearEquiv.toHomeomorph /-
/-- A continuous linear equivalence induces a homeomorphism. -/
def toHomeomorph (e : M₁ ≃SL[σ₁₂] M₂) : M₁ ≃ₜ M₂ :=
{ e with toEquiv := e.toLinearEquiv.toEquiv }
#align continuous_linear_equiv.to_homeomorph ContinuousLinearEquiv.toHomeomorph
+-/
+/- warning: continuous_linear_equiv.coe_to_homeomorph -> ContinuousLinearEquiv.coe_toHomeomorph 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 continuous_linear_equiv.coe_to_homeomorph ContinuousLinearEquiv.coe_toHomeomorphₓ'. -/
@[simp]
theorem coe_toHomeomorph (e : M₁ ≃SL[σ₁₂] M₂) : ⇑e.toHomeomorph = e :=
rfl
#align continuous_linear_equiv.coe_to_homeomorph ContinuousLinearEquiv.coe_toHomeomorph
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+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (s : Set.{u3} M₁), Eq.{succ u4} (Set.{u4} M₂) (Set.image.{u3, u4} M₁ M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e) (closure.{u3} M₁ _inst_12 s)) (closure.{u4} M₂ _inst_16 (Set.image.{u3, u4} M₁ M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e) s))
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (s : Set.{u2} M₁), Eq.{succ u1} (Set.{u1} M₂) (Set.image.{u2, u1} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e) (closure.{u2} M₁ _inst_12 s)) (closure.{u1} M₂ _inst_16 (Set.image.{u2, u1} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e) s))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.image_closure ContinuousLinearEquiv.image_closureₓ'. -/
theorem image_closure (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₁) : e '' closure s = closure (e '' s) :=
e.toHomeomorph.image_closure s
#align continuous_linear_equiv.image_closure ContinuousLinearEquiv.image_closure
+/- warning: continuous_linear_equiv.preimage_closure -> ContinuousLinearEquiv.preimage_closure is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (s : Set.{u4} M₂), Eq.{succ u3} (Set.{u3} M₁) (Set.preimage.{u3, u4} M₁ M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e) (closure.{u4} M₂ _inst_16 s)) (closure.{u3} M₁ _inst_12 (Set.preimage.{u3, u4} M₁ M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e) s))
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (s : Set.{u1} M₂), Eq.{succ u2} (Set.{u2} M₁) (Set.preimage.{u2, u1} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e) (closure.{u1} M₂ _inst_16 s)) (closure.{u2} M₁ _inst_12 (Set.preimage.{u2, u1} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e) s))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.preimage_closure ContinuousLinearEquiv.preimage_closureₓ'. -/
theorem preimage_closure (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₂) : e ⁻¹' closure s = closure (e ⁻¹' s) :=
e.toHomeomorph.preimage_closure s
#align continuous_linear_equiv.preimage_closure ContinuousLinearEquiv.preimage_closure
+/- warning: continuous_linear_equiv.is_closed_image -> ContinuousLinearEquiv.isClosed_image is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) {s : Set.{u3} M₁}, Iff (IsClosed.{u4} M₂ _inst_16 (Set.image.{u3, u4} M₁ M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e) s)) (IsClosed.{u3} M₁ _inst_12 s)
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) {s : Set.{u2} M₁}, Iff (IsClosed.{u1} M₂ _inst_16 (Set.image.{u2, u1} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e) s)) (IsClosed.{u2} M₁ _inst_12 s)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.is_closed_image ContinuousLinearEquiv.isClosed_imageₓ'. -/
@[simp]
theorem isClosed_image (e : M₁ ≃SL[σ₁₂] M₂) {s : Set M₁} : IsClosed (e '' s) ↔ IsClosed s :=
e.toHomeomorph.isClosed_image
#align continuous_linear_equiv.is_closed_image ContinuousLinearEquiv.isClosed_image
+/- warning: continuous_linear_equiv.map_nhds_eq -> ContinuousLinearEquiv.map_nhds_eq is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (x : M₁), Eq.{succ u4} (Filter.{u4} M₂) (Filter.map.{u3, u4} M₁ M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e) (nhds.{u3} M₁ _inst_12 x)) (nhds.{u4} M₂ _inst_16 (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e x))
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (x : M₁), Eq.{succ u1} (Filter.{u1} M₂) (Filter.map.{u2, u1} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e) (nhds.{u2} M₁ _inst_12 x)) (nhds.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_16 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e x))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_nhds_eq ContinuousLinearEquiv.map_nhds_eqₓ'. -/
theorem map_nhds_eq (e : M₁ ≃SL[σ₁₂] M₂) (x : M₁) : map e (𝓝 x) = 𝓝 (e x) :=
e.toHomeomorph.map_nhds_eq x
#align continuous_linear_equiv.map_nhds_eq ContinuousLinearEquiv.map_nhds_eq
+/- warning: continuous_linear_equiv.map_zero -> ContinuousLinearEquiv.map_zero is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24), Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e (OfNat.ofNat.{u3} M₁ 0 (OfNat.mk.{u3} M₁ 0 (Zero.zero.{u3} M₁ (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_13))))))) (OfNat.ofNat.{u4} M₂ 0 (OfNat.mk.{u4} M₂ 0 (Zero.zero.{u4} M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_17))))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_zero ContinuousLinearEquiv.map_zeroₓ'. -/
-- Make some straightforward lemmas available to `simp`.
@[simp]
theorem map_zero (e : M₁ ≃SL[σ₁₂] M₂) : e (0 : M₁) = 0 :=
(e : M₁ →SL[σ₁₂] M₂).map_zero
#align continuous_linear_equiv.map_zero ContinuousLinearEquiv.map_zero
+/- warning: continuous_linear_equiv.map_add -> ContinuousLinearEquiv.map_add is a dubious translation:
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_inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e y))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_add ContinuousLinearEquiv.map_addₓ'. -/
@[simp]
theorem map_add (e : M₁ ≃SL[σ₁₂] M₂) (x y : M₁) : e (x + y) = e x + e y :=
(e : M₁ →SL[σ₁₂] M₂).map_add x y
#align continuous_linear_equiv.map_add ContinuousLinearEquiv.map_add
+/- warning: continuous_linear_equiv.map_smulₛₗ -> ContinuousLinearEquiv.map_smulₛₗ is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (c : R₁) (x : M₁), Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e (SMul.smul.{u1, u3} R₁ M₁ (SMulZeroClass.toHasSmul.{u1, u3} R₁ M₁ (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_13))) (SMulWithZero.toSmulZeroClass.{u1, u3} R₁ M₁ (MulZeroClass.toHasZero.{u1} R₁ (MulZeroOneClass.toMulZeroClass.{u1} R₁ (MonoidWithZero.toMulZeroOneClass.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)))) (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_13))) (MulActionWithZero.toSMulWithZero.{u1, u3} R₁ M₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_13))) (Module.toMulActionWithZero.{u1, u3} R₁ M₁ _inst_1 _inst_13 _inst_22)))) c x)) (SMul.smul.{u2, u4} R₂ M₂ (SMulZeroClass.toHasSmul.{u2, u4} R₂ M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_17))) (SMulWithZero.toSmulZeroClass.{u2, u4} R₂ M₂ (MulZeroClass.toHasZero.{u2} R₂ (MulZeroOneClass.toMulZeroClass.{u2} R₂ (MonoidWithZero.toMulZeroOneClass.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2)))) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_17))) (MulActionWithZero.toSMulWithZero.{u2, u4} R₂ M₂ (Semiring.toMonoidWithZero.{u2} R₂ _inst_2) (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_17))) (Module.toMulActionWithZero.{u2, u4} R₂ M₂ _inst_2 _inst_17 _inst_24)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)) (fun (_x : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)) => R₁ -> R₂) (RingHom.hasCoeToFun.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)) σ₁₂ c) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e x))
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (c : R₁) (x : M₁), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) (HSMul.hSMul.{u4, u2, u2} R₁ M₁ M₁ (instHSMul.{u4, u2} R₁ M₁ (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_13)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_13)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_13)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_13 _inst_22))))) c x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e (HSMul.hSMul.{u4, u2, u2} R₁ M₁ M₁ (instHSMul.{u4, u2} R₁ M₁ (SMulZeroClass.toSMul.{u4, u2} R₁ M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_13)) (SMulWithZero.toSMulZeroClass.{u4, u2} R₁ M₁ (MonoidWithZero.toZero.{u4} R₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1)) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_13)) (MulActionWithZero.toSMulWithZero.{u4, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u4} R₁ _inst_1) (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_13)) (Module.toMulActionWithZero.{u4, u2} R₁ M₁ _inst_1 _inst_13 _inst_22))))) c x)) (HSMul.hSMul.{u3, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (instHSMul.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (SMulZeroClass.toSMul.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_17)) (SMulWithZero.toSMulZeroClass.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) _inst_2)) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_17)) (MulActionWithZero.toSMulWithZero.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) _inst_2) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_17)) (Module.toMulActionWithZero.{u3, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) c) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_2 _inst_17 _inst_24))))) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) R₁ (fun (_x : R₁) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R₁) => R₂) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) R₁ R₂ (NonUnitalNonAssocSemiring.toMul.{u4} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u3} R₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) R₁ R₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R₂ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)) R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (RingHom.instRingHomClassRingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2))))) σ₁₂ c) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e x))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_smulₛₗ ContinuousLinearEquiv.map_smulₛₗₓ'. -/
@[simp]
theorem map_smulₛₗ (e : M₁ ≃SL[σ₁₂] M₂) (c : R₁) (x : M₁) : e (c • x) = σ₁₂ c • e x :=
(e : M₁ →SL[σ₁₂] M₂).map_smulₛₗ c x
@@ -1950,6 +3120,12 @@ theorem map_smulₛₗ (e : M₁ ≃SL[σ₁₂] M₂) (c : R₁) (x : M₁) : e
omit σ₂₁
+/- warning: continuous_linear_equiv.map_smul -> ContinuousLinearEquiv.map_smul is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_16 : TopologicalSpace.{u3} M₂] [_inst_17 : AddCommMonoid.{u3} M₂] [_inst_22 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_13] [_inst_26 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_17] (e : ContinuousLinearEquiv.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHomInvPair.ids.{u1} R₁ _inst_1) (RingHomInvPair.ids.{u1} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26) (c : R₁) (x : M₁), Eq.{succ u3} M₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearEquiv.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHomInvPair.ids.{u1} R₁ _inst_1) (RingHomInvPair.ids.{u1} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26) (fun (_x : ContinuousLinearEquiv.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHomInvPair.ids.{u1} R₁ _inst_1) (RingHomInvPair.ids.{u1} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHomInvPair.ids.{u1} R₁ _inst_1) (RingHomInvPair.ids.{u1} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26) e (SMul.smul.{u1, u2} R₁ M₁ (SMulZeroClass.toHasSmul.{u1, u2} R₁ M₁ (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_13))) (SMulWithZero.toSmulZeroClass.{u1, u2} R₁ M₁ (MulZeroClass.toHasZero.{u1} R₁ (MulZeroOneClass.toMulZeroClass.{u1} R₁ (MonoidWithZero.toMulZeroOneClass.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)))) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_13))) (MulActionWithZero.toSMulWithZero.{u1, u2} R₁ M₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddZeroClass.toHasZero.{u2} M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_13))) (Module.toMulActionWithZero.{u1, u2} R₁ M₁ _inst_1 _inst_13 _inst_22)))) c x)) (SMul.smul.{u1, u3} R₁ M₂ (SMulZeroClass.toHasSmul.{u1, u3} R₁ M₂ (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_17))) (SMulWithZero.toSmulZeroClass.{u1, u3} R₁ M₂ (MulZeroClass.toHasZero.{u1} R₁ (MulZeroOneClass.toMulZeroClass.{u1} R₁ (MonoidWithZero.toMulZeroOneClass.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1)))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_17))) (MulActionWithZero.toSMulWithZero.{u1, u3} R₁ M₂ (Semiring.toMonoidWithZero.{u1} R₁ _inst_1) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_17))) (Module.toMulActionWithZero.{u1, u3} R₁ M₂ _inst_1 _inst_17 _inst_26)))) c (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearEquiv.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHomInvPair.ids.{u1} R₁ _inst_1) (RingHomInvPair.ids.{u1} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26) (fun (_x : ContinuousLinearEquiv.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHomInvPair.ids.{u1} R₁ _inst_1) (RingHomInvPair.ids.{u1} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHomInvPair.ids.{u1} R₁ _inst_1) (RingHomInvPair.ids.{u1} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26) e x))
+but is expected to have type
+ forall {R₁ : Type.{u3}} [_inst_1 : Semiring.{u3} R₁] {M₁ : Type.{u1}} [_inst_12 : TopologicalSpace.{u1} M₁] [_inst_13 : AddCommMonoid.{u1} M₁] {M₂ : Type.{u2}} [_inst_16 : TopologicalSpace.{u2} M₂] [_inst_17 : AddCommMonoid.{u2} M₂] [_inst_22 : Module.{u3, u1} R₁ M₁ _inst_1 _inst_13] [_inst_26 : Module.{u3, u2} R₁ M₂ _inst_1 _inst_17] (e : ContinuousLinearEquiv.{u3, u3, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) (RingHomInvPair.ids.{u3} R₁ _inst_1) (RingHomInvPair.ids.{u3} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26) (c : R₁) (x : M₁), Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) (HSMul.hSMul.{u3, u1, u1} R₁ M₁ M₁ (instHSMul.{u3, u1} R₁ M₁ (SMulZeroClass.toSMul.{u3, u1} R₁ M₁ (AddMonoid.toZero.{u1} M₁ (AddCommMonoid.toAddMonoid.{u1} M₁ _inst_13)) (SMulWithZero.toSMulZeroClass.{u3, u1} R₁ M₁ 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_inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) (RingHomInvPair.ids.{u3} R₁ _inst_1) (RingHomInvPair.ids.{u3} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) (RingHomInvPair.ids.{u3} R₁ _inst_1) (RingHomInvPair.ids.{u3} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u3, u3, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) (RingHomInvPair.ids.{u3} R₁ _inst_1) (RingHomInvPair.ids.{u3} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26)))) e (HSMul.hSMul.{u3, u1, u1} R₁ M₁ M₁ (instHSMul.{u3, u1} R₁ M₁ (SMulZeroClass.toSMul.{u3, u1} R₁ M₁ (AddMonoid.toZero.{u1} M₁ (AddCommMonoid.toAddMonoid.{u1} M₁ _inst_13)) (SMulWithZero.toSMulZeroClass.{u3, u1} R₁ M₁ (MonoidWithZero.toZero.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ _inst_1)) (AddMonoid.toZero.{u1} M₁ (AddCommMonoid.toAddMonoid.{u1} M₁ _inst_13)) (MulActionWithZero.toSMulWithZero.{u3, u1} R₁ M₁ (Semiring.toMonoidWithZero.{u3} R₁ _inst_1) (AddMonoid.toZero.{u1} M₁ (AddCommMonoid.toAddMonoid.{u1} M₁ _inst_13)) (Module.toMulActionWithZero.{u3, u1} R₁ M₁ _inst_1 _inst_13 _inst_22))))) c x)) (HSMul.hSMul.{u3, u2, u2} R₁ ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (instHSMul.{u3, u2} R₁ ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (SMulZeroClass.toSMul.{u3, u2} R₁ ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_17)) (SMulWithZero.toSMulZeroClass.{u3, u2} R₁ ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (MonoidWithZero.toZero.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ _inst_1)) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_17)) (MulActionWithZero.toSMulWithZero.{u3, u2} R₁ ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (Semiring.toMonoidWithZero.{u3} R₁ _inst_1) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_17)) (Module.toMulActionWithZero.{u3, u2} R₁ ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_1 _inst_17 _inst_26))))) c (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (ContinuousLinearEquiv.{u3, u3, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) (RingHomInvPair.ids.{u3} R₁ _inst_1) (RingHomInvPair.ids.{u3} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (ContinuousLinearEquiv.{u3, u3, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) (RingHomInvPair.ids.{u3} R₁ _inst_1) (RingHomInvPair.ids.{u3} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u1 u2, u3, u3, u1, u2} (ContinuousLinearEquiv.{u3, u3, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) (RingHomInvPair.ids.{u3} R₁ _inst_1) (RingHomInvPair.ids.{u3} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u1 u2, u3, u3, u1, u2} (ContinuousLinearEquiv.{u3, u3, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) (RingHomInvPair.ids.{u3} R₁ _inst_1) (RingHomInvPair.ids.{u3} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26) R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) (RingHomInvPair.ids.{u3} R₁ _inst_1) (RingHomInvPair.ids.{u3} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u3, u3, u1, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ _inst_1)) (RingHomInvPair.ids.{u3} R₁ _inst_1) (RingHomInvPair.ids.{u3} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26)))) e x))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_smul ContinuousLinearEquiv.map_smulₓ'. -/
@[simp]
theorem map_smul [Module R₁ M₂] (e : M₁ ≃L[R₁] M₂) (c : R₁) (x : M₁) : e (c • x) = c • e x :=
(e : M₁ →L[R₁] M₂).map_smul c x
@@ -1957,6 +3133,12 @@ theorem map_smul [Module R₁ M₂] (e : M₁ ≃L[R₁] M₂) (c : R₁) (x : M
include σ₂₁
+/- warning: continuous_linear_equiv.map_eq_zero_iff -> ContinuousLinearEquiv.map_eq_zero_iff is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) {x : M₁}, Iff (Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e x) (OfNat.ofNat.{u4} M₂ 0 (OfNat.mk.{u4} M₂ 0 (Zero.zero.{u4} M₂ (AddZeroClass.toHasZero.{u4} M₂ (AddMonoid.toAddZeroClass.{u4} M₂ (AddCommMonoid.toAddMonoid.{u4} M₂ _inst_17))))))) (Eq.{succ u3} M₁ x (OfNat.ofNat.{u3} M₁ 0 (OfNat.mk.{u3} M₁ 0 (Zero.zero.{u3} M₁ (AddZeroClass.toHasZero.{u3} M₁ (AddMonoid.toAddZeroClass.{u3} M₁ (AddCommMonoid.toAddMonoid.{u3} M₁ _inst_13)))))))
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) {x : M₁}, Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) _inst_17))))) (Eq.{succ u2} M₁ x (OfNat.ofNat.{u2} M₁ 0 (Zero.toOfNat0.{u2} M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_13)))))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_eq_zero_iff ContinuousLinearEquiv.map_eq_zero_iffₓ'. -/
@[simp]
theorem map_eq_zero_iff (e : M₁ ≃SL[σ₁₂] M₂) {x : M₁} : e x = 0 ↔ x = 0 :=
e.toLinearEquiv.map_eq_zero_iff
@@ -1965,29 +3147,65 @@ theorem map_eq_zero_iff (e : M₁ ≃SL[σ₁₂] M₂) {x : M₁} : e x = 0 ↔
attribute [continuity]
ContinuousLinearEquiv.continuous_toFun ContinuousLinearEquiv.continuous_invFun
+/- warning: continuous_linear_equiv.continuous -> ContinuousLinearEquiv.continuous is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24), Continuous.{u3, u4} M₁ M₂ _inst_12 _inst_16 (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e)
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24), Continuous.{u2, u1} M₁ M₂ _inst_12 _inst_16 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.continuous ContinuousLinearEquiv.continuousₓ'. -/
@[continuity]
protected theorem continuous (e : M₁ ≃SL[σ₁₂] M₂) : Continuous (e : M₁ → M₂) :=
e.continuous_toFun
#align continuous_linear_equiv.continuous ContinuousLinearEquiv.continuous
+/- warning: continuous_linear_equiv.continuous_on -> ContinuousLinearEquiv.continuousOn is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) {s : Set.{u3} M₁}, ContinuousOn.{u3, u4} M₁ M₂ _inst_12 _inst_16 (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e) s
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) {s : Set.{u2} M₁}, ContinuousOn.{u2, u1} M₁ M₂ _inst_12 _inst_16 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e) s
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.continuous_on ContinuousLinearEquiv.continuousOnₓ'. -/
protected theorem continuousOn (e : M₁ ≃SL[σ₁₂] M₂) {s : Set M₁} : ContinuousOn (e : M₁ → M₂) s :=
e.Continuous.ContinuousOn
#align continuous_linear_equiv.continuous_on ContinuousLinearEquiv.continuousOn
+/- warning: continuous_linear_equiv.continuous_at -> ContinuousLinearEquiv.continuousAt is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) {x : M₁}, ContinuousAt.{u3, u4} M₁ M₂ _inst_12 _inst_16 (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e) x
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) {x : M₁}, ContinuousAt.{u2, u1} M₁ M₂ _inst_12 _inst_16 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e) x
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.continuous_at ContinuousLinearEquiv.continuousAtₓ'. -/
protected theorem continuousAt (e : M₁ ≃SL[σ₁₂] M₂) {x : M₁} : ContinuousAt (e : M₁ → M₂) x :=
e.Continuous.ContinuousAt
#align continuous_linear_equiv.continuous_at ContinuousLinearEquiv.continuousAt
+/- warning: continuous_linear_equiv.continuous_within_at -> ContinuousLinearEquiv.continuousWithinAt is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) {s : Set.{u3} M₁} {x : M₁}, ContinuousWithinAt.{u3, u4} M₁ M₂ _inst_12 _inst_16 (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e) s x
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) {s : Set.{u2} M₁} {x : M₁}, ContinuousWithinAt.{u2, u1} M₁ M₂ _inst_12 _inst_16 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e) s x
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.continuous_within_at ContinuousLinearEquiv.continuousWithinAtₓ'. -/
protected theorem continuousWithinAt (e : M₁ ≃SL[σ₁₂] M₂) {s : Set M₁} {x : M₁} :
ContinuousWithinAt (e : M₁ → M₂) s x :=
e.Continuous.ContinuousWithinAt
#align continuous_linear_equiv.continuous_within_at ContinuousLinearEquiv.continuousWithinAt
+/- warning: continuous_linear_equiv.comp_continuous_on_iff -> ContinuousLinearEquiv.comp_continuousOn_iff is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] {α : Type.{u5}} [_inst_26 : TopologicalSpace.{u5} α] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) {f : α -> M₁} {s : Set.{u5} α}, Iff (ContinuousOn.{u5, u4} α M₂ _inst_26 _inst_16 (Function.comp.{succ u5, succ u3, succ u4} α M₁ M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e) f) s) (ContinuousOn.{u5, u3} α M₁ _inst_26 _inst_12 f s)
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] {α : Type.{u5}} [_inst_26 : TopologicalSpace.{u5} α] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) {f : α -> M₁} {s : Set.{u5} α}, Iff (ContinuousOn.{u5, u1} α M₂ _inst_26 _inst_16 (Function.comp.{succ u5, succ u2, succ u1} α M₁ M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e) f) s) (ContinuousOn.{u5, u2} α M₁ _inst_26 _inst_12 f s)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.comp_continuous_on_iff ContinuousLinearEquiv.comp_continuousOn_iffₓ'. -/
theorem comp_continuousOn_iff {α : Type _} [TopologicalSpace α] (e : M₁ ≃SL[σ₁₂] M₂) {f : α → M₁}
{s : Set α} : ContinuousOn (e ∘ f) s ↔ ContinuousOn f s :=
e.toHomeomorph.comp_continuousOn_iff _ _
#align continuous_linear_equiv.comp_continuous_on_iff ContinuousLinearEquiv.comp_continuousOn_iff
+/- warning: continuous_linear_equiv.comp_continuous_iff -> ContinuousLinearEquiv.comp_continuous_iff is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] {α : Type.{u5}} [_inst_26 : TopologicalSpace.{u5} α] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) {f : α -> M₁}, Iff (Continuous.{u5, u4} α M₂ _inst_26 _inst_16 (Function.comp.{succ u5, succ u3, succ u4} α M₁ M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e) f)) (Continuous.{u5, u3} α M₁ _inst_26 _inst_12 f)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.comp_continuous_iff ContinuousLinearEquiv.comp_continuous_iffₓ'. -/
theorem comp_continuous_iff {α : Type _} [TopologicalSpace α] (e : M₁ ≃SL[σ₁₂] M₂) {f : α → M₁} :
Continuous (e ∘ f) ↔ Continuous f :=
e.toHomeomorph.comp_continuous_iff
@@ -1995,6 +3213,12 @@ theorem comp_continuous_iff {α : Type _} [TopologicalSpace α] (e : M₁ ≃SL[
omit σ₂₁
+/- warning: continuous_linear_equiv.ext₁ -> ContinuousLinearEquiv.ext₁ is a dubious translation:
+lean 3 declaration is
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) M₁ _inst_12 _inst_13 (Semiring.toModule.{u2} R₁ _inst_1) _inst_22)))) f (OfNat.ofNat.{u2} R₁ 1 (One.toOfNat1.{u2} R₁ (Semiring.toOne.{u2} R₁ _inst_1)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u2, u2, u2, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (RingHomInvPair.ids.{u2} R₁ _inst_1) (RingHomInvPair.ids.{u2} R₁ _inst_1) R₁ _inst_26 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) M₁ _inst_12 _inst_13 (Semiring.toModule.{u2} R₁ _inst_1) _inst_22) R₁ (fun (_x : R₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R₁) => M₁) _x) (ContinuousMapClass.toFunLike.{max 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_inst_1))) M₁ _inst_12 _inst_13 (Semiring.toModule.{u2} R₁ _inst_1) _inst_22)))) g (OfNat.ofNat.{u2} R₁ 1 (One.toOfNat1.{u2} R₁ (Semiring.toOne.{u2} R₁ _inst_1))))) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearEquiv.{u2, u2, u2, u1} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (RingHom.id.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)) (RingHomInvPair.ids.{u2} R₁ _inst_1) (RingHomInvPair.ids.{u2} R₁ _inst_1) R₁ _inst_26 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1))) M₁ _inst_12 _inst_13 (Semiring.toModule.{u2} R₁ _inst_1) _inst_22) f g)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.ext₁ ContinuousLinearEquiv.ext₁ₓ'. -/
/-- An extensionality lemma for `R ≃L[R] M`. -/
theorem ext₁ [TopologicalSpace R₁] {f g : R₁ ≃L[R₁] M₁} (h : f 1 = g 1) : f = g :=
ext <| funext fun x => mul_one x ▸ by rw [← smul_eq_mul, map_smul, h, map_smul]
@@ -2004,6 +3228,7 @@ section
variable (R₁ M₁)
+#print ContinuousLinearEquiv.refl /-
/-- The identity map as a continuous linear equivalence. -/
@[refl]
protected def refl : M₁ ≃L[R₁] M₁ :=
@@ -2011,19 +3236,25 @@ protected def refl : M₁ ≃L[R₁] M₁ :=
continuous_toFun := continuous_id
continuous_invFun := continuous_id }
#align continuous_linear_equiv.refl ContinuousLinearEquiv.refl
+-/
end
+#print ContinuousLinearEquiv.coe_refl /-
@[simp, norm_cast]
theorem coe_refl : ↑(ContinuousLinearEquiv.refl R₁ M₁) = ContinuousLinearMap.id R₁ M₁ :=
rfl
#align continuous_linear_equiv.coe_refl ContinuousLinearEquiv.coe_refl
+-/
+#print ContinuousLinearEquiv.coe_refl' /-
@[simp, norm_cast]
theorem coe_refl' : ⇑(ContinuousLinearEquiv.refl R₁ M₁) = id :=
rfl
#align continuous_linear_equiv.coe_refl' ContinuousLinearEquiv.coe_refl'
+-/
+#print ContinuousLinearEquiv.symm /-
/-- The inverse of a continuous linear equivalence as a continuous linear equivalence-/
@[symm]
protected def symm (e : M₁ ≃SL[σ₁₂] M₂) : M₂ ≃SL[σ₂₁] M₁ :=
@@ -2031,9 +3262,16 @@ protected def symm (e : M₁ ≃SL[σ₁₂] M₂) : M₂ ≃SL[σ₂₁] M₁ :
continuous_toFun := e.continuous_invFun
continuous_invFun := e.continuous_toFun }
#align continuous_linear_equiv.symm ContinuousLinearEquiv.symm
+-/
include σ₂₁
+/- warning: continuous_linear_equiv.symm_to_linear_equiv -> ContinuousLinearEquiv.symm_toLinearEquiv is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24), Eq.{max (succ u4) (succ u3)} (LinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ M₁ _inst_17 _inst_13 _inst_24 _inst_22) (ContinuousLinearEquiv.toLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearEquiv.symm.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) (LinearEquiv.symm.{u1, u2, u3, u4} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_13 _inst_17 _inst_22 _inst_24 σ₁₂ σ₂₁ _inst_4 _inst_5 (ContinuousLinearEquiv.toLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e))
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24), Eq.{max (succ u2) (succ u1)} (LinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ M₁ _inst_17 _inst_13 _inst_24 _inst_22) (ContinuousLinearEquiv.toLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearEquiv.symm.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) (LinearEquiv.symm.{u4, u3, u2, u1} R₁ R₂ M₁ M₂ _inst_1 _inst_2 _inst_13 _inst_17 _inst_22 _inst_24 σ₁₂ σ₂₁ _inst_4 _inst_5 (ContinuousLinearEquiv.toLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_to_linear_equiv ContinuousLinearEquiv.symm_toLinearEquivₓ'. -/
@[simp]
theorem symm_toLinearEquiv (e : M₁ ≃SL[σ₁₂] M₂) : e.symm.toLinearEquiv = e.toLinearEquiv.symm :=
by
@@ -2041,25 +3279,41 @@ theorem symm_toLinearEquiv (e : M₁ ≃SL[σ₁₂] M₂) : e.symm.toLinearEqui
rfl
#align continuous_linear_equiv.symm_to_linear_equiv ContinuousLinearEquiv.symm_toLinearEquiv
+/- warning: continuous_linear_equiv.symm_to_homeomorph -> ContinuousLinearEquiv.symm_toHomeomorph is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24), Eq.{max (succ u4) (succ u3)} (Homeomorph.{u4, u3} M₂ M₁ _inst_16 _inst_12) (Homeomorph.symm.{u3, u4} M₁ M₂ _inst_12 _inst_16 (ContinuousLinearEquiv.toHomeomorph.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) (ContinuousLinearEquiv.toHomeomorph.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearEquiv.symm.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e))
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24), Eq.{max (succ u2) (succ u1)} (Homeomorph.{u1, u2} M₂ M₁ _inst_16 _inst_12) (Homeomorph.symm.{u2, u1} M₁ M₂ _inst_12 _inst_16 (ContinuousLinearEquiv.toHomeomorph.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) (ContinuousLinearEquiv.toHomeomorph.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearEquiv.symm.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_to_homeomorph ContinuousLinearEquiv.symm_toHomeomorphₓ'. -/
@[simp]
theorem symm_toHomeomorph (e : M₁ ≃SL[σ₁₂] M₂) : e.toHomeomorph.symm = e.symm.toHomeomorph :=
rfl
#align continuous_linear_equiv.symm_to_homeomorph ContinuousLinearEquiv.symm_toHomeomorph
+#print ContinuousLinearEquiv.Simps.apply /-
/-- See Note [custom simps projection]. We need to specify this projection explicitly in this case,
because it is a composition of multiple projections. -/
def Simps.apply (h : M₁ ≃SL[σ₁₂] M₂) : M₁ → M₂ :=
h
#align continuous_linear_equiv.simps.apply ContinuousLinearEquiv.Simps.apply
+-/
+#print ContinuousLinearEquiv.Simps.symm_apply /-
/-- See Note [custom simps projection] -/
-def Simps.symmApply (h : M₁ ≃SL[σ₁₂] M₂) : M₂ → M₁ :=
+def Simps.symm_apply (h : M₁ ≃SL[σ₁₂] M₂) : M₂ → M₁ :=
h.symm
-#align continuous_linear_equiv.simps.symm_apply ContinuousLinearEquiv.Simps.symmApply
+#align continuous_linear_equiv.simps.symm_apply ContinuousLinearEquiv.Simps.symm_apply
+-/
initialize_simps_projections ContinuousLinearEquiv (to_linear_equiv_to_fun → apply,
to_linear_equiv_inv_fun → symm_apply)
+/- warning: continuous_linear_equiv.symm_map_nhds_eq -> ContinuousLinearEquiv.symm_map_nhds_eq is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (x : M₁), Eq.{succ u3} (Filter.{u3} M₁) (Filter.map.{u4, u3} M₂ M₁ (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (fun (_x : ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) => M₂ -> M₁) (ContinuousLinearEquiv.hasCoeToFun.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (ContinuousLinearEquiv.symm.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) (nhds.{u4} M₂ _inst_16 (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e x))) (nhds.{u3} M₁ _inst_12 x)
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (x : M₁), Eq.{succ u2} (Filter.{u2} M₁) (Filter.map.{u1, u2} M₂ M₁ (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M₁) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ M₁ _inst_16 _inst_12 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22)))) (ContinuousLinearEquiv.symm.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) (nhds.{u1} M₂ _inst_16 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e x))) (nhds.{u2} M₁ _inst_12 x)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_map_nhds_eq ContinuousLinearEquiv.symm_map_nhds_eqₓ'. -/
theorem symm_map_nhds_eq (e : M₁ ≃SL[σ₁₂] M₂) (x : M₁) : map e.symm (𝓝 (e x)) = 𝓝 x :=
e.toHomeomorph.symm_map_nhds_eq x
#align continuous_linear_equiv.symm_map_nhds_eq ContinuousLinearEquiv.symm_map_nhds_eq
@@ -2068,6 +3322,7 @@ omit σ₂₁
include σ₂₁ σ₃₂ σ₃₁
+#print ContinuousLinearEquiv.trans /-
/-- The composition of two continuous linear equivalences as a continuous linear equivalence. -/
@[trans]
protected def trans (e₁ : M₁ ≃SL[σ₁₂] M₂) (e₂ : M₂ ≃SL[σ₂₃] M₃) : M₁ ≃SL[σ₁₃] M₃ :=
@@ -2077,9 +3332,16 @@ protected def trans (e₁ : M₁ ≃SL[σ₁₂] M₂) (e₂ : M₂ ≃SL[σ₂
continuous_toFun := e₂.continuous_toFun.comp e₁.continuous_toFun
continuous_invFun := e₁.continuous_invFun.comp e₂.continuous_invFun }
#align continuous_linear_equiv.trans ContinuousLinearEquiv.trans
+-/
include σ₁₃
+/- warning: continuous_linear_equiv.trans_to_linear_equiv -> ContinuousLinearEquiv.trans_toLinearEquiv is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} {R₃ : Type.{u3}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : Semiring.{u3} R₃] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {σ₂₃ : RingHom.{u2, u3} R₂ R₃ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {σ₃₂ : RingHom.{u3, u2} R₃ R₂ (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} [_inst_6 : RingHomInvPair.{u2, u3} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂] [_inst_7 : RingHomInvPair.{u3, u2} R₃ R₂ _inst_3 _inst_2 σ₃₂ σ₂₃] {σ₁₃ : RingHom.{u1, u3} R₁ R₃ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {σ₃₁ : RingHom.{u3, u1} R₃ R₁ (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_8 : RingHomInvPair.{u1, u3} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁] [_inst_9 : RingHomInvPair.{u3, u1} R₃ R₁ _inst_3 _inst_1 σ₃₁ σ₁₃] [_inst_10 : RingHomCompTriple.{u1, u2, u3} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] [_inst_11 : RingHomCompTriple.{u3, u2, u1} R₃ R₂ R₁ _inst_3 _inst_2 _inst_1 σ₃₂ σ₂₁ σ₃₁] {M₁ : Type.{u4}} [_inst_12 : TopologicalSpace.{u4} M₁] [_inst_13 : AddCommMonoid.{u4} M₁] {M₂ : Type.{u5}} [_inst_16 : TopologicalSpace.{u5} M₂] [_inst_17 : AddCommMonoid.{u5} M₂] {M₃ : Type.{u6}} [_inst_18 : TopologicalSpace.{u6} M₃] [_inst_19 : AddCommMonoid.{u6} M₃] [_inst_22 : Module.{u1, u4} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u5} R₂ M₂ _inst_2 _inst_17] [_inst_25 : Module.{u3, u6} R₃ M₃ _inst_3 _inst_19] (e₁ : ContinuousLinearEquiv.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (e₂ : ContinuousLinearEquiv.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25), Eq.{max (succ u4) (succ u6)} (LinearEquiv.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁ _inst_8 _inst_9 M₁ M₃ _inst_13 _inst_19 _inst_22 _inst_25) (ContinuousLinearEquiv.toLinearEquiv.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁ _inst_8 _inst_9 M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25 (ContinuousLinearEquiv.trans.{u1, u2, u3, u4, u5, u6} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₁ _inst_4 _inst_5 σ₂₃ σ₃₂ _inst_6 _inst_7 σ₁₃ σ₃₁ _inst_8 _inst_9 _inst_10 _inst_11 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_22 _inst_24 _inst_25 e₁ e₂)) (LinearEquiv.trans.{u1, u2, u3, u4, u5, u6} R₁ R₂ R₃ M₁ M₂ M₃ _inst_1 _inst_2 _inst_3 _inst_13 _inst_17 _inst_19 _inst_22 _inst_24 _inst_25 σ₁₂ σ₂₃ σ₁₃ σ₂₁ σ₃₂ σ₃₁ _inst_10 _inst_11 _inst_4 _inst_6 _inst_8 _inst_5 _inst_7 _inst_9 (ContinuousLinearEquiv.toLinearEquiv.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e₁) (ContinuousLinearEquiv.toLinearEquiv.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25 e₂))
+but is expected to have type
+ forall {R₁ : Type.{u6}} {R₂ : Type.{u5}} {R₃ : Type.{u2}} [_inst_1 : Semiring.{u6} R₁] [_inst_2 : Semiring.{u5} R₂] [_inst_3 : Semiring.{u2} R₃] {σ₁₂ : RingHom.{u6, u5} R₁ R₂ (Semiring.toNonAssocSemiring.{u6} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u5} R₂ _inst_2)} {σ₂₁ : RingHom.{u5, u6} R₂ R₁ (Semiring.toNonAssocSemiring.{u5} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u6} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u6, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u5, u6} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {σ₂₃ : RingHom.{u5, u2} R₂ R₃ (Semiring.toNonAssocSemiring.{u5} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u2} R₃ _inst_3)} {σ₃₂ : RingHom.{u2, u5} R₃ R₂ (Semiring.toNonAssocSemiring.{u2} R₃ _inst_3) (Semiring.toNonAssocSemiring.{u5} R₂ _inst_2)} [_inst_6 : RingHomInvPair.{u5, u2} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂] [_inst_7 : RingHomInvPair.{u2, u5} R₃ R₂ _inst_3 _inst_2 σ₃₂ σ₂₃] {σ₁₃ : RingHom.{u6, u2} R₁ R₃ (Semiring.toNonAssocSemiring.{u6} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₃ _inst_3)} {σ₃₁ : RingHom.{u2, u6} R₃ R₁ (Semiring.toNonAssocSemiring.{u2} R₃ _inst_3) (Semiring.toNonAssocSemiring.{u6} R₁ _inst_1)} [_inst_8 : RingHomInvPair.{u6, u2} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁] [_inst_9 : RingHomInvPair.{u2, u6} R₃ R₁ _inst_3 _inst_1 σ₃₁ σ₁₃] [_inst_10 : RingHomCompTriple.{u6, u5, u2} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] [_inst_11 : RingHomCompTriple.{u2, u5, u6} R₃ R₂ R₁ _inst_3 _inst_2 _inst_1 σ₃₂ σ₂₁ σ₃₁] {M₁ : Type.{u4}} [_inst_12 : TopologicalSpace.{u4} M₁] [_inst_13 : AddCommMonoid.{u4} M₁] {M₂ : Type.{u3}} [_inst_16 : TopologicalSpace.{u3} M₂] [_inst_17 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u1}} [_inst_18 : TopologicalSpace.{u1} M₃] [_inst_19 : AddCommMonoid.{u1} M₃] [_inst_22 : Module.{u6, u4} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u5, u3} R₂ M₂ _inst_2 _inst_17] [_inst_25 : Module.{u2, u1} R₃ M₃ _inst_3 _inst_19] (e₁ : ContinuousLinearEquiv.{u6, u5, u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (e₂ : ContinuousLinearEquiv.{u5, u2, u3, u1} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25), Eq.{max (succ u4) (succ u1)} (LinearEquiv.{u6, u2, u4, u1} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁ _inst_8 _inst_9 M₁ M₃ _inst_13 _inst_19 _inst_22 _inst_25) (ContinuousLinearEquiv.toLinearEquiv.{u6, u2, u4, u1} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁ _inst_8 _inst_9 M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25 (ContinuousLinearEquiv.trans.{u6, u5, u2, u4, u3, u1} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₁ _inst_4 _inst_5 σ₂₃ σ₃₂ _inst_6 _inst_7 σ₁₃ σ₃₁ _inst_8 _inst_9 _inst_10 _inst_11 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_22 _inst_24 _inst_25 e₁ e₂)) (LinearEquiv.trans.{u6, u5, u2, u4, u3, u1} R₁ R₂ R₃ M₁ M₂ M₃ _inst_1 _inst_2 _inst_3 _inst_13 _inst_17 _inst_19 _inst_22 _inst_24 _inst_25 σ₁₂ σ₂₃ σ₁₃ σ₂₁ σ₃₂ σ₃₁ _inst_10 _inst_11 _inst_4 _inst_6 _inst_8 _inst_5 _inst_7 _inst_9 (ContinuousLinearEquiv.toLinearEquiv.{u6, u5, u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e₁) (ContinuousLinearEquiv.toLinearEquiv.{u5, u2, u3, u1} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25 e₂))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.trans_to_linear_equiv ContinuousLinearEquiv.trans_toLinearEquivₓ'. -/
@[simp]
theorem trans_toLinearEquiv (e₁ : M₁ ≃SL[σ₁₂] M₂) (e₂ : M₂ ≃SL[σ₂₃] M₃) :
(e₁.trans e₂).toLinearEquiv = e₁.toLinearEquiv.trans e₂.toLinearEquiv :=
@@ -2090,6 +3352,12 @@ theorem trans_toLinearEquiv (e₁ : M₁ ≃SL[σ₁₂] M₂) (e₂ : M₂ ≃S
omit σ₁₃ σ₂₁ σ₃₂ σ₃₁
+/- warning: continuous_linear_equiv.prod -> ContinuousLinearEquiv.prod is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.prod ContinuousLinearEquiv.prodₓ'. -/
/-- Product of two continuous linear equivalences. The map comes from `equiv.prod_congr`. -/
def prod [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M₁ ≃L[R₁] M₂) (e' : M₃ ≃L[R₁] M₄) :
(M₁ × M₃) ≃L[R₁] M₂ × M₄ :=
@@ -2100,12 +3368,24 @@ def prod [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M₁ ≃L
continuous_invFun := e.continuous_invFun.Prod_map e'.continuous_invFun }
#align continuous_linear_equiv.prod ContinuousLinearEquiv.prod
+/- warning: continuous_linear_equiv.prod_apply -> ContinuousLinearEquiv.prod_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.prod_apply ContinuousLinearEquiv.prod_applyₓ'. -/
@[simp, norm_cast]
theorem prod_apply [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M₁ ≃L[R₁] M₂)
(e' : M₃ ≃L[R₁] M₄) (x) : e.Prod e' x = (e x.1, e' x.2) :=
rfl
#align continuous_linear_equiv.prod_apply ContinuousLinearEquiv.prod_apply
+/- warning: continuous_linear_equiv.coe_prod -> ContinuousLinearEquiv.coe_prod is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_16 : TopologicalSpace.{u3} M₂] [_inst_17 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u4}} [_inst_18 : TopologicalSpace.{u4} M₃] [_inst_19 : AddCommMonoid.{u4} M₃] {M₄ : Type.{u5}} [_inst_20 : TopologicalSpace.{u5} M₄] [_inst_21 : AddCommMonoid.{u5} M₄] [_inst_22 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_13] [_inst_26 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_17] [_inst_27 : Module.{u1, u4} R₁ M₃ _inst_1 _inst_19] [_inst_28 : Module.{u1, u5} R₁ M₄ _inst_1 _inst_21] (e : ContinuousLinearEquiv.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHomInvPair.ids.{u1} R₁ _inst_1) (RingHomInvPair.ids.{u1} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26) (e' : ContinuousLinearEquiv.{u1, u1, u4, 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+but is expected to have type
+ forall {R₁ : Type.{u5}} [_inst_1 : Semiring.{u5} R₁] {M₁ : Type.{u1}} [_inst_12 : TopologicalSpace.{u1} M₁] [_inst_13 : AddCommMonoid.{u1} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] {M₃ : Type.{u3}} [_inst_18 : TopologicalSpace.{u3} M₃] [_inst_19 : AddCommMonoid.{u3} M₃] {M₄ : Type.{u2}} [_inst_20 : TopologicalSpace.{u2} M₄] [_inst_21 : AddCommMonoid.{u2} M₄] [_inst_22 : Module.{u5, u1} R₁ M₁ _inst_1 _inst_13] [_inst_26 : Module.{u5, u4} R₁ M₂ _inst_1 _inst_17] [_inst_27 : Module.{u5, u3} R₁ M₃ _inst_1 _inst_19] [_inst_28 : Module.{u5, u2} R₁ M₄ _inst_1 _inst_21] (e : ContinuousLinearEquiv.{u5, u5, u1, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHomInvPair.ids.{u5} R₁ _inst_1) (RingHomInvPair.ids.{u5} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26) (e' : ContinuousLinearEquiv.{u5, u5, u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHomInvPair.ids.{u5} R₁ _inst_1) (RingHomInvPair.ids.{u5} R₁ _inst_1) M₃ _inst_18 _inst_19 M₄ _inst_20 _inst_21 _inst_27 _inst_28), Eq.{max (max (max (succ u1) (succ u4)) (succ u3)) (succ u2)} (ContinuousLinearMap.{u5, u5, max u1 u3, max u4 u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (Prod.{u1, u3} M₁ M₃) (instTopologicalSpaceProd.{u1, u3} M₁ M₃ _inst_12 _inst_18) (Prod.instAddCommMonoidSum.{u1, u3} M₁ M₃ _inst_13 _inst_19) (Prod.{u4, u2} M₂ M₄) (instTopologicalSpaceProd.{u4, u2} M₂ M₄ _inst_16 _inst_20) (Prod.instAddCommMonoidSum.{u4, u2} M₂ M₄ _inst_17 _inst_21) (Prod.module.{u5, u1, u3} R₁ M₁ M₃ _inst_1 _inst_13 _inst_19 _inst_22 _inst_27) (Prod.module.{u5, u4, u2} R₁ M₂ M₄ _inst_1 _inst_17 _inst_21 _inst_26 _inst_28)) (ContinuousLinearEquiv.toContinuousLinearMap.{u5, u5, max u1 u3, max u4 u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHomInvPair.ids.{u5} R₁ _inst_1) (RingHomInvPair.ids.{u5} R₁ _inst_1) (Prod.{u1, u3} M₁ M₃) (instTopologicalSpaceProd.{u1, u3} M₁ M₃ _inst_12 _inst_18) (Prod.instAddCommMonoidSum.{u1, u3} M₁ M₃ _inst_13 _inst_19) (Prod.{u4, u2} M₂ M₄) (instTopologicalSpaceProd.{u4, u2} M₂ M₄ _inst_16 _inst_20) (Prod.instAddCommMonoidSum.{u4, u2} M₂ M₄ _inst_17 _inst_21) (Prod.module.{u5, u1, u3} R₁ M₁ M₃ _inst_1 _inst_13 _inst_19 _inst_22 _inst_27) (Prod.module.{u5, u4, u2} R₁ M₂ M₄ _inst_1 _inst_17 _inst_21 _inst_26 _inst_28) (ContinuousLinearEquiv.prod.{u5, u1, u4, u3, u2} R₁ _inst_1 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 M₄ _inst_20 _inst_21 _inst_22 _inst_26 _inst_27 _inst_28 e e')) (ContinuousLinearMap.prodMap.{u5, u1, u4, u3, u2} R₁ _inst_1 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 M₄ _inst_20 _inst_21 _inst_22 _inst_26 _inst_27 _inst_28 (ContinuousLinearEquiv.toContinuousLinearMap.{u5, u5, u1, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHomInvPair.ids.{u5} R₁ _inst_1) (RingHomInvPair.ids.{u5} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26 e) (ContinuousLinearEquiv.toContinuousLinearMap.{u5, u5, u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHomInvPair.ids.{u5} R₁ _inst_1) (RingHomInvPair.ids.{u5} R₁ _inst_1) M₃ _inst_18 _inst_19 M₄ _inst_20 _inst_21 _inst_27 _inst_28 e'))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_prod ContinuousLinearEquiv.coe_prodₓ'. -/
@[simp, norm_cast]
theorem coe_prod [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M₁ ≃L[R₁] M₂)
(e' : M₃ ≃L[R₁] M₄) :
@@ -2113,6 +3393,12 @@ theorem coe_prod [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M
rfl
#align continuous_linear_equiv.coe_prod ContinuousLinearEquiv.coe_prod
+/- warning: continuous_linear_equiv.prod_symm -> ContinuousLinearEquiv.prod_symm is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} [_inst_1 : Semiring.{u1} R₁] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u3}} [_inst_16 : TopologicalSpace.{u3} M₂] [_inst_17 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u4}} [_inst_18 : TopologicalSpace.{u4} M₃] [_inst_19 : AddCommMonoid.{u4} M₃] {M₄ : Type.{u5}} [_inst_20 : TopologicalSpace.{u5} M₄] [_inst_21 : AddCommMonoid.{u5} M₄] [_inst_22 : Module.{u1, u2} R₁ M₁ _inst_1 _inst_13] [_inst_26 : Module.{u1, u3} R₁ M₂ _inst_1 _inst_17] [_inst_27 : Module.{u1, u4} R₁ M₃ _inst_1 _inst_19] [_inst_28 : Module.{u1, u5} R₁ M₄ _inst_1 _inst_21] (e : ContinuousLinearEquiv.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHomInvPair.ids.{u1} R₁ _inst_1) (RingHomInvPair.ids.{u1} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26) (e' : ContinuousLinearEquiv.{u1, u1, u4, u5} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHomInvPair.ids.{u1} R₁ _inst_1) (RingHomInvPair.ids.{u1} R₁ _inst_1) M₃ _inst_18 _inst_19 M₄ _inst_20 _inst_21 _inst_27 _inst_28), Eq.{max (succ (max u3 u5)) (succ (max u2 u4))} (ContinuousLinearEquiv.{u1, u1, max u3 u5, max u2 u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHomInvPair.ids.{u1} R₁ _inst_1) (RingHomInvPair.ids.{u1} R₁ _inst_1) (Prod.{u3, u5} M₂ M₄) (Prod.topologicalSpace.{u3, u5} M₂ M₄ _inst_16 _inst_20) (Prod.addCommMonoid.{u3, u5} M₂ M₄ _inst_17 _inst_21) (Prod.{u2, u4} M₁ M₃) (Prod.topologicalSpace.{u2, u4} M₁ M₃ _inst_12 _inst_18) (Prod.addCommMonoid.{u2, u4} M₁ M₃ _inst_13 _inst_19) (Prod.module.{u1, u3, u5} R₁ M₂ M₄ _inst_1 _inst_17 _inst_21 _inst_26 _inst_28) (Prod.module.{u1, u2, u4} R₁ M₁ M₃ _inst_1 _inst_13 _inst_19 _inst_22 _inst_27)) (ContinuousLinearEquiv.symm.{u1, u1, max u2 u4, max u3 u5} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHomInvPair.ids.{u1} R₁ _inst_1) (RingHomInvPair.ids.{u1} R₁ _inst_1) (Prod.{u2, u4} M₁ M₃) (Prod.topologicalSpace.{u2, u4} M₁ M₃ _inst_12 _inst_18) (Prod.addCommMonoid.{u2, u4} M₁ M₃ _inst_13 _inst_19) (Prod.{u3, u5} M₂ M₄) (Prod.topologicalSpace.{u3, u5} M₂ M₄ _inst_16 _inst_20) (Prod.addCommMonoid.{u3, u5} M₂ M₄ _inst_17 _inst_21) (Prod.module.{u1, u2, u4} R₁ M₁ M₃ _inst_1 _inst_13 _inst_19 _inst_22 _inst_27) (Prod.module.{u1, u3, u5} R₁ M₂ M₄ _inst_1 _inst_17 _inst_21 _inst_26 _inst_28) (ContinuousLinearEquiv.prod.{u1, u2, u3, u4, u5} R₁ _inst_1 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 M₄ _inst_20 _inst_21 _inst_22 _inst_26 _inst_27 _inst_28 e e')) (ContinuousLinearEquiv.prod.{u1, u3, u2, u5, u4} R₁ _inst_1 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 M₄ _inst_20 _inst_21 M₃ _inst_18 _inst_19 _inst_26 _inst_22 _inst_28 _inst_27 (ContinuousLinearEquiv.symm.{u1, u1, u2, u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHomInvPair.ids.{u1} R₁ _inst_1) (RingHomInvPair.ids.{u1} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26 e) (ContinuousLinearEquiv.symm.{u1, u1, u4, u5} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHom.id.{u1} R₁ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)) (RingHomInvPair.ids.{u1} R₁ _inst_1) (RingHomInvPair.ids.{u1} R₁ _inst_1) M₃ _inst_18 _inst_19 M₄ _inst_20 _inst_21 _inst_27 _inst_28 e'))
+but is expected to have type
+ forall {R₁ : Type.{u5}} [_inst_1 : Semiring.{u5} R₁] {M₁ : Type.{u1}} [_inst_12 : TopologicalSpace.{u1} M₁] [_inst_13 : AddCommMonoid.{u1} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] {M₃ : Type.{u3}} [_inst_18 : TopologicalSpace.{u3} M₃] [_inst_19 : AddCommMonoid.{u3} M₃] {M₄ : Type.{u2}} [_inst_20 : TopologicalSpace.{u2} M₄] [_inst_21 : AddCommMonoid.{u2} M₄] [_inst_22 : Module.{u5, u1} R₁ M₁ _inst_1 _inst_13] [_inst_26 : Module.{u5, u4} R₁ M₂ _inst_1 _inst_17] [_inst_27 : Module.{u5, u3} R₁ M₃ _inst_1 _inst_19] [_inst_28 : Module.{u5, u2} R₁ M₄ _inst_1 _inst_21] (e : ContinuousLinearEquiv.{u5, u5, u1, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHomInvPair.ids.{u5} R₁ _inst_1) (RingHomInvPair.ids.{u5} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26) (e' : ContinuousLinearEquiv.{u5, u5, u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHomInvPair.ids.{u5} R₁ _inst_1) (RingHomInvPair.ids.{u5} R₁ _inst_1) M₃ _inst_18 _inst_19 M₄ _inst_20 _inst_21 _inst_27 _inst_28), Eq.{max (max (max (succ u1) (succ u4)) (succ u3)) (succ u2)} (ContinuousLinearEquiv.{u5, u5, max u4 u2, max u1 u3} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHomInvPair.ids.{u5} R₁ _inst_1) (RingHomInvPair.ids.{u5} R₁ _inst_1) (Prod.{u4, u2} M₂ M₄) (instTopologicalSpaceProd.{u4, u2} M₂ M₄ _inst_16 _inst_20) (Prod.instAddCommMonoidSum.{u4, u2} M₂ M₄ _inst_17 _inst_21) (Prod.{u1, u3} M₁ M₃) (instTopologicalSpaceProd.{u1, u3} M₁ M₃ _inst_12 _inst_18) (Prod.instAddCommMonoidSum.{u1, u3} M₁ M₃ _inst_13 _inst_19) (Prod.module.{u5, u4, u2} R₁ M₂ M₄ _inst_1 _inst_17 _inst_21 _inst_26 _inst_28) (Prod.module.{u5, u1, u3} R₁ M₁ M₃ _inst_1 _inst_13 _inst_19 _inst_22 _inst_27)) (ContinuousLinearEquiv.symm.{u5, u5, max u1 u3, max u4 u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHomInvPair.ids.{u5} R₁ _inst_1) (RingHomInvPair.ids.{u5} R₁ _inst_1) (Prod.{u1, u3} M₁ M₃) (instTopologicalSpaceProd.{u1, u3} M₁ M₃ _inst_12 _inst_18) (Prod.instAddCommMonoidSum.{u1, u3} M₁ M₃ _inst_13 _inst_19) (Prod.{u4, u2} M₂ M₄) (instTopologicalSpaceProd.{u4, u2} M₂ M₄ _inst_16 _inst_20) (Prod.instAddCommMonoidSum.{u4, u2} M₂ M₄ _inst_17 _inst_21) (Prod.module.{u5, u1, u3} R₁ M₁ M₃ _inst_1 _inst_13 _inst_19 _inst_22 _inst_27) (Prod.module.{u5, u4, u2} R₁ M₂ M₄ _inst_1 _inst_17 _inst_21 _inst_26 _inst_28) (ContinuousLinearEquiv.prod.{u5, u1, u4, u3, u2} R₁ _inst_1 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 M₄ _inst_20 _inst_21 _inst_22 _inst_26 _inst_27 _inst_28 e e')) (ContinuousLinearEquiv.prod.{u5, u4, u1, u2, u3} R₁ _inst_1 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 M₄ _inst_20 _inst_21 M₃ _inst_18 _inst_19 _inst_26 _inst_22 _inst_28 _inst_27 (ContinuousLinearEquiv.symm.{u5, u5, u1, u4} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHomInvPair.ids.{u5} R₁ _inst_1) (RingHomInvPair.ids.{u5} R₁ _inst_1) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_26 e) (ContinuousLinearEquiv.symm.{u5, u5, u3, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHom.id.{u5} R₁ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)) (RingHomInvPair.ids.{u5} R₁ _inst_1) (RingHomInvPair.ids.{u5} R₁ _inst_1) M₃ _inst_18 _inst_19 M₄ _inst_20 _inst_21 _inst_27 _inst_28 e'))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.prod_symm ContinuousLinearEquiv.prod_symmₓ'. -/
theorem prod_symm [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M₁ ≃L[R₁] M₂)
(e' : M₃ ≃L[R₁] M₄) : (e.Prod e').symm = e.symm.Prod e'.symm :=
rfl
@@ -2120,20 +3406,44 @@ theorem prod_symm [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e :
include σ₂₁
+/- warning: continuous_linear_equiv.bijective -> ContinuousLinearEquiv.bijective is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24), Function.Bijective.{succ u3, succ u4} M₁ M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e)
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24), Function.Bijective.{succ u2, succ u1} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.bijective ContinuousLinearEquiv.bijectiveₓ'. -/
protected theorem bijective (e : M₁ ≃SL[σ₁₂] M₂) : Function.Bijective e :=
e.toLinearEquiv.toEquiv.Bijective
#align continuous_linear_equiv.bijective ContinuousLinearEquiv.bijective
+/- warning: continuous_linear_equiv.injective -> ContinuousLinearEquiv.injective is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24), Function.Injective.{succ u3, succ u4} M₁ M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e)
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24), Function.Injective.{succ u2, succ u1} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.injective ContinuousLinearEquiv.injectiveₓ'. -/
protected theorem injective (e : M₁ ≃SL[σ₁₂] M₂) : Function.Injective e :=
e.toLinearEquiv.toEquiv.Injective
#align continuous_linear_equiv.injective ContinuousLinearEquiv.injective
+/- warning: continuous_linear_equiv.surjective -> ContinuousLinearEquiv.surjective is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24), Function.Surjective.{succ u3, succ u4} M₁ M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e)
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24), Function.Surjective.{succ u2, succ u1} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.surjective ContinuousLinearEquiv.surjectiveₓ'. -/
protected theorem surjective (e : M₁ ≃SL[σ₁₂] M₂) : Function.Surjective e :=
e.toLinearEquiv.toEquiv.Surjective
#align continuous_linear_equiv.surjective ContinuousLinearEquiv.surjective
include σ₃₂ σ₃₁ σ₁₃
+/- warning: continuous_linear_equiv.trans_apply -> ContinuousLinearEquiv.trans_apply is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} {R₃ : Type.{u3}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : Semiring.{u3} R₃] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {σ₂₃ : RingHom.{u2, u3} R₂ R₃ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {σ₃₂ : RingHom.{u3, u2} R₃ R₂ (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} [_inst_6 : RingHomInvPair.{u2, u3} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂] [_inst_7 : RingHomInvPair.{u3, u2} R₃ R₂ _inst_3 _inst_2 σ₃₂ σ₂₃] {σ₁₃ : RingHom.{u1, u3} R₁ R₃ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {σ₃₁ : RingHom.{u3, u1} R₃ R₁ (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_8 : RingHomInvPair.{u1, u3} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁] [_inst_9 : RingHomInvPair.{u3, u1} R₃ R₁ _inst_3 _inst_1 σ₃₁ σ₁₃] [_inst_10 : RingHomCompTriple.{u1, u2, u3} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] [_inst_11 : RingHomCompTriple.{u3, u2, u1} R₃ R₂ R₁ _inst_3 _inst_2 _inst_1 σ₃₂ σ₂₁ σ₃₁] {M₁ : Type.{u4}} [_inst_12 : TopologicalSpace.{u4} M₁] [_inst_13 : AddCommMonoid.{u4} M₁] {M₂ : Type.{u5}} [_inst_16 : TopologicalSpace.{u5} M₂] [_inst_17 : AddCommMonoid.{u5} M₂] {M₃ : Type.{u6}} [_inst_18 : TopologicalSpace.{u6} M₃] [_inst_19 : AddCommMonoid.{u6} M₃] [_inst_22 : Module.{u1, u4} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u5} R₂ M₂ _inst_2 _inst_17] [_inst_25 : Module.{u3, u6} R₃ M₃ _inst_3 _inst_19] (e₁ : ContinuousLinearEquiv.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (e₂ : ContinuousLinearEquiv.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25) (c : M₁), Eq.{succ u6} M₃ (coeFn.{max (succ u4) (succ u6), max (succ u4) (succ u6)} (ContinuousLinearEquiv.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁ _inst_8 _inst_9 M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25) (fun (_x : ContinuousLinearEquiv.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁ _inst_8 _inst_9 M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25) => M₁ -> M₃) (ContinuousLinearEquiv.hasCoeToFun.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁ _inst_8 _inst_9 M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25) (ContinuousLinearEquiv.trans.{u1, u2, u3, u4, u5, u6} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₁ _inst_4 _inst_5 σ₂₃ σ₃₂ _inst_6 _inst_7 σ₁₃ σ₃₁ _inst_8 _inst_9 _inst_10 _inst_11 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_22 _inst_24 _inst_25 e₁ e₂) c) (coeFn.{max (succ u5) (succ u6), max (succ u5) (succ u6)} (ContinuousLinearEquiv.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25) (fun (_x : ContinuousLinearEquiv.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25) => M₂ -> M₃) (ContinuousLinearEquiv.hasCoeToFun.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25) e₂ (coeFn.{max (succ u4) (succ u5), max (succ u4) (succ u5)} (ContinuousLinearEquiv.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e₁ c))
+but is expected to have type
+ forall {R₁ : Type.{u6}} {R₂ : Type.{u5}} {R₃ : Type.{u2}} [_inst_1 : Semiring.{u6} R₁] [_inst_2 : Semiring.{u5} R₂] [_inst_3 : Semiring.{u2} R₃] {σ₁₂ : RingHom.{u6, u5} R₁ R₂ (Semiring.toNonAssocSemiring.{u6} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u5} R₂ _inst_2)} {σ₂₁ : RingHom.{u5, u6} R₂ R₁ (Semiring.toNonAssocSemiring.{u5} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u6} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u6, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u5, u6} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {σ₂₃ : RingHom.{u5, u2} R₂ R₃ (Semiring.toNonAssocSemiring.{u5} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u2} R₃ _inst_3)} {σ₃₂ : RingHom.{u2, u5} R₃ R₂ (Semiring.toNonAssocSemiring.{u2} R₃ _inst_3) (Semiring.toNonAssocSemiring.{u5} R₂ _inst_2)} [_inst_6 : RingHomInvPair.{u5, u2} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂] [_inst_7 : RingHomInvPair.{u2, u5} R₃ R₂ _inst_3 _inst_2 σ₃₂ σ₂₃] {σ₁₃ : RingHom.{u6, u2} R₁ R₃ (Semiring.toNonAssocSemiring.{u6} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₃ _inst_3)} {σ₃₁ : RingHom.{u2, u6} R₃ R₁ (Semiring.toNonAssocSemiring.{u2} R₃ _inst_3) (Semiring.toNonAssocSemiring.{u6} R₁ _inst_1)} [_inst_8 : RingHomInvPair.{u6, u2} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁] [_inst_9 : RingHomInvPair.{u2, u6} R₃ R₁ _inst_3 _inst_1 σ₃₁ σ₁₃] [_inst_10 : RingHomCompTriple.{u6, u5, u2} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] [_inst_11 : RingHomCompTriple.{u2, u5, u6} R₃ R₂ R₁ _inst_3 _inst_2 _inst_1 σ₃₂ σ₂₁ σ₃₁] {M₁ : Type.{u4}} [_inst_12 : TopologicalSpace.{u4} M₁] [_inst_13 : AddCommMonoid.{u4} M₁] {M₂ : Type.{u3}} [_inst_16 : TopologicalSpace.{u3} M₂] [_inst_17 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u1}} [_inst_18 : TopologicalSpace.{u1} M₃] [_inst_19 : AddCommMonoid.{u1} M₃] [_inst_22 : Module.{u6, u4} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u5, u3} R₂ M₂ _inst_2 _inst_17] [_inst_25 : Module.{u2, u1} R₃ M₃ _inst_3 _inst_19] (e₁ : ContinuousLinearEquiv.{u6, u5, u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (e₂ : ContinuousLinearEquiv.{u5, u2, u3, u1} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25) (c : M₁), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₃) c) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (ContinuousLinearEquiv.{u6, u2, u4, u1} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁ _inst_8 _inst_9 M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₃) _x) (ContinuousMapClass.toFunLike.{max u4 u1, u4, u1} (ContinuousLinearEquiv.{u6, u2, u4, u1} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁ _inst_8 _inst_9 M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25) M₁ M₃ _inst_12 _inst_18 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u4 u1, u6, u2, u4, u1} (ContinuousLinearEquiv.{u6, u2, u4, u1} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁ _inst_8 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+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.trans_apply ContinuousLinearEquiv.trans_applyₓ'. -/
@[simp]
theorem trans_apply (e₁ : M₁ ≃SL[σ₁₂] M₂) (e₂ : M₂ ≃SL[σ₂₃] M₃) (c : M₁) :
(e₁.trans e₂) c = e₂ (e₁ c) :=
@@ -2142,11 +3452,23 @@ theorem trans_apply (e₁ : M₁ ≃SL[σ₁₂] M₂) (e₂ : M₂ ≃SL[σ₂
omit σ₃₂ σ₃₁ σ₁₃
+/- warning: continuous_linear_equiv.apply_symm_apply -> ContinuousLinearEquiv.apply_symm_apply is a dubious translation:
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+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (c : M₂), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ (fun (a : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M₁) a) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ M₁ _inst_16 _inst_12 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22)))) (ContinuousLinearEquiv.symm.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e) c)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M₁) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ M₁ _inst_16 _inst_12 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22)))) (ContinuousLinearEquiv.symm.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e) c)) c
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.apply_symm_apply ContinuousLinearEquiv.apply_symm_applyₓ'. -/
@[simp]
theorem apply_symm_apply (e : M₁ ≃SL[σ₁₂] M₂) (c : M₂) : e (e.symm c) = c :=
e.1.right_inv c
#align continuous_linear_equiv.apply_symm_apply ContinuousLinearEquiv.apply_symm_apply
+/- warning: continuous_linear_equiv.symm_apply_apply -> ContinuousLinearEquiv.symm_apply_apply is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (b : M₁), Eq.{succ u3} M₁ (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (fun (_x : ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) => M₂ -> M₁) (ContinuousLinearEquiv.hasCoeToFun.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (ContinuousLinearEquiv.symm.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e b)) b
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (b : M₁), Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M₁) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (a : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) a) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e b)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M₁) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ M₁ _inst_16 _inst_12 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22)))) (ContinuousLinearEquiv.symm.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e b)) b
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_apply_apply ContinuousLinearEquiv.symm_apply_applyₓ'. -/
@[simp]
theorem symm_apply_apply (e : M₁ ≃SL[σ₁₂] M₂) (b : M₁) : e.symm (e b) = b :=
e.1.left_inv b
@@ -2154,6 +3476,12 @@ theorem symm_apply_apply (e : M₁ ≃SL[σ₁₂] M₂) (b : M₁) : e.symm (e
include σ₁₂ σ₂₃ σ₁₃ σ₃₁
+/- warning: continuous_linear_equiv.symm_trans_apply -> ContinuousLinearEquiv.symm_trans_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+ forall {R₁ : Type.{u5}} {R₂ : Type.{u6}} {R₃ : Type.{u2}} [_inst_1 : Semiring.{u5} R₁] [_inst_2 : Semiring.{u6} R₂] [_inst_3 : Semiring.{u2} R₃] {σ₁₂ : RingHom.{u5, u6} R₁ R₂ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2)} {σ₂₁ : RingHom.{u6, u5} R₂ R₁ (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u5, u6} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u6, u5} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {σ₂₃ : RingHom.{u6, u2} R₂ R₃ (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u2} R₃ _inst_3)} {σ₃₂ : RingHom.{u2, u6} R₃ R₂ (Semiring.toNonAssocSemiring.{u2} R₃ _inst_3) (Semiring.toNonAssocSemiring.{u6} R₂ _inst_2)} [_inst_6 : RingHomInvPair.{u6, u2} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂] [_inst_7 : RingHomInvPair.{u2, u6} R₃ R₂ _inst_3 _inst_2 σ₃₂ σ₂₃] {σ₁₃ : RingHom.{u5, u2} R₁ R₃ (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₃ _inst_3)} {σ₃₁ : RingHom.{u2, u5} R₃ R₁ (Semiring.toNonAssocSemiring.{u2} R₃ _inst_3) (Semiring.toNonAssocSemiring.{u5} R₁ _inst_1)} [_inst_8 : RingHomInvPair.{u5, u2} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁] [_inst_9 : RingHomInvPair.{u2, u5} R₃ R₁ _inst_3 _inst_1 σ₃₁ σ₁₃] [_inst_10 : RingHomCompTriple.{u5, u6, u2} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] [_inst_11 : RingHomCompTriple.{u2, u6, u5} R₃ R₂ R₁ _inst_3 _inst_2 _inst_1 σ₃₂ σ₂₁ σ₃₁] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] {M₃ : Type.{u1}} [_inst_18 : TopologicalSpace.{u1} M₃] [_inst_19 : AddCommMonoid.{u1} M₃] [_inst_22 : Module.{u5, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u6, u4} R₂ M₂ _inst_2 _inst_17] [_inst_25 : Module.{u2, u1} R₃ M₃ _inst_3 _inst_19] (e₁ : ContinuousLinearEquiv.{u6, u5, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (e₂ : ContinuousLinearEquiv.{u2, u6, u1, u4} R₃ R₂ _inst_3 _inst_2 σ₃₂ σ₂₃ _inst_7 _inst_6 M₃ _inst_18 _inst_19 M₂ _inst_16 _inst_17 _inst_25 _inst_24) (c : M₁), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₃) c) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (ContinuousLinearEquiv.{u5, u2, u3, u1} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁ _inst_8 _inst_9 M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₃) _x) (ContinuousMapClass.toFunLike.{max u3 u1, u3, u1} (ContinuousLinearEquiv.{u5, u2, u3, u1} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁ _inst_8 _inst_9 M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25) M₁ M₃ _inst_12 _inst_18 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u1, u5, u2, u3, u1} (ContinuousLinearEquiv.{u5, u2, u3, u1} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁ _inst_8 _inst_9 M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25) R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u3 u1, u5, u2, u3, u1} (ContinuousLinearEquiv.{u5, u2, u3, u1} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁ _inst_8 _inst_9 M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25) R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁ _inst_8 _inst_9 M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u5, u2, u3, u1} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁ _inst_8 _inst_9 M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25)))) (ContinuousLinearEquiv.symm.{u2, u5, u1, u3} R₃ R₁ _inst_3 _inst_1 σ₃₁ σ₁₃ _inst_9 _inst_8 M₃ _inst_18 _inst_19 M₁ _inst_12 _inst_13 _inst_25 _inst_22 (ContinuousLinearEquiv.trans.{u2, u6, u5, u1, u4, u3} R₃ R₂ R₁ _inst_3 _inst_2 _inst_1 σ₃₂ σ₂₃ _inst_7 _inst_6 σ₂₁ σ₁₂ _inst_5 _inst_4 σ₃₁ σ₁₃ _inst_9 _inst_8 _inst_11 _inst_10 M₃ _inst_18 _inst_19 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_25 _inst_24 _inst_22 e₂ e₁)) c) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (ContinuousLinearEquiv.{u6, u2, u4, u1} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M₃) _x) (ContinuousMapClass.toFunLike.{max u4 u1, u4, u1} (ContinuousLinearEquiv.{u6, u2, u4, u1} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25) M₂ M₃ _inst_16 _inst_18 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u4 u1, u6, u2, u4, u1} (ContinuousLinearEquiv.{u6, u2, u4, u1} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25) R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u4 u1, u6, u2, u4, u1} (ContinuousLinearEquiv.{u6, u2, u4, u1} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25) R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u6, u2, u4, u1} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25)))) (ContinuousLinearEquiv.symm.{u2, u6, u1, u4} R₃ R₂ _inst_3 _inst_2 σ₃₂ σ₂₃ _inst_7 _inst_6 M₃ _inst_18 _inst_19 M₂ _inst_16 _inst_17 _inst_25 _inst_24 e₂) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (ContinuousLinearEquiv.{u5, u6, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u3 u4, u3, u4} (ContinuousLinearEquiv.{u5, u6, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u4, u5, u6, u3, u4} (ContinuousLinearEquiv.{u5, u6, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u3 u4, u5, u6, u3, u4} (ContinuousLinearEquiv.{u5, u6, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u5, u6, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) (ContinuousLinearEquiv.symm.{u6, u5, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 e₁) c))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_trans_apply ContinuousLinearEquiv.symm_trans_applyₓ'. -/
@[simp]
theorem symm_trans_apply (e₁ : M₂ ≃SL[σ₂₁] M₁) (e₂ : M₃ ≃SL[σ₃₂] M₂) (c : M₁) :
(e₂.trans e₁).symm c = e₂.symm (e₁.symm c) :=
@@ -2162,11 +3490,23 @@ theorem symm_trans_apply (e₁ : M₂ ≃SL[σ₂₁] M₁) (e₂ : M₃ ≃SL[
omit σ₁₂ σ₂₃ σ₁₃ σ₃₁
+/- warning: continuous_linear_equiv.symm_image_image -> ContinuousLinearEquiv.symm_image_image is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (s : Set.{u3} M₁), Eq.{succ u3} (Set.{u3} M₁) (Set.image.{u4, u3} M₂ M₁ (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (fun (_x : ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) => M₂ -> M₁) (ContinuousLinearEquiv.hasCoeToFun.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (ContinuousLinearEquiv.symm.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) (Set.image.{u3, u4} M₁ M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e) s)) s
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (s : Set.{u2} M₁), Eq.{succ u2} (Set.{u2} M₁) (Set.image.{u1, u2} M₂ M₁ (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M₁) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ M₁ _inst_16 _inst_12 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22)))) (ContinuousLinearEquiv.symm.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) (Set.image.{u2, u1} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e) s)) s
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_image_image ContinuousLinearEquiv.symm_image_imageₓ'. -/
@[simp]
theorem symm_image_image (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₁) : e.symm '' (e '' s) = s :=
e.toLinearEquiv.toEquiv.symm_image_image s
#align continuous_linear_equiv.symm_image_image ContinuousLinearEquiv.symm_image_image
+/- warning: continuous_linear_equiv.image_symm_image -> ContinuousLinearEquiv.image_symm_image is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (s : Set.{u4} M₂), Eq.{succ u4} (Set.{u4} M₂) (Set.image.{u3, u4} M₁ M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e) (Set.image.{u4, u3} M₂ M₁ (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (fun (_x : ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) => M₂ -> M₁) (ContinuousLinearEquiv.hasCoeToFun.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (ContinuousLinearEquiv.symm.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) s)) s
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (s : Set.{u1} M₂), Eq.{succ u1} (Set.{u1} M₂) (Set.image.{u2, u1} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e) (Set.image.{u1, u2} M₂ M₁ (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M₁) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ M₁ _inst_16 _inst_12 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22)))) (ContinuousLinearEquiv.symm.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) s)) s
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.image_symm_image ContinuousLinearEquiv.image_symm_imageₓ'. -/
@[simp]
theorem image_symm_image (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₂) : e '' (e.symm '' s) = s :=
e.symm.symm_image_image s
@@ -2174,6 +3514,12 @@ theorem image_symm_image (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₂) : e '' (
include σ₃₂ σ₃₁
+/- warning: continuous_linear_equiv.comp_coe -> ContinuousLinearEquiv.comp_coe is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} {R₃ : Type.{u3}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : Semiring.{u3} R₃] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {σ₂₃ : RingHom.{u2, u3} R₂ R₃ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {σ₃₂ : RingHom.{u3, u2} R₃ R₂ (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} [_inst_6 : RingHomInvPair.{u2, u3} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂] [_inst_7 : RingHomInvPair.{u3, u2} R₃ R₂ _inst_3 _inst_2 σ₃₂ σ₂₃] {σ₁₃ : RingHom.{u1, u3} R₁ R₃ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3)} {σ₃₁ : RingHom.{u3, u1} R₃ R₁ (Semiring.toNonAssocSemiring.{u3} R₃ _inst_3) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_8 : RingHomInvPair.{u1, u3} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁] [_inst_9 : RingHomInvPair.{u3, u1} R₃ R₁ _inst_3 _inst_1 σ₃₁ σ₁₃] [_inst_10 : RingHomCompTriple.{u1, u2, u3} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] [_inst_11 : RingHomCompTriple.{u3, u2, u1} R₃ R₂ R₁ _inst_3 _inst_2 _inst_1 σ₃₂ σ₂₁ σ₃₁] {M₁ : Type.{u4}} [_inst_12 : TopologicalSpace.{u4} M₁] [_inst_13 : AddCommMonoid.{u4} M₁] {M₂ : Type.{u5}} [_inst_16 : TopologicalSpace.{u5} M₂] [_inst_17 : AddCommMonoid.{u5} M₂] {M₃ : Type.{u6}} [_inst_18 : TopologicalSpace.{u6} M₃] [_inst_19 : AddCommMonoid.{u6} M₃] [_inst_22 : Module.{u1, u4} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u5} R₂ M₂ _inst_2 _inst_17] [_inst_25 : Module.{u3, u6} R₃ M₃ _inst_3 _inst_19] (f : ContinuousLinearEquiv.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (f' : ContinuousLinearEquiv.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25), Eq.{max (succ u4) (succ u6)} (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25) (ContinuousLinearMap.comp.{u1, u2, u3, u4, u5, u6} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_22 _inst_24 _inst_25 _inst_10 ((fun (a : Sort.{max (succ u5) (succ u6)}) (b : Sort.{max (succ u5) (succ u6)}) [self : HasLiftT.{max (succ u5) (succ u6), max (succ u5) (succ u6)} a b] => self.0) (ContinuousLinearEquiv.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25) (ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25) (HasLiftT.mk.{max (succ u5) (succ u6), max (succ u5) (succ u6)} (ContinuousLinearEquiv.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25) (ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25) (CoeTCₓ.coe.{max (succ u5) (succ u6), max (succ u5) (succ u6)} (ContinuousLinearEquiv.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25) (ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25) (coeBase.{max (succ u5) (succ u6), max (succ u5) (succ u6)} (ContinuousLinearEquiv.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25) (ContinuousLinearMap.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u2, u3, u5, u6} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25)))) f') ((fun (a : Sort.{max (succ u4) (succ u5)}) (b : Sort.{max (succ u4) (succ u5)}) [self : HasLiftT.{max (succ u4) (succ u5), max (succ u4) (succ u5)} a b] => self.0) (ContinuousLinearEquiv.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (ContinuousLinearMap.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (HasLiftT.mk.{max (succ u4) (succ u5), max (succ u4) (succ u5)} (ContinuousLinearEquiv.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (ContinuousLinearMap.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (CoeTCₓ.coe.{max (succ u4) (succ u5), max (succ u4) (succ u5)} (ContinuousLinearEquiv.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (ContinuousLinearMap.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (coeBase.{max (succ u4) (succ u5), max (succ u4) (succ u5)} (ContinuousLinearEquiv.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (ContinuousLinearMap.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u1, u2, u4, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) f)) ((fun (a : Sort.{max (succ u4) (succ u6)}) (b : Sort.{max (succ u4) (succ u6)}) [self : HasLiftT.{max (succ u4) (succ u6), max (succ u4) (succ u6)} a b] => self.0) (ContinuousLinearEquiv.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁ _inst_8 _inst_9 M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25) (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25) (HasLiftT.mk.{max (succ u4) (succ u6), max (succ u4) (succ u6)} (ContinuousLinearEquiv.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁ _inst_8 _inst_9 M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25) (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25) (CoeTCₓ.coe.{max (succ u4) (succ u6), max (succ u4) (succ u6)} (ContinuousLinearEquiv.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁ _inst_8 _inst_9 M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25) (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25) (coeBase.{max (succ u4) (succ u6), max (succ u4) (succ u6)} (ContinuousLinearEquiv.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁ _inst_8 _inst_9 M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25) (ContinuousLinearMap.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u1, u3, u4, u6} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁ _inst_8 _inst_9 M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25)))) (ContinuousLinearEquiv.trans.{u1, u2, u3, u4, u5, u6} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₁ _inst_4 _inst_5 σ₂₃ σ₃₂ _inst_6 _inst_7 σ₁₃ σ₃₁ _inst_8 _inst_9 _inst_10 _inst_11 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_22 _inst_24 _inst_25 f f'))
+but is expected to have type
+ forall {R₁ : Type.{u6}} {R₂ : Type.{u5}} {R₃ : Type.{u2}} [_inst_1 : Semiring.{u6} R₁] [_inst_2 : Semiring.{u5} R₂] [_inst_3 : Semiring.{u2} R₃] {σ₁₂ : RingHom.{u6, u5} R₁ R₂ (Semiring.toNonAssocSemiring.{u6} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u5} R₂ _inst_2)} {σ₂₁ : RingHom.{u5, u6} R₂ R₁ (Semiring.toNonAssocSemiring.{u5} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u6} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u6, u5} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u5, u6} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {σ₂₃ : RingHom.{u5, u2} R₂ R₃ (Semiring.toNonAssocSemiring.{u5} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u2} R₃ _inst_3)} {σ₃₂ : RingHom.{u2, u5} R₃ R₂ (Semiring.toNonAssocSemiring.{u2} R₃ _inst_3) (Semiring.toNonAssocSemiring.{u5} R₂ _inst_2)} [_inst_6 : RingHomInvPair.{u5, u2} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂] [_inst_7 : RingHomInvPair.{u2, u5} R₃ R₂ _inst_3 _inst_2 σ₃₂ σ₂₃] {σ₁₃ : RingHom.{u6, u2} R₁ R₃ (Semiring.toNonAssocSemiring.{u6} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₃ _inst_3)} {σ₃₁ : RingHom.{u2, u6} R₃ R₁ (Semiring.toNonAssocSemiring.{u2} R₃ _inst_3) (Semiring.toNonAssocSemiring.{u6} R₁ _inst_1)} [_inst_8 : RingHomInvPair.{u6, u2} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁] [_inst_9 : RingHomInvPair.{u2, u6} R₃ R₁ _inst_3 _inst_1 σ₃₁ σ₁₃] [_inst_10 : RingHomCompTriple.{u6, u5, u2} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃] [_inst_11 : RingHomCompTriple.{u2, u5, u6} R₃ R₂ R₁ _inst_3 _inst_2 _inst_1 σ₃₂ σ₂₁ σ₃₁] {M₁ : Type.{u4}} [_inst_12 : TopologicalSpace.{u4} M₁] [_inst_13 : AddCommMonoid.{u4} M₁] {M₂ : Type.{u3}} [_inst_16 : TopologicalSpace.{u3} M₂] [_inst_17 : AddCommMonoid.{u3} M₂] {M₃ : Type.{u1}} [_inst_18 : TopologicalSpace.{u1} M₃] [_inst_19 : AddCommMonoid.{u1} M₃] [_inst_22 : Module.{u6, u4} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u5, u3} R₂ M₂ _inst_2 _inst_17] [_inst_25 : Module.{u2, u1} R₃ M₃ _inst_3 _inst_19] (f : ContinuousLinearEquiv.{u6, u5, u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (f' : ContinuousLinearEquiv.{u5, u2, u3, u1} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25), Eq.{max (succ u4) (succ u1)} (ContinuousLinearMap.{u6, u2, u4, u1} R₁ R₃ _inst_1 _inst_3 σ₁₃ M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25) (ContinuousLinearMap.comp.{u6, u5, u2, u4, u3, u1} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₃ σ₁₃ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_22 _inst_24 _inst_25 _inst_10 (ContinuousLinearEquiv.toContinuousLinearMap.{u5, u2, u3, u1} R₂ R₃ _inst_2 _inst_3 σ₂₃ σ₃₂ _inst_6 _inst_7 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_24 _inst_25 f') (ContinuousLinearEquiv.toContinuousLinearMap.{u6, u5, u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 f)) (ContinuousLinearEquiv.toContinuousLinearMap.{u6, u2, u4, u1} R₁ R₃ _inst_1 _inst_3 σ₁₃ σ₃₁ _inst_8 _inst_9 M₁ _inst_12 _inst_13 M₃ _inst_18 _inst_19 _inst_22 _inst_25 (ContinuousLinearEquiv.trans.{u6, u5, u2, u4, u3, u1} R₁ R₂ R₃ _inst_1 _inst_2 _inst_3 σ₁₂ σ₂₁ _inst_4 _inst_5 σ₂₃ σ₃₂ _inst_6 _inst_7 σ₁₃ σ₃₁ _inst_8 _inst_9 _inst_10 _inst_11 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 M₃ _inst_18 _inst_19 _inst_22 _inst_24 _inst_25 f f'))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.comp_coe ContinuousLinearEquiv.comp_coeₓ'. -/
@[simp, norm_cast]
theorem comp_coe (f : M₁ ≃SL[σ₁₂] M₂) (f' : M₂ ≃SL[σ₂₃] M₃) :
(f' : M₂ →SL[σ₂₃] M₃).comp (f : M₁ →SL[σ₁₂] M₂) = (f.trans f' : M₁ →SL[σ₁₃] M₃) :=
@@ -2182,12 +3528,24 @@ theorem comp_coe (f : M₁ ≃SL[σ₁₂] M₂) (f' : M₂ ≃SL[σ₂₃] M₃
omit σ₃₂ σ₃₁ σ₂₁
+/- warning: continuous_linear_equiv.coe_comp_coe_symm -> ContinuousLinearEquiv.coe_comp_coe_symm is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_comp_coe_symm ContinuousLinearEquiv.coe_comp_coe_symmₓ'. -/
@[simp]
theorem coe_comp_coe_symm (e : M₁ ≃SL[σ₁₂] M₂) :
(e : M₁ →SL[σ₁₂] M₂).comp (e.symm : M₂ →SL[σ₂₁] M₁) = ContinuousLinearMap.id R₂ M₂ :=
ContinuousLinearMap.ext e.apply_symm_apply
#align continuous_linear_equiv.coe_comp_coe_symm ContinuousLinearEquiv.coe_comp_coe_symm
+/- warning: continuous_linear_equiv.coe_symm_comp_coe -> ContinuousLinearEquiv.coe_symm_comp_coe is a dubious translation:
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+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24), Eq.{succ u2} (ContinuousLinearMap.{u4, u4, u2, u2} R₁ R₁ _inst_1 _inst_1 (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_12 _inst_13 M₁ _inst_12 _inst_13 _inst_22 _inst_22) (ContinuousLinearMap.comp.{u4, u3, u4, u2, u1, u2} R₁ R₂ R₁ _inst_1 _inst_2 _inst_1 σ₁₂ σ₂₁ (RingHom.id.{u4} R₁ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)) M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_22 _inst_24 _inst_22 (RingHomInvPair.triples₂.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5) (ContinuousLinearEquiv.toContinuousLinearMap.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearEquiv.symm.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) (ContinuousLinearEquiv.toContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) (ContinuousLinearMap.id.{u4, u2} R₁ _inst_1 M₁ _inst_12 _inst_13 _inst_22)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_symm_comp_coe ContinuousLinearEquiv.coe_symm_comp_coeₓ'. -/
@[simp]
theorem coe_symm_comp_coe (e : M₁ ≃SL[σ₁₂] M₂) :
(e.symm : M₂ →SL[σ₂₁] M₁).comp (e : M₁ →SL[σ₁₂] M₂) = ContinuousLinearMap.id R₁ M₁ :=
@@ -2196,6 +3554,12 @@ theorem coe_symm_comp_coe (e : M₁ ≃SL[σ₁₂] M₂) :
include σ₂₁
+/- warning: continuous_linear_equiv.symm_comp_self -> ContinuousLinearEquiv.symm_comp_self is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24), Eq.{succ u3} (M₁ -> M₁) (Function.comp.{succ u3, succ u4, succ u3} M₁ M₂ M₁ (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (fun (_x : ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) => M₂ -> M₁) (ContinuousLinearEquiv.hasCoeToFun.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (ContinuousLinearEquiv.symm.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e)) (id.{succ u3} M₁)
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24), Eq.{succ u2} (M₁ -> M₁) (Function.comp.{succ u2, succ u1, succ u2} M₁ M₂ M₁ (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M₁) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ M₁ _inst_16 _inst_12 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22)))) (ContinuousLinearEquiv.symm.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e)) (id.{succ u2} M₁)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_comp_self ContinuousLinearEquiv.symm_comp_selfₓ'. -/
@[simp]
theorem symm_comp_self (e : M₁ ≃SL[σ₁₂] M₂) : (e.symm : M₂ → M₁) ∘ (e : M₁ → M₂) = id :=
by
@@ -2203,6 +3567,12 @@ theorem symm_comp_self (e : M₁ ≃SL[σ₁₂] M₂) : (e.symm : M₂ → M₁
exact symm_apply_apply e x
#align continuous_linear_equiv.symm_comp_self ContinuousLinearEquiv.symm_comp_self
+/- warning: continuous_linear_equiv.self_comp_symm -> ContinuousLinearEquiv.self_comp_symm is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24), Eq.{succ u4} (M₂ -> M₂) (Function.comp.{succ u4, succ u3, succ u4} M₂ M₁ M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e) (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (fun (_x : ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) => M₂ -> M₁) (ContinuousLinearEquiv.hasCoeToFun.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (ContinuousLinearEquiv.symm.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e))) (id.{succ u4} M₂)
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24), Eq.{succ u1} (M₂ -> M₂) (Function.comp.{succ u1, succ u2, succ u1} M₂ M₁ M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M₁) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ M₁ _inst_16 _inst_12 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22)))) (ContinuousLinearEquiv.symm.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e))) (id.{succ u1} M₂)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.self_comp_symm ContinuousLinearEquiv.self_comp_symmₓ'. -/
@[simp]
theorem self_comp_symm (e : M₁ ≃SL[σ₁₂] M₂) : (e : M₁ → M₂) ∘ (e.symm : M₂ → M₁) = id :=
by
@@ -2210,6 +3580,12 @@ theorem self_comp_symm (e : M₁ ≃SL[σ₁₂] M₂) : (e : M₁ → M₂) ∘
exact apply_symm_apply e x
#align continuous_linear_equiv.self_comp_symm ContinuousLinearEquiv.self_comp_symm
+/- warning: continuous_linear_equiv.symm_symm -> ContinuousLinearEquiv.symm_symm is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24), Eq.{max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (ContinuousLinearEquiv.symm.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearEquiv.symm.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) e
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24), Eq.{max (succ u2) (succ u1)} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (ContinuousLinearEquiv.symm.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearEquiv.symm.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) e
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_symm ContinuousLinearEquiv.symm_symmₓ'. -/
@[simp]
theorem symm_symm (e : M₁ ≃SL[σ₁₂] M₂) : e.symm.symm = e :=
by
@@ -2219,45 +3595,95 @@ theorem symm_symm (e : M₁ ≃SL[σ₁₂] M₂) : e.symm.symm = e :=
omit σ₂₁
+#print ContinuousLinearEquiv.refl_symm /-
@[simp]
theorem refl_symm : (ContinuousLinearEquiv.refl R₁ M₁).symm = ContinuousLinearEquiv.refl R₁ M₁ :=
rfl
#align continuous_linear_equiv.refl_symm ContinuousLinearEquiv.refl_symm
+-/
include σ₂₁
+/- warning: continuous_linear_equiv.symm_symm_apply -> ContinuousLinearEquiv.symm_symm_apply is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (x : M₁), Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (ContinuousLinearEquiv.symm.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearEquiv.symm.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) x) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e x)
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (x : M₁), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) (ContinuousLinearEquiv.symm.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearEquiv.symm.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e x)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_symm_apply ContinuousLinearEquiv.symm_symm_applyₓ'. -/
theorem symm_symm_apply (e : M₁ ≃SL[σ₁₂] M₂) (x : M₁) : e.symm.symm x = e x :=
rfl
#align continuous_linear_equiv.symm_symm_apply ContinuousLinearEquiv.symm_symm_apply
+/- warning: continuous_linear_equiv.symm_apply_eq -> ContinuousLinearEquiv.symm_apply_eq is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) {x : M₂} {y : M₁}, Iff (Eq.{succ u3} M₁ (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (fun (_x : ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) => M₂ -> M₁) (ContinuousLinearEquiv.hasCoeToFun.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (ContinuousLinearEquiv.symm.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e) x) y) (Eq.{succ u4} M₂ x (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e y))
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) {x : M₂} {y : (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M₁) x}, Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M₁) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M₁) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ M₁ _inst_16 _inst_12 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22)))) (ContinuousLinearEquiv.symm.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e) x) y) (Eq.{succ u1} M₂ x (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e y))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_apply_eq ContinuousLinearEquiv.symm_apply_eqₓ'. -/
theorem symm_apply_eq (e : M₁ ≃SL[σ₁₂] M₂) {x y} : e.symm x = y ↔ x = e y :=
e.toLinearEquiv.symm_apply_eq
#align continuous_linear_equiv.symm_apply_eq ContinuousLinearEquiv.symm_apply_eq
+/- warning: continuous_linear_equiv.eq_symm_apply -> ContinuousLinearEquiv.eq_symm_apply is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) {x : M₂} {y : M₁}, Iff (Eq.{succ u3} M₁ y (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (fun (_x : ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) => M₂ -> M₁) (ContinuousLinearEquiv.hasCoeToFun.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (ContinuousLinearEquiv.symm.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e) x)) (Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e y) x)
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) {x : M₂} {y : (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M₁) x}, Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M₁) x) y (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M₁) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ M₁ _inst_16 _inst_12 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22)))) (ContinuousLinearEquiv.symm.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e) x)) (Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) y) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e y) x)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.eq_symm_apply ContinuousLinearEquiv.eq_symm_applyₓ'. -/
theorem eq_symm_apply (e : M₁ ≃SL[σ₁₂] M₂) {x y} : y = e.symm x ↔ e y = x :=
e.toLinearEquiv.eq_symm_apply
#align continuous_linear_equiv.eq_symm_apply ContinuousLinearEquiv.eq_symm_apply
+/- warning: continuous_linear_equiv.image_eq_preimage -> ContinuousLinearEquiv.image_eq_preimage is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (s : Set.{u3} M₁), Eq.{succ u4} (Set.{u4} M₂) (Set.image.{u3, u4} M₁ M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e) s) (Set.preimage.{u4, u3} M₂ M₁ (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (fun (_x : ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) => M₂ -> M₁) (ContinuousLinearEquiv.hasCoeToFun.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (ContinuousLinearEquiv.symm.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) s)
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (s : Set.{u2} M₁), Eq.{succ u1} (Set.{u1} M₂) (Set.image.{u2, u1} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e) s) (Set.preimage.{u1, u2} M₂ M₁ (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M₁) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ M₁ _inst_16 _inst_12 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22)))) (ContinuousLinearEquiv.symm.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) s)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.image_eq_preimage ContinuousLinearEquiv.image_eq_preimageₓ'. -/
protected theorem image_eq_preimage (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₁) : e '' s = e.symm ⁻¹' s :=
e.toLinearEquiv.toEquiv.image_eq_preimage s
#align continuous_linear_equiv.image_eq_preimage ContinuousLinearEquiv.image_eq_preimage
+/- warning: continuous_linear_equiv.image_symm_eq_preimage -> ContinuousLinearEquiv.image_symm_eq_preimage is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (s : Set.{u4} M₂), Eq.{succ u3} (Set.{u3} M₁) (Set.image.{u4, u3} M₂ M₁ (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (fun (_x : ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) => M₂ -> M₁) (ContinuousLinearEquiv.hasCoeToFun.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (ContinuousLinearEquiv.symm.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) s) (Set.preimage.{u3, u4} M₁ M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e) s)
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (s : Set.{u1} M₂), Eq.{succ u2} (Set.{u2} M₁) (Set.image.{u1, u2} M₂ M₁ (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M₁) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ M₁ _inst_16 _inst_12 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22)))) (ContinuousLinearEquiv.symm.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) s) (Set.preimage.{u2, u1} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e) s)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.image_symm_eq_preimage ContinuousLinearEquiv.image_symm_eq_preimageₓ'. -/
protected theorem image_symm_eq_preimage (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₂) :
e.symm '' s = e ⁻¹' s := by rw [e.symm.image_eq_preimage, e.symm_symm]
#align continuous_linear_equiv.image_symm_eq_preimage ContinuousLinearEquiv.image_symm_eq_preimage
+/- warning: continuous_linear_equiv.symm_preimage_preimage -> ContinuousLinearEquiv.symm_preimage_preimage is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (s : Set.{u4} M₂), Eq.{succ u4} (Set.{u4} M₂) (Set.preimage.{u4, u3} M₂ M₁ (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (fun (_x : ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) => M₂ -> M₁) (ContinuousLinearEquiv.hasCoeToFun.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (ContinuousLinearEquiv.symm.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) (Set.preimage.{u3, u4} M₁ M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e) s)) s
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (s : Set.{u1} M₂), Eq.{succ u1} (Set.{u1} M₂) (Set.preimage.{u1, u2} M₂ M₁ (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M₁) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ M₁ _inst_16 _inst_12 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22)))) (ContinuousLinearEquiv.symm.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) (Set.preimage.{u2, u1} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e) s)) s
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_preimage_preimage ContinuousLinearEquiv.symm_preimage_preimageₓ'. -/
@[simp]
protected theorem symm_preimage_preimage (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₂) :
e.symm ⁻¹' (e ⁻¹' s) = s :=
e.toLinearEquiv.toEquiv.symm_preimage_preimage s
#align continuous_linear_equiv.symm_preimage_preimage ContinuousLinearEquiv.symm_preimage_preimage
+/- warning: continuous_linear_equiv.preimage_symm_preimage -> ContinuousLinearEquiv.preimage_symm_preimage is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (s : Set.{u3} M₁), Eq.{succ u3} (Set.{u3} M₁) (Set.preimage.{u3, u4} M₁ M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) e) (Set.preimage.{u4, u3} M₂ M₁ (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (fun (_x : ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) => M₂ -> M₁) (ContinuousLinearEquiv.hasCoeToFun.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (ContinuousLinearEquiv.symm.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) s)) s
+but is expected to have type
+ forall {R₁ : Type.{u4}} {R₂ : Type.{u3}} [_inst_1 : Semiring.{u4} R₁] [_inst_2 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R₁ R₂ (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} {σ₂₁ : RingHom.{u3, u4} R₂ R₁ (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u4} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u4, u3} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u3, u4} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u2}} [_inst_12 : TopologicalSpace.{u2} M₁] [_inst_13 : AddCommMonoid.{u2} M₁] {M₂ : Type.{u1}} [_inst_16 : TopologicalSpace.{u1} M₂] [_inst_17 : AddCommMonoid.{u1} M₂] [_inst_22 : Module.{u4, u2} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u3, u1} R₂ M₂ _inst_2 _inst_17] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (s : Set.{u2} M₁), Eq.{succ u2} (Set.{u2} M₁) (Set.preimage.{u2, u1} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) e) (Set.preimage.{u1, u2} M₂ M₁ (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M₁) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ M₁ _inst_16 _inst_12 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u3, u4, u1, u2} (ContinuousLinearEquiv.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u3, u4, u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22)))) (ContinuousLinearEquiv.symm.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 e)) s)) s
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.preimage_symm_preimage ContinuousLinearEquiv.preimage_symm_preimageₓ'. -/
@[simp]
protected theorem preimage_symm_preimage (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₁) :
e ⁻¹' (e.symm ⁻¹' s) = s :=
e.symm.symm_preimage_preimage s
#align continuous_linear_equiv.preimage_symm_preimage ContinuousLinearEquiv.preimage_symm_preimage
+/- warning: continuous_linear_equiv.uniform_embedding -> ContinuousLinearEquiv.uniformEmbedding is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {E₁ : Type.{u3}} {E₂ : Type.{u4}} [_inst_26 : UniformSpace.{u3} E₁] [_inst_27 : UniformSpace.{u4} E₂] [_inst_28 : AddCommGroup.{u3} E₁] [_inst_29 : AddCommGroup.{u4} E₂] [_inst_30 : Module.{u1, u3} R₁ E₁ _inst_1 (AddCommGroup.toAddCommMonoid.{u3} E₁ _inst_28)] [_inst_31 : Module.{u2, u4} R₂ E₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} E₂ _inst_29)] [_inst_32 : UniformAddGroup.{u3} E₁ _inst_26 (AddCommGroup.toAddGroup.{u3} E₁ _inst_28)] [_inst_33 : UniformAddGroup.{u4} E₂ _inst_27 (AddCommGroup.toAddGroup.{u4} E₂ _inst_29)] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 E₁ (UniformSpace.toTopologicalSpace.{u3} E₁ _inst_26) (AddCommGroup.toAddCommMonoid.{u3} E₁ _inst_28) E₂ (UniformSpace.toTopologicalSpace.{u4} E₂ _inst_27) (AddCommGroup.toAddCommMonoid.{u4} E₂ _inst_29) _inst_30 _inst_31), UniformEmbedding.{u3, u4} E₁ E₂ _inst_26 _inst_27 (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 E₁ (UniformSpace.toTopologicalSpace.{u3} E₁ _inst_26) (AddCommGroup.toAddCommMonoid.{u3} E₁ _inst_28) E₂ (UniformSpace.toTopologicalSpace.{u4} E₂ _inst_27) (AddCommGroup.toAddCommMonoid.{u4} E₂ _inst_29) _inst_30 _inst_31) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 E₁ (UniformSpace.toTopologicalSpace.{u3} E₁ _inst_26) (AddCommGroup.toAddCommMonoid.{u3} E₁ _inst_28) E₂ (UniformSpace.toTopologicalSpace.{u4} E₂ _inst_27) (AddCommGroup.toAddCommMonoid.{u4} E₂ _inst_29) _inst_30 _inst_31) => E₁ -> E₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 E₁ (UniformSpace.toTopologicalSpace.{u3} E₁ _inst_26) (AddCommGroup.toAddCommMonoid.{u3} E₁ _inst_28) E₂ (UniformSpace.toTopologicalSpace.{u4} E₂ _inst_27) (AddCommGroup.toAddCommMonoid.{u4} E₂ _inst_29) _inst_30 _inst_31) e)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.uniform_embedding ContinuousLinearEquiv.uniformEmbeddingₓ'. -/
protected theorem uniformEmbedding {E₁ E₂ : Type _} [UniformSpace E₁] [UniformSpace E₂]
[AddCommGroup E₁] [AddCommGroup E₂] [Module R₁ E₁] [Module R₂ E₂] [UniformAddGroup E₁]
[UniformAddGroup E₂] (e : E₁ ≃SL[σ₁₂] E₂) : UniformEmbedding e :=
@@ -2265,6 +3691,12 @@ protected theorem uniformEmbedding {E₁ E₂ : Type _} [UniformSpace E₁] [Uni
e.symm.toContinuousLinearMap.UniformContinuous
#align continuous_linear_equiv.uniform_embedding ContinuousLinearEquiv.uniformEmbedding
+/- warning: linear_equiv.uniform_embedding -> LinearEquiv.uniformEmbedding is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+ forall {R₁ : Type.{u2}} {R₂ : Type.{u1}} [_inst_1 : Semiring.{u2} R₁] [_inst_2 : Semiring.{u1} R₂] {σ₁₂ : RingHom.{u2, u1} R₁ R₂ (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u1} R₂ _inst_2)} {σ₂₁ : RingHom.{u1, u2} R₂ R₁ (Semiring.toNonAssocSemiring.{u1} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u2} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u1, u2} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {E₁ : Type.{u4}} {E₂ : Type.{u3}} [_inst_26 : UniformSpace.{u4} E₁] [_inst_27 : UniformSpace.{u3} E₂] [_inst_28 : AddCommGroup.{u4} E₁] [_inst_29 : AddCommGroup.{u3} E₂] [_inst_30 : Module.{u2, u4} R₁ E₁ _inst_1 (AddCommGroup.toAddCommMonoid.{u4} E₁ _inst_28)] [_inst_31 : Module.{u1, u3} R₂ E₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} E₂ _inst_29)] [_inst_32 : UniformAddGroup.{u4} E₁ _inst_26 (AddCommGroup.toAddGroup.{u4} E₁ _inst_28)] [_inst_33 : UniformAddGroup.{u3} E₂ _inst_27 (AddCommGroup.toAddGroup.{u3} E₂ 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(AddCommGroup.toAddCommMonoid.{u3} E₂ _inst_29) _inst_30 _inst_31 σ₁₂ σ₂₁ _inst_4 _inst_5))))) e))
+Case conversion may be inaccurate. Consider using '#align linear_equiv.uniform_embedding LinearEquiv.uniformEmbeddingₓ'. -/
protected theorem LinearEquiv.uniformEmbedding {E₁ E₂ : Type _} [UniformSpace E₁] [UniformSpace E₂]
[AddCommGroup E₁] [AddCommGroup E₂] [Module R₁ E₁] [Module R₂ E₂] [UniformAddGroup E₁]
[UniformAddGroup E₂] (e : E₁ ≃ₛₗ[σ₁₂] E₂) (h₁ : Continuous e) (h₂ : Continuous e.symm) :
@@ -2278,6 +3710,12 @@ protected theorem LinearEquiv.uniformEmbedding {E₁ E₂ : Type _} [UniformSpac
omit σ₂₁
+/- warning: continuous_linear_equiv.equiv_of_inverse -> ContinuousLinearEquiv.equivOfInverse is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (f₁ : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (f₂ : ContinuousLinearMap.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22), (Function.LeftInverse.{succ u3, succ u4} M₁ M₂ (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (ContinuousLinearMap.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (fun (_x : ContinuousLinearMap.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) => M₂ -> M₁) (ContinuousLinearMap.toFun.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) f₂) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) f₁)) -> (Function.RightInverse.{succ u3, succ u4} M₁ M₂ (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (ContinuousLinearMap.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (fun (_x : ContinuousLinearMap.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) => M₂ -> M₁) (ContinuousLinearMap.toFun.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) f₂) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) f₁)) -> (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)
+but is expected to have type
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (f₁ : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (f₂ : ContinuousLinearMap.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22), (Function.LeftInverse.{succ u3, succ u4} M₁ M₂ (FunLike.coe.{max (succ u3) (succ u4), succ u4, succ u3} (ContinuousLinearMap.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M₁) _x) (ContinuousMapClass.toFunLike.{max u3 u4, u4, u3} (ContinuousLinearMap.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ M₁ _inst_16 _inst_12 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u4, u2, u1, u4, u3} (ContinuousLinearMap.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22))) f₂) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u3 u4, u3, u4} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u4, u1, u2, u3, u4} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24))) f₁)) -> (Function.RightInverse.{succ u3, succ u4} M₁ M₂ (FunLike.coe.{max (succ u3) (succ u4), succ u4, succ u3} (ContinuousLinearMap.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M₁) _x) (ContinuousMapClass.toFunLike.{max u3 u4, u4, u3} (ContinuousLinearMap.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) M₂ M₁ _inst_16 _inst_12 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u4, u2, u1, u4, u3} (ContinuousLinearMap.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22))) f₂) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u3 u4, u3, u4} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u4, u1, u2, u3, u4} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24))) f₁)) -> (ContinuousLinearEquiv.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.equiv_of_inverse ContinuousLinearEquiv.equivOfInverseₓ'. -/
/-- Create a `continuous_linear_equiv` from two `continuous_linear_map`s that are
inverse of each other. -/
def equivOfInverse (f₁ : M₁ →SL[σ₁₂] M₂) (f₂ : M₂ →SL[σ₂₁] M₁) (h₁ : Function.LeftInverse f₂ f₁)
@@ -2293,12 +3731,24 @@ def equivOfInverse (f₁ : M₁ →SL[σ₁₂] M₂) (f₂ : M₂ →SL[σ₂
include σ₂₁
+/- warning: continuous_linear_equiv.equiv_of_inverse_apply -> ContinuousLinearEquiv.equivOfInverse_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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_inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24)))) (ContinuousLinearEquiv.equivOfInverse.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 f₁ f₂ h₁ h₂) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₁) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) M₁ M₂ _inst_12 _inst_16 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+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.equiv_of_inverse_apply ContinuousLinearEquiv.equivOfInverse_applyₓ'. -/
@[simp]
theorem equivOfInverse_apply (f₁ : M₁ →SL[σ₁₂] M₂) (f₂ h₁ h₂ x) :
equivOfInverse f₁ f₂ h₁ h₂ x = f₁ x :=
rfl
#align continuous_linear_equiv.equiv_of_inverse_apply ContinuousLinearEquiv.equivOfInverse_apply
+/- warning: continuous_linear_equiv.symm_equiv_of_inverse -> ContinuousLinearEquiv.symm_equivOfInverse is a dubious translation:
+lean 3 declaration is
+ forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : Semiring.{u1} R₁] [_inst_2 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R₁ R₂ (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} {σ₂₁ : RingHom.{u2, u1} R₂ R₁ (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2) (Semiring.toNonAssocSemiring.{u1} R₁ _inst_1)} [_inst_4 : RingHomInvPair.{u1, u2} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁] [_inst_5 : RingHomInvPair.{u2, u1} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂] {M₁ : Type.{u3}} [_inst_12 : TopologicalSpace.{u3} M₁] [_inst_13 : AddCommMonoid.{u3} M₁] {M₂ : Type.{u4}} [_inst_16 : TopologicalSpace.{u4} M₂] [_inst_17 : AddCommMonoid.{u4} M₂] [_inst_22 : Module.{u1, u3} R₁ M₁ _inst_1 _inst_13] [_inst_24 : Module.{u2, u4} R₂ M₂ _inst_2 _inst_17] (f₁ : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (f₂ : ContinuousLinearMap.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (h₁ : Function.LeftInverse.{succ u3, succ u4} M₁ M₂ (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (ContinuousLinearMap.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (fun (_x : ContinuousLinearMap.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) => M₂ -> M₁) (ContinuousLinearMap.toFun.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) f₂) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) f₁)) (h₂ : Function.RightInverse.{succ u3, succ u4} M₁ M₂ (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (ContinuousLinearMap.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (fun (_x : ContinuousLinearMap.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) => M₂ -> M₁) (ContinuousLinearMap.toFun.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) f₂) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) (fun (_x : ContinuousLinearMap.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) => M₁ -> M₂) (ContinuousLinearMap.toFun.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24) f₁)), Eq.{max (succ u4) (succ u3)} (ContinuousLinearEquiv.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22) (ContinuousLinearEquiv.symm.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 (ContinuousLinearEquiv.equivOfInverse.{u1, u2, u3, u4} R₁ R₂ _inst_1 _inst_2 σ₁₂ σ₂₁ _inst_4 _inst_5 M₁ _inst_12 _inst_13 M₂ _inst_16 _inst_17 _inst_22 _inst_24 f₁ f₂ h₁ h₂)) (ContinuousLinearEquiv.equivOfInverse.{u2, u1, u4, u3} R₂ R₁ _inst_2 _inst_1 σ₂₁ σ₁₂ _inst_5 _inst_4 M₂ _inst_16 _inst_17 M₁ _inst_12 _inst_13 _inst_24 _inst_22 f₂ f₁ h₂ h₁)
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.symm_equiv_of_inverse ContinuousLinearEquiv.symm_equivOfInverseₓ'. -/
@[simp]
theorem symm_equivOfInverse (f₁ : M₁ →SL[σ₁₂] M₂) (f₂ h₁ h₂) :
(equivOfInverse f₁ f₂ h₁ h₂).symm = equivOfInverse f₂ f₁ h₂ h₁ :=
@@ -2309,6 +3759,7 @@ omit σ₂₁
variable (M₁)
+#print ContinuousLinearEquiv.automorphismGroup /-
/-- The continuous linear equivalences from `M` to itself form a group under composition. -/
instance automorphismGroup : Group (M₁ ≃L[R₁] M₁)
where
@@ -2328,11 +3779,13 @@ instance automorphismGroup : Group (M₁ ≃L[R₁] M₁)
ext
exact f.left_inv x
#align continuous_linear_equiv.automorphism_group ContinuousLinearEquiv.automorphismGroup
+-/
variable {M₁} {R₄ : Type _} [Semiring R₄] [Module R₄ M₄] {σ₃₄ : R₃ →+* R₄} {σ₄₃ : R₄ →+* R₃}
[RingHomInvPair σ₃₄ σ₄₃] [RingHomInvPair σ₄₃ σ₃₄] {σ₂₄ : R₂ →+* R₄} {σ₁₄ : R₁ →+* R₄}
[RingHomCompTriple σ₂₁ σ₁₄ σ₂₄] [RingHomCompTriple σ₂₄ σ₄₃ σ₂₃] [RingHomCompTriple σ₁₃ σ₃₄ σ₁₄]
+#print ContinuousLinearEquiv.ulift /-
/-- The continuous linear equivalence between `ulift M₁` and `M₁`. -/
def ulift : ULift M₁ ≃L[R₁] M₁ :=
{ Equiv.ulift with
@@ -2341,9 +3794,11 @@ def ulift : ULift M₁ ≃L[R₁] M₁ :=
continuous_toFun := continuous_uLift_down
continuous_invFun := continuous_uLift_up }
#align continuous_linear_equiv.ulift ContinuousLinearEquiv.ulift
+-/
include σ₂₁ σ₃₄ σ₂₃ σ₂₄ σ₁₃
+#print ContinuousLinearEquiv.arrowCongrEquiv /-
/-- A pair of continuous (semi)linear equivalences generates an equivalence between the spaces of
continuous linear maps. See also `continuous_linear_equiv.arrow_congr`. -/
@[simps]
@@ -2359,6 +3814,7 @@ def arrowCongrEquiv (e₁₂ : M₁ ≃SL[σ₁₂] M₂) (e₄₃ : M₄ ≃SL[
ContinuousLinearMap.ext fun x => by
simp only [ContinuousLinearMap.comp_apply, apply_symm_apply, coe_coe]
#align continuous_linear_equiv.arrow_congr_equiv ContinuousLinearEquiv.arrowCongrEquiv
+-/
end AddCommMonoid
@@ -2371,6 +3827,12 @@ variable {R : Type _} [Semiring R] {M : Type _} [TopologicalSpace M] [AddCommGro
variable [TopologicalAddGroup M₄]
+/- warning: continuous_linear_equiv.skew_prod -> ContinuousLinearEquiv.skewProd is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommGroup.{u2} M] {M₂ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₂] [_inst_5 : AddCommGroup.{u3} M₂] {M₃ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₃] [_inst_7 : AddCommGroup.{u4} M₃] {M₄ : Type.{u5}} [_inst_8 : TopologicalSpace.{u5} M₄] [_inst_9 : AddCommGroup.{u5} M₄] [_inst_10 : Module.{u1, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] [_inst_11 : Module.{u1, u3} R M₂ _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5)] [_inst_12 : Module.{u1, u4} R M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_7)] [_inst_13 : Module.{u1, u5} R M₄ _inst_1 (AddCommGroup.toAddCommMonoid.{u5} M₄ _inst_9)] [_inst_14 : TopologicalAddGroup.{u5} M₄ _inst_8 (AddCommGroup.toAddGroup.{u5} M₄ _inst_9)], (ContinuousLinearEquiv.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_10 _inst_11) -> (ContinuousLinearEquiv.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M₃ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_7) M₄ _inst_8 (AddCommGroup.toAddCommMonoid.{u5} M₄ _inst_9) _inst_12 _inst_13) -> (ContinuousLinearMap.{u1, u1, u2, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₄ _inst_8 (AddCommGroup.toAddCommMonoid.{u5} M₄ _inst_9) _inst_10 _inst_13) -> (ContinuousLinearEquiv.{u1, u1, max u2 u4, max u3 u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Prod.{u2, u4} M M₃) (Prod.topologicalSpace.{u2, u4} M M₃ _inst_2 _inst_6) (Prod.addCommMonoid.{u2, u4} M M₃ (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_7)) (Prod.{u3, u5} M₂ M₄) (Prod.topologicalSpace.{u3, u5} M₂ M₄ _inst_4 _inst_8) (Prod.addCommMonoid.{u3, u5} M₂ M₄ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₄ _inst_9)) (Prod.module.{u1, u2, u4} R M M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_7) _inst_10 _inst_12) (Prod.module.{u1, u3, u5} R M₂ M₄ _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₄ _inst_9) _inst_11 _inst_13))
+but is expected to have type
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommGroup.{u2} M] {M₂ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₂] [_inst_5 : AddCommGroup.{u3} M₂] {M₃ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₃] [_inst_7 : AddCommGroup.{u4} M₃] {M₄ : Type.{u5}} [_inst_8 : TopologicalSpace.{u5} M₄] [_inst_9 : AddCommGroup.{u5} M₄] [_inst_10 : Module.{u1, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] [_inst_11 : Module.{u1, u3} R M₂ _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5)] [_inst_12 : Module.{u1, u4} R M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_7)] [_inst_13 : Module.{u1, u5} R M₄ _inst_1 (AddCommGroup.toAddCommMonoid.{u5} M₄ _inst_9)] [_inst_14 : TopologicalAddGroup.{u5} M₄ _inst_8 (AddCommGroup.toAddGroup.{u5} M₄ _inst_9)], (ContinuousLinearEquiv.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_10 _inst_11) -> (ContinuousLinearEquiv.{u1, u1, u4, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M₃ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_7) M₄ _inst_8 (AddCommGroup.toAddCommMonoid.{u5} M₄ _inst_9) _inst_12 _inst_13) -> (ContinuousLinearMap.{u1, u1, u2, u5} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₄ _inst_8 (AddCommGroup.toAddCommMonoid.{u5} M₄ _inst_9) _inst_10 _inst_13) -> (ContinuousLinearEquiv.{u1, u1, max u4 u2, max u5 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Prod.{u2, u4} M M₃) (instTopologicalSpaceProd.{u2, u4} M M₃ _inst_2 _inst_6) (Prod.instAddCommMonoidSum.{u2, u4} M M₃ (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_7)) (Prod.{u3, u5} M₂ M₄) (instTopologicalSpaceProd.{u3, u5} M₂ M₄ _inst_4 _inst_8) (Prod.instAddCommMonoidSum.{u3, u5} M₂ M₄ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₄ _inst_9)) (Prod.module.{u1, u2, u4} R M M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_7) _inst_10 _inst_12) (Prod.module.{u1, u3, u5} R M₂ M₄ _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) (AddCommGroup.toAddCommMonoid.{u5} M₄ _inst_9) _inst_11 _inst_13))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.skew_prod ContinuousLinearEquiv.skewProdₓ'. -/
/-- Equivalence given by a block lower diagonal matrix. `e` and `e'` are diagonal square blocks,
and `f` is a rectangular block below the diagonal. -/
def skewProd (e : M ≃L[R] M₂) (e' : M₃ ≃L[R] M₄) (f : M →L[R] M₄) : (M × M₃) ≃L[R] M₂ × M₄ :=
@@ -2386,12 +3848,24 @@ def skewProd (e : M ≃L[R] M₂) (e' : M₃ ≃L[R] M₄) (f : M →L[R] M₄)
continuous_snd.sub <| f.Continuous.comp <| e.continuous_invFun.comp continuous_fst) }
#align continuous_linear_equiv.skew_prod ContinuousLinearEquiv.skewProd
+/- warning: continuous_linear_equiv.skew_prod_apply -> ContinuousLinearEquiv.skewProd_apply is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {M : Type.{u2}} [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommGroup.{u2} M] {M₂ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₂] [_inst_5 : AddCommGroup.{u3} M₂] {M₃ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₃] [_inst_7 : AddCommGroup.{u4} M₃] {M₄ : Type.{u5}} [_inst_8 : TopologicalSpace.{u5} M₄] [_inst_9 : AddCommGroup.{u5} M₄] [_inst_10 : Module.{u1, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] [_inst_11 : Module.{u1, u3} R M₂ _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5)] [_inst_12 : Module.{u1, u4} R M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_7)] [_inst_13 : Module.{u1, u5} R M₄ _inst_1 (AddCommGroup.toAddCommMonoid.{u5} M₄ _inst_9)] [_inst_14 : TopologicalAddGroup.{u5} M₄ _inst_8 (AddCommGroup.toAddGroup.{u5} M₄ _inst_9)] (e : ContinuousLinearEquiv.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R 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+but is expected to have type
+ forall {R : Type.{u5}} [_inst_1 : Semiring.{u5} R] {M : Type.{u4}} [_inst_2 : TopologicalSpace.{u4} M] [_inst_3 : AddCommGroup.{u4} M] {M₂ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₂] [_inst_5 : AddCommGroup.{u3} M₂] {M₃ : Type.{u2}} [_inst_6 : TopologicalSpace.{u2} M₃] [_inst_7 : AddCommGroup.{u2} M₃] {M₄ : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} M₄] [_inst_9 : AddCommGroup.{u1} M₄] [_inst_10 : Module.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3)] [_inst_11 : Module.{u5, u3} R M₂ _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5)] [_inst_12 : Module.{u5, u2} R M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M₃ _inst_7)] [_inst_13 : Module.{u5, u1} R M₄ _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M₄ _inst_9)] [_inst_14 : TopologicalAddGroup.{u1} M₄ _inst_8 (AddCommGroup.toAddGroup.{u1} M₄ _inst_9)] (e : ContinuousLinearEquiv.{u5, u5, u4, u3} R R _inst_1 _inst_1 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R _inst_1)) (RingHom.id.{u5} R 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+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.skew_prod_apply ContinuousLinearEquiv.skewProd_applyₓ'. -/
@[simp]
theorem skewProd_apply (e : M ≃L[R] M₂) (e' : M₃ ≃L[R] M₄) (f : M →L[R] M₄) (x) :
e.skewProd e' f x = (e x.1, e' x.2 + f x.1) :=
rfl
#align continuous_linear_equiv.skew_prod_apply ContinuousLinearEquiv.skewProd_apply
+/- warning: continuous_linear_equiv.skew_prod_symm_apply -> ContinuousLinearEquiv.skewProd_symm_apply is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.skew_prod_symm_apply ContinuousLinearEquiv.skewProd_symm_applyₓ'. -/
@[simp]
theorem skewProd_symm_apply (e : M ≃L[R] M₂) (e' : M₃ ≃L[R] M₄) (f : M →L[R] M₄) (x) :
(e.skewProd e' f).symm x = (e.symm x.1, e'.symm (x.2 - f (e.symm x.1))) :=
@@ -2409,11 +3883,23 @@ variable {σ₁₂ : R →+* R₂} {σ₂₁ : R₂ →+* R} [RingHomInvPair σ
include σ₂₁
+/- warning: continuous_linear_equiv.map_sub -> ContinuousLinearEquiv.map_sub is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_3 : TopologicalSpace.{u3} M] [_inst_4 : AddCommGroup.{u3} M] [_inst_5 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_8 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u1} R₂ R (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))} [_inst_9 : RingHomInvPair.{u1, u2} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_10 : RingHomInvPair.{u2, u1} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ σ₁₂] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) (x : M) (y : M), Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) => M -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) e (HSub.hSub.{u3, u3, u3} M M M (instHSub.{u3} M (SubNegMonoid.toHasSub.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_4)))) x y)) (HSub.hSub.{u4, u4, u4} M₂ M₂ M₂ (instHSub.{u4} M₂ (SubNegMonoid.toHasSub.{u4} M₂ (AddGroup.toSubNegMonoid.{u4} M₂ (AddCommGroup.toAddGroup.{u4} M₂ _inst_7)))) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) => M -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) e x) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) => M -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) e y))
+but is expected to have type
+ forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_8 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2))} {σ₂₁ : RingHom.{u3, u4} R₂ R (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))} [_inst_9 : RingHomInvPair.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_10 : RingHomInvPair.{u3, u4} R₂ R (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u4} R _inst_1) σ₂₁ σ₁₂] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) (x : M) (y : M), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) (HSub.hSub.{u2, u2, u2} M M M (instHSub.{u2} M (SubNegMonoid.toSub.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_4)))) x y)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) M (fun (_x : M) => (fun 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+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_sub ContinuousLinearEquiv.map_subₓ'. -/
@[simp]
theorem map_sub (e : M ≃SL[σ₁₂] M₂) (x y : M) : e (x - y) = e x - e y :=
(e : M →SL[σ₁₂] M₂).map_sub x y
#align continuous_linear_equiv.map_sub ContinuousLinearEquiv.map_sub
+/- warning: continuous_linear_equiv.map_neg -> ContinuousLinearEquiv.map_neg is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {R₂ : Type.{u2}} [_inst_2 : Ring.{u2} R₂] {M : Type.{u3}} [_inst_3 : TopologicalSpace.{u3} M] [_inst_4 : AddCommGroup.{u3} M] [_inst_5 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_4)] {M₂ : Type.{u4}} [_inst_6 : TopologicalSpace.{u4} M₂] [_inst_7 : AddCommGroup.{u4} M₂] [_inst_8 : Module.{u2, u4} R₂ M₂ (Ring.toSemiring.{u2} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7)] {σ₁₂ : RingHom.{u1, u2} R R₂ (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2))} {σ₂₁ : RingHom.{u2, u1} R₂ R (NonAssocRing.toNonAssocSemiring.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))} [_inst_9 : RingHomInvPair.{u1, u2} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_10 : RingHomInvPair.{u2, u1} R₂ R (Ring.toSemiring.{u2} R₂ _inst_2) (Ring.toSemiring.{u1} R _inst_1) σ₂₁ σ₁₂] (e : ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) (x : M), Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) => M -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) e (Neg.neg.{u3} M (SubNegMonoid.toHasNeg.{u3} M (AddGroup.toSubNegMonoid.{u3} M (AddCommGroup.toAddGroup.{u3} M _inst_4))) x)) (Neg.neg.{u4} M₂ (SubNegMonoid.toHasNeg.{u4} M₂ (AddGroup.toSubNegMonoid.{u4} M₂ (AddCommGroup.toAddGroup.{u4} M₂ _inst_7))) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) (fun (_x : ContinuousLinearEquiv.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) => M -> M₂) (ContinuousLinearEquiv.hasCoeToFun.{u1, u2, u3, u4} R R₂ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_7) _inst_5 _inst_8) e x))
+but is expected to have type
+ forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {R₂ : Type.{u3}} [_inst_2 : Ring.{u3} R₂] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u4, u2} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_8 : Module.{u3, u1} R₂ M₂ (Ring.toSemiring.{u3} R₂ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] {σ₁₂ : RingHom.{u4, u3} R R₂ (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2))} {σ₂₁ : RingHom.{u3, u4} R₂ R (NonAssocRing.toNonAssocSemiring.{u3} R₂ (Ring.toNonAssocRing.{u3} R₂ _inst_2)) (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R _inst_1))} [_inst_9 : RingHomInvPair.{u4, u3} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁] [_inst_10 : RingHomInvPair.{u3, u4} R₂ R (Ring.toSemiring.{u3} R₂ _inst_2) (Ring.toSemiring.{u4} R _inst_1) σ₂₁ σ₁₂] (e : ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) (Neg.neg.{u2} M (NegZeroClass.toNeg.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_4))))) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) M M₂ _inst_3 _inst_6 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8)))) e (Neg.neg.{u2} M (NegZeroClass.toNeg.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_4))))) x)) (Neg.neg.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (NegZeroClass.toNeg.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) x) _inst_7))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ 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_inst_8) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8 (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearEquiv.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8) R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8 (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u4, u3, u2, u1} R R₂ (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} R₂ _inst_2) σ₁₂ σ₂₁ _inst_9 _inst_10 M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_8)))) e x))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.map_neg ContinuousLinearEquiv.map_negₓ'. -/
@[simp]
theorem map_neg (e : M ≃SL[σ₁₂] M₂) (x : M) : e (-x) = -e x :=
(e : M →SL[σ₁₂] M₂).map_neg x
@@ -2429,6 +3915,12 @@ section
variable [TopologicalAddGroup M]
+/- warning: continuous_linear_equiv.of_unit -> ContinuousLinearEquiv.ofUnit is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_11 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)], (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) -> (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.ofUnit._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.ofUnit._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5)
+but is expected to have type
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)], (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))) -> (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.of_unit ContinuousLinearEquiv.ofUnitₓ'. -/
/-- An invertible continuous linear map `f` determines a continuous equivalence from `M` to itself.
-/
def ofUnit (f : (M →L[R] M)ˣ) : M ≃L[R] M
@@ -2450,6 +3942,12 @@ def ofUnit (f : (M →L[R] M)ˣ) : M ≃L[R] M
continuous_invFun := f.inv.Continuous
#align continuous_linear_equiv.of_unit ContinuousLinearEquiv.ofUnit
+/- warning: continuous_linear_equiv.to_unit -> ContinuousLinearEquiv.toUnit is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_11 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)], (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.toUnit._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.toUnit._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) -> (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11)))
+but is expected to have type
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)], (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) -> (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.to_unit ContinuousLinearEquiv.toUnitₓ'. -/
/-- A continuous equivalence from `M` to itself determines an invertible continuous linear map. -/
def toUnit (f : M ≃L[R] M) : (M →L[R] M)ˣ where
val := f
@@ -2464,6 +3962,12 @@ def toUnit (f : M ≃L[R] M) : (M →L[R] M)ˣ where
variable (R M)
+/- warning: continuous_linear_equiv.units_equiv -> ContinuousLinearEquiv.unitsEquiv is a dubious translation:
+lean 3 declaration is
+ forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (M : Type.{u2}) [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_11 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)], MulEquiv.{u2, u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MulOneClass.toHasMul.{u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (Units.mulOneClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11)))) (MulOneClass.toHasMul.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Monoid.toMulOneClass.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (DivInvMonoid.toMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Group.toDivInvMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearEquiv.automorphismGroup.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))))
+but is expected to have type
+ forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (M : Type.{u2}) [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)], MulEquiv.{u2, u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))) (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MulOneClass.toMul.{u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))) (Units.instMulOneClassUnits.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))) (MulOneClass.toMul.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Monoid.toMulOneClass.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (DivInvMonoid.toMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Group.toDivInvMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearEquiv.automorphismGroup.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv ContinuousLinearEquiv.unitsEquivₓ'. -/
/-- The units of the algebra of continuous `R`-linear endomorphisms of `M` is multiplicatively
equivalent to the type of continuous linear equivalences between `M` and itself. -/
def unitsEquiv : (M →L[R] M)ˣ ≃* M ≃L[R] M
@@ -2481,6 +3985,12 @@ def unitsEquiv : (M →L[R] M)ˣ ≃* M ≃L[R] M
rfl
#align continuous_linear_equiv.units_equiv ContinuousLinearEquiv.unitsEquiv
+/- warning: continuous_linear_equiv.units_equiv_apply -> ContinuousLinearEquiv.unitsEquiv_apply is a dubious translation:
+lean 3 declaration is
+ forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (M : Type.{u2}) [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_11 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)] (f : Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (x : M), Eq.{succ u2} M (coeFn.{succ u2, succ u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (fun (_x : ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) => M -> M) (ContinuousLinearEquiv.hasCoeToFun.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (coeFn.{succ u2, succ u2} (MulEquiv.{u2, u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MulOneClass.toHasMul.{u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (Units.mulOneClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11)))) (MulOneClass.toHasMul.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Monoid.toMulOneClass.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (DivInvMonoid.toMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Group.toDivInvMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearEquiv.automorphismGroup.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))))) (fun (_x : MulEquiv.{u2, u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MulOneClass.toHasMul.{u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (Units.mulOneClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11)))) (MulOneClass.toHasMul.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Monoid.toMulOneClass.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (DivInvMonoid.toMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Group.toDivInvMonoid.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearEquiv.automorphismGroup.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))))) => (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) -> (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5)) (MulEquiv.hasCoeToFun.{u2, u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquiv._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquiv._proof_2.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MulOneClass.toHasMul.{u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (Units.mulOneClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11)))) (MulOneClass.toHasMul.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) => M -> M) (ContinuousLinearMap.toFun.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (coeBaseAux.{succ u2, succ u2} (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))) (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Units.hasCoe.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Ring.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.ring.{u1, u2} R _inst_1 M _inst_3 _inst_4 _inst_5 _inst_11))))) f x)
+but is expected to have type
+ forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (M : Type.{u2}) [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] (_inst_11 : Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))) (f : M), Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M) f) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5))) => ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) _inst_11) M (fun (a : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M) a) (ContinuousMapClass.toFunLike.{u2, u2, u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Units.{u2} (ContinuousLinearMap.{u1, 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(ContinuousLinearEquiv.automorphismGroup.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))))) (Units.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)))) (MulOneClass.toMul.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (Monoid.toMulOneClass.{u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R 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_inst_5) M (fun (a : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M) a) (ContinuousMapClass.toFunLike.{u2, u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) M M _inst_3 _inst_3 (ContinuousSemilinearMapClass.toContinuousMapClass.{u2, u1, u1, u2, u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5 (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5))) (Units.val.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (MonoidWithZero.toMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_1) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) _inst_11) f)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv_apply ContinuousLinearEquiv.unitsEquiv_applyₓ'. -/
@[simp]
theorem unitsEquiv_apply (f : (M →L[R] M)ˣ) (x : M) : unitsEquiv R M f x = f x :=
rfl
@@ -2492,6 +4002,12 @@ section
variable (R) [TopologicalSpace R] [ContinuousMul R]
+/- warning: continuous_linear_equiv.units_equiv_aut -> ContinuousLinearEquiv.unitsEquivAut is a dubious translation:
+lean 3 declaration is
+ forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))], Equiv.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))
+but is expected to have type
+ forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))], Equiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv_aut ContinuousLinearEquiv.unitsEquivAutₓ'. -/
/-- Continuous linear equivalences `R ≃L[R] R` are enumerated by `Rˣ`. -/
def unitsEquivAut : Rˣ ≃ R ≃L[R] R
where
@@ -2507,16 +4023,34 @@ def unitsEquivAut : Rˣ ≃ R ≃L[R] R
variable {R}
+/- warning: continuous_linear_equiv.units_equiv_aut_apply -> ContinuousLinearEquiv.unitsEquivAut_apply is a dubious translation:
+lean 3 declaration is
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(Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : Equiv.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R 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+but is expected to have type
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))] (u : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) x) (FunLike.coe.{succ u1, succ u1, succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u) R (fun (_x : R) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u) R R _inst_11 _inst_11 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u1, u1, u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{u1, u1, u1, u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.unitsEquivAut.{u1} R _inst_1 _inst_11 _inst_12) u) x) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) x (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) u))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv_aut_apply ContinuousLinearEquiv.unitsEquivAut_applyₓ'. -/
@[simp]
theorem unitsEquivAut_apply (u : Rˣ) (x : R) : unitsEquivAut R u x = x * u :=
rfl
#align continuous_linear_equiv.units_equiv_aut_apply ContinuousLinearEquiv.unitsEquivAut_apply
+/- warning: continuous_linear_equiv.units_equiv_aut_apply_symm -> ContinuousLinearEquiv.unitsEquivAut_apply_symm is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))] (u : Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (x : R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (_x : ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => R -> R) (ContinuousLinearEquiv.hasCoeToFun.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.symm.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : Equiv.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) -> (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Equiv.hasCoeToFun.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (ContinuousLinearEquiv.unitsEquivAut._proof_1.{u1} R _inst_1) (ContinuousLinearEquiv.unitsEquivAut._proof_2.{u1} R _inst_1) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (ContinuousLinearEquiv.unitsEquivAut.{u1} R _inst_1 _inst_11 _inst_12) u)) x) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))) x ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (coeBase.{succ u1, succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) R (Units.hasCoe.{u1} R (Ring.toMonoid.{u1} R _inst_1))))) (Inv.inv.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R _inst_1)) (Units.hasInv.{u1} R (Ring.toMonoid.{u1} R _inst_1)) u)))
+but is expected to have type
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))] (u : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) x) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R _inst_11 _inst_11 (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u1, u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{u1, u1, u1, u1, u1} (ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 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(ContinuousLinearEquiv.unitsEquivAut.{u1} R _inst_1 _inst_11 _inst_12) u)) x) (HMul.hMul.{u1, u1, u1} R ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : R) => R) x) R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) x (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Inv.inv.{u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Units.instInvUnits.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) u)))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv_aut_apply_symm ContinuousLinearEquiv.unitsEquivAut_apply_symmₓ'. -/
@[simp]
theorem unitsEquivAut_apply_symm (u : Rˣ) (x : R) : (unitsEquivAut R u).symm x = x * ↑u⁻¹ :=
rfl
#align continuous_linear_equiv.units_equiv_aut_apply_symm ContinuousLinearEquiv.unitsEquivAut_apply_symm
+/- warning: continuous_linear_equiv.units_equiv_aut_symm_apply -> ContinuousLinearEquiv.unitsEquivAut_symm_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_11 : TopologicalSpace.{u1} R] [_inst_12 : ContinuousMul.{u1} R _inst_11 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))] (e : ContinuousLinearEquiv.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R _inst_11 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R 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+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.units_equiv_aut_symm_apply ContinuousLinearEquiv.unitsEquivAut_symm_applyₓ'. -/
@[simp]
theorem unitsEquivAut_symm_apply (e : R ≃L[R] R) : ↑((unitsEquivAut R).symm e) = e 1 :=
rfl
@@ -2530,6 +4064,12 @@ open _Root_.ContinuousLinearMap (id fst snd)
open _Root_.LinearMap (mem_ker)
+/- warning: continuous_linear_equiv.equiv_of_right_inverse -> ContinuousLinearEquiv.equivOfRightInverse is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] [_inst_11 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_12 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)] (f₁ : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11) (f₂ : ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_11 _inst_5), (Function.RightInverse.{succ u2, succ u3} M M₂ (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_11 _inst_5) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M) _x) (ContinuousMapClass.toFunLike.{max u2 u3, u3, u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R 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+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.equiv_of_right_inverse ContinuousLinearEquiv.equivOfRightInverseₓ'. -/
/-- A pair of continuous linear maps such that `f₁ ∘ f₂ = id` generates a continuous
linear equivalence `e` between `M` and `M₂ × f₁.ker` such that `(e x).2 = x` for `x ∈ f₁.ker`,
`(e x).1 = f₁ x`, and `(e (f₂ y)).2 = 0`. The map is given by `e x = (f₁ x, x - f₂ (f₁ x))`. -/
@@ -2539,12 +4079,24 @@ def equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M) (h : Fun
(fun x => by simp) fun ⟨x, y⟩ => by simp [h x]
#align continuous_linear_equiv.equiv_of_right_inverse ContinuousLinearEquiv.equivOfRightInverse
+/- warning: continuous_linear_equiv.fst_equiv_of_right_inverse -> ContinuousLinearEquiv.fst_equivOfRightInverse is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+ forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] {M₂ : Type.{u1}} [_inst_6 : TopologicalSpace.{u1} M₂] [_inst_7 : AddCommGroup.{u1} M₂] [_inst_11 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7)] [_inst_12 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)] (f₁ : ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (f₂ : ContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) 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_inst_5 _inst_11)) f₁)) _inst_3)) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u3, u2, max u2 u1} (ContinuousLinearEquiv.{u3, u3, u2, max u2 u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_1)) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (Prod.{u1, u2} M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R 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_inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))) _inst_6 (instTopologicalSpaceSubtype.{u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) 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(RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (Submodule.addCommMonoid.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 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+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.fst_equiv_of_right_inverse ContinuousLinearEquiv.fst_equivOfRightInverseₓ'. -/
@[simp]
theorem fst_equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
(h : Function.RightInverse f₂ f₁) (x : M) : (equivOfRightInverse f₁ f₂ h x).1 = f₁ x :=
rfl
#align continuous_linear_equiv.fst_equiv_of_right_inverse ContinuousLinearEquiv.fst_equivOfRightInverse
+/- warning: continuous_linear_equiv.snd_equiv_of_right_inverse -> ContinuousLinearEquiv.snd_equivOfRightInverse is a dubious translation:
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+but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R 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u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁)))) 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(Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))) _inst_6 (instTopologicalSpaceSubtype.{u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R 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_inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 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_inst_5 _inst_11)) f₁))) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (Submodule.addCommMonoid.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R 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+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.snd_equiv_of_right_inverse ContinuousLinearEquiv.snd_equivOfRightInverseₓ'. -/
@[simp]
theorem snd_equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
(h : Function.RightInverse f₂ f₁) (x : M) :
@@ -2552,6 +4104,12 @@ theorem snd_equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
rfl
#align continuous_linear_equiv.snd_equiv_of_right_inverse ContinuousLinearEquiv.snd_equivOfRightInverse
+/- warning: continuous_linear_equiv.equiv_of_right_inverse_symm_apply -> ContinuousLinearEquiv.equivOfRightInverse_symm_apply is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_3 : TopologicalSpace.{u2} M] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] {M₂ : Type.{u3}} [_inst_6 : TopologicalSpace.{u3} M₂] [_inst_7 : AddCommGroup.{u3} M₂] [_inst_11 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] [_inst_12 : TopologicalAddGroup.{u2} M _inst_3 (AddCommGroup.toAddGroup.{u2} M _inst_4)] (f₁ : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_5 _inst_11) (f₂ : ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R 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+but is expected to have type
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_inst_11)) f₁)))) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Prod.{u1, u2} M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R 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_inst_5 _inst_11)) f₁)))) (instTopologicalSpaceProd.{u1, u2} M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} 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_inst_5 _inst_11)) f₁))) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (Submodule.addCommMonoid.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁)))) M (instTopologicalSpaceProd.{u1, u2} M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R 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_inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))) _inst_6 (instTopologicalSpaceSubtype.{u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) 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(Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (Prod.module.{u3, u1, u2} R M₂ (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) x (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) 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(RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11)) f₁))) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (Submodule.addCommMonoid.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) 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_inst_5 _inst_11)) f₁))) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) (Submodule.addCommMonoid.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_6 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_7) _inst_5 _inst_11) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R 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+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.equiv_of_right_inverse_symm_apply ContinuousLinearEquiv.equivOfRightInverse_symm_applyₓ'. -/
@[simp]
theorem equivOfRightInverse_symm_apply (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
(h : Function.RightInverse f₂ f₁) (y : M₂ × ker f₁) :
@@ -2566,18 +4124,32 @@ section
variable (ι R M : Type _) [Unique ι] [Semiring R] [AddCommMonoid M] [Module R M]
[TopologicalSpace M]
+#print ContinuousLinearEquiv.funUnique /-
/-- If `ι` has a unique element, then `ι → M` is continuously linear equivalent to `M`. -/
def funUnique : (ι → M) ≃L[R] M :=
{ Homeomorph.funUnique ι M with toLinearEquiv := LinearEquiv.funUnique ι R M }
#align continuous_linear_equiv.fun_unique ContinuousLinearEquiv.funUnique
+-/
variable {ι R M}
+/- warning: continuous_linear_equiv.coe_fun_unique -> ContinuousLinearEquiv.coe_funUnique is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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u3} ι (Unique.instInhabited.{succ u3} ι _inst_1)))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.coe_fun_unique ContinuousLinearEquiv.coe_funUniqueₓ'. -/
@[simp]
theorem coe_funUnique : ⇑(funUnique ι R M) = Function.eval default :=
rfl
#align continuous_linear_equiv.coe_fun_unique ContinuousLinearEquiv.coe_funUnique
+/- warning: continuous_linear_equiv.coe_fun_unique_symm -> ContinuousLinearEquiv.coe_funUnique_symm 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 continuous_linear_equiv.coe_fun_unique_symm ContinuousLinearEquiv.coe_funUnique_symmₓ'. -/
@[simp]
theorem coe_funUnique_symm : ⇑(funUnique ι R M).symm = Function.const ι :=
rfl
@@ -2585,6 +4157,12 @@ theorem coe_funUnique_symm : ⇑(funUnique ι R M).symm = Function.const ι :=
variable (R M)
+/- warning: continuous_linear_equiv.pi_fin_two -> ContinuousLinearEquiv.piFinTwo is a dubious translation:
+lean 3 declaration is
+ forall (R : Type.{u1}) [_inst_2 : Semiring.{u1} R] (M : (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> Type.{u2}) [_inst_6 : forall (i : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))), AddCommMonoid.{u2} (M i)] [_inst_7 : forall (i : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))), Module.{u1, u2} R (M i) _inst_2 (_inst_6 i)] [_inst_8 : forall (i : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))), TopologicalSpace.{u2} (M i)], ContinuousLinearEquiv.{u1, u1, u2, u2} R R _inst_2 _inst_2 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)) (RingHomInvPair.ids.{u1} R _inst_2) (RingHomInvPair.ids.{u1} R _inst_2) (forall (i : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat 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+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.pi_fin_two ContinuousLinearEquiv.piFinTwoₓ'. -/
/-- Continuous linear equivalence between dependent functions `Π i : fin 2, M i` and `M 0 × M 1`. -/
@[simps (config := { fullyApplied := false })]
def piFinTwo (M : Fin 2 → Type _) [∀ i, AddCommMonoid (M i)] [∀ i, Module R (M i)]
@@ -2592,6 +4170,12 @@ def piFinTwo (M : Fin 2 → Type _) [∀ i, AddCommMonoid (M i)] [∀ i, Module
{ Homeomorph.piFinTwo M with toLinearEquiv := LinearEquiv.piFinTwo R M }
#align continuous_linear_equiv.pi_fin_two ContinuousLinearEquiv.piFinTwo
+/- warning: continuous_linear_equiv.fin_two_arrow -> ContinuousLinearEquiv.finTwoArrow is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_equiv.fin_two_arrow ContinuousLinearEquiv.finTwoArrowₓ'. -/
/-- Continuous linear equivalence between vectors in `M² = fin 2 → M` and `M × M`. -/
@[simps (config := { fullyApplied := false })]
def finTwoArrow : (Fin 2 → M) ≃L[R] M × M :=
@@ -2616,6 +4200,7 @@ variable [AddCommMonoid M₂] [Module R M₂]
variable [AddCommMonoid M] [Module R M]
+#print ContinuousLinearMap.inverse /-
/-- Introduce a function `inverse` from `M →L[R] M₂` to `M₂ →L[R] M`, which sends `f` to `f.symm` if
`f` is a continuous linear equivalence and to `0` otherwise. This definition is somewhat ad hoc,
but one needs a fully (rather than partially) defined inverse function for some purposes, including
@@ -2623,7 +4208,14 @@ for calculus. -/
noncomputable def inverse : (M →L[R] M₂) → M₂ →L[R] M := fun f =>
if h : ∃ e : M ≃L[R] M₂, (e : M →L[R] M₂) = f then ((Classical.choose h).symm : M₂ →L[R] M) else 0
#align continuous_linear_map.inverse ContinuousLinearMap.inverse
+-/
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/-- By definition, if `f` is invertible then `inverse f = f.symm`. -/
@[simp]
theorem inverse_equiv (e : M ≃L[R] M₂) : inverse (e : M →L[R] M₂) = e.symm :=
@@ -2634,6 +4226,12 @@ theorem inverse_equiv (e : M ≃L[R] M₂) : inverse (e : M →L[R] M₂) = e.sy
exact_mod_cast Classical.choose_spec h
#align continuous_linear_map.inverse_equiv ContinuousLinearMap.inverse_equiv
+/- warning: continuous_linear_map.inverse_non_equiv -> ContinuousLinearMap.inverse_non_equiv is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.inverse_non_equiv ContinuousLinearMap.inverse_non_equivₓ'. -/
/-- By definition, if `f` is not invertible then `inverse f = 0`. -/
@[simp]
theorem inverse_non_equiv (f : M →L[R] M₂) (h : ¬∃ e' : M ≃L[R] M₂, ↑e' = f) : inverse f = 0 :=
@@ -2650,6 +4248,12 @@ variable [AddCommGroup M] [TopologicalAddGroup M] [Module R M]
variable [AddCommGroup M₂] [Module R M₂]
+/- warning: continuous_linear_map.ring_inverse_equiv -> ContinuousLinearMap.ring_inverse_equiv is a dubious translation:
+lean 3 declaration is
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(RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (Ring.inverse.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_3) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (HasLiftT.mk.{succ u2, succ u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (CoeTCₓ.coe.{succ u2, succ u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (coeBase.{succ u2, succ u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6)))) e)) (ContinuousLinearMap.inverse.{u1, u2, u2} R M M _inst_1 _inst_1 (Ring.toSemiring.{u1} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (HasLiftT.mk.{succ u2, succ u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (CoeTCₓ.coe.{succ u2, succ u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (coeBase.{succ u2, succ u2} (ContinuousLinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6)))) e))
+but is expected to have type
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} M] [_inst_3 : Ring.{u2} R] [_inst_4 : AddCommGroup.{u1} M] [_inst_5 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4)] (_inst_6 : ContinuousLinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5 _inst_5), Eq.{succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5 _inst_5) (Ring.inverse.{u1} (ContinuousLinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u2, u1} R (Ring.toSemiring.{u2} R _inst_3) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5) (ContinuousLinearEquiv.toContinuousLinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5 _inst_5 _inst_6)) (ContinuousLinearMap.inverse.{u2, u1, u1} R M M _inst_1 _inst_1 (Ring.toSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5 (ContinuousLinearEquiv.toContinuousLinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_3) (Ring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_3))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_3))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_3)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M _inst_4) _inst_5 _inst_5 _inst_6))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ring_inverse_equiv ContinuousLinearMap.ring_inverse_equivₓ'. -/
@[simp]
theorem ring_inverse_equiv (e : M ≃L[R] M) : Ring.inverse ↑e = inverse (e : M →L[R] M) :=
by
@@ -2659,6 +4263,12 @@ theorem ring_inverse_equiv (e : M ≃L[R] M) : Ring.inverse ↑e = inverse (e :
rfl
#align continuous_linear_map.ring_inverse_equiv ContinuousLinearMap.ring_inverse_equiv
+/- warning: continuous_linear_map.to_ring_inverse -> ContinuousLinearMap.to_ring_inverse is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {M : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} M] [_inst_2 : TopologicalSpace.{u3} M₂] [_inst_3 : Ring.{u1} R] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : TopologicalAddGroup.{u2} M _inst_1 (AddCommGroup.toAddGroup.{u2} M _inst_4)] [_inst_6 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_7 : AddCommGroup.{u3} M₂] [_inst_8 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7)] (e : ContinuousLinearEquiv.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_6 _inst_8) (f : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_6 _inst_8), Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_8 _inst_6) (ContinuousLinearMap.inverse.{u1, u2, u3} R M M₂ _inst_1 _inst_2 (Ring.toSemiring.{u1} R _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_7) _inst_8 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 f) 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+but is expected to have type
+ forall {R : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} M] [_inst_2 : TopologicalSpace.{u1} M₂] [_inst_3 : Ring.{u3} R] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)] [_inst_6 : AddCommGroup.{u1} M₂] [_inst_7 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6)] (_inst_8 : ContinuousLinearEquiv.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_3))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) _inst_5 _inst_7) (e : ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) _inst_5 _inst_7), Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_7 _inst_5) (ContinuousLinearMap.inverse.{u3, u2, u1} R M M₂ _inst_1 _inst_2 (Ring.toSemiring.{u3} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) _inst_7 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 e) (ContinuousLinearMap.comp.{u3, u3, u3, u1, u2, u2} R R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_7 _inst_5 _inst_5 (RingHomCompTriple.ids.{u3, u3} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3)))) (Ring.inverse.{u2} (ContinuousLinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u3, u2} R (Ring.toSemiring.{u3} R _inst_3) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5) (ContinuousLinearMap.comp.{u3, u3, u3, u2, u1, u2} R R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_3))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_7 _inst_5 (RingHomCompTriple.ids.{u3, u3} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3)))) (ContinuousLinearEquiv.toContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_3))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_7 _inst_5 (ContinuousLinearEquiv.symm.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_3))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) _inst_5 _inst_7 _inst_8)) e)) (ContinuousLinearEquiv.toContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_3))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_7 _inst_5 (ContinuousLinearEquiv.symm.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R _inst_3) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_3))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_3))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R _inst_3)) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_6) _inst_5 _inst_7 _inst_8)))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.to_ring_inverse ContinuousLinearMap.to_ring_inverseₓ'. -/
/-- The function `continuous_linear_equiv.inverse` can be written in terms of `ring.inverse` for the
ring of self-maps of the domain. -/
theorem to_ring_inverse (e : M ≃L[R] M₂) (f : M →L[R] M₂) :
@@ -2680,6 +4290,12 @@ theorem to_ring_inverse (e : M ≃L[R] M₂) (f : M →L[R] M₂) :
simp
#align continuous_linear_map.to_ring_inverse ContinuousLinearMap.to_ring_inverse
+/- warning: continuous_linear_map.ring_inverse_eq_map_inverse -> ContinuousLinearMap.ring_inverse_eq_map_inverse is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} M] [_inst_3 : Ring.{u1} R] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : TopologicalAddGroup.{u2} M _inst_1 (AddCommGroup.toAddGroup.{u2} M _inst_4)] [_inst_6 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)], Eq.{succ u2} ((ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) -> (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6)) (Ring.inverse.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 _inst_6) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_3) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6)) (ContinuousLinearMap.inverse.{u1, u2, u2} R M M _inst_1 _inst_1 (Ring.toSemiring.{u1} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_6)
+but is expected to have type
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} M] [_inst_3 : Ring.{u1} R] [_inst_4 : AddCommGroup.{u2} M] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4)], Eq.{succ u2} ((ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) -> (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5)) (Ring.inverse.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_3) (Ring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_3))) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 _inst_5) (ContinuousLinearMap.monoidWithZero.{u1, u2} R (Ring.toSemiring.{u1} R _inst_3) M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)) (ContinuousLinearMap.inverse.{u1, u2, u2} R M M _inst_1 _inst_1 (Ring.toSemiring.{u1} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5 (AddCommGroup.toAddCommMonoid.{u2} M _inst_4) _inst_5)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.ring_inverse_eq_map_inverse ContinuousLinearMap.ring_inverse_eq_map_inverseₓ'. -/
theorem ring_inverse_eq_map_inverse : Ring.inverse = @inverse R M M _ _ _ _ _ _ _ :=
by
ext
@@ -2697,16 +4313,25 @@ variable {R : Type _} [Ring R] {M : Type _} [TopologicalSpace M] [AddCommGroup M
open ContinuousLinearMap
+#print Submodule.ClosedComplemented /-
/-- A submodule `p` is called *complemented* if there exists a continuous projection `M →ₗ[R] p`. -/
def ClosedComplemented (p : Submodule R M) : Prop :=
∃ f : M →L[R] p, ∀ x : p, f x = x
#align submodule.closed_complemented Submodule.ClosedComplemented
+-/
+/- warning: submodule.closed_complemented.has_closed_complement -> Submodule.ClosedComplemented.has_closed_complement is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4} [_inst_8 : T1Space.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) p) (Subtype.topologicalSpace.{u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) x p) _inst_2)], (Submodule.ClosedComplemented.{u1, u2} R _inst_1 M _inst_2 _inst_3 _inst_4 p) -> (Exists.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (fun (q : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) => Exists.{0} (IsClosed.{u2} M _inst_2 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) q)) (fun (hq : IsClosed.{u2} M _inst_2 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) q)) => IsCompl.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) p q)))
+but is expected to have type
+ forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {M : Type.{u1}} [_inst_2 : TopologicalSpace.{u1} M] [_inst_3 : AddCommGroup.{u1} M] [_inst_4 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3)] {p : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_4} [_inst_8 : T1Space.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_4) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_4)) x p)) (instTopologicalSpaceSubtype.{u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_4) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_4)) x p) _inst_2)], (Submodule.ClosedComplemented.{u2, u1} R _inst_1 M _inst_2 _inst_3 _inst_4 p) -> (Exists.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_4) (fun (q : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_4) => Exists.{0} (IsClosed.{u1} M _inst_2 (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_4) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_4) q)) (fun (hq : IsClosed.{u1} M _inst_2 (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_4) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_4) q)) => IsCompl.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_4) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_4))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_4) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_4)) p q)))
+Case conversion may be inaccurate. Consider using '#align submodule.closed_complemented.has_closed_complement Submodule.ClosedComplemented.has_closed_complementₓ'. -/
theorem ClosedComplemented.has_closed_complement {p : Submodule R M} [T1Space p]
(h : ClosedComplemented p) : ∃ (q : Submodule R M)(hq : IsClosed (q : Set M)), IsCompl p q :=
Exists.elim h fun f hf => ⟨ker f, f.isClosed_ker, LinearMap.isCompl_of_proj hf⟩
#align submodule.closed_complemented.has_closed_complement Submodule.ClosedComplemented.has_closed_complement
+#print Submodule.ClosedComplemented.isClosed /-
protected theorem ClosedComplemented.isClosed [TopologicalAddGroup M] [T1Space M]
{p : Submodule R M} (h : ClosedComplemented p) : IsClosed (p : Set M) :=
by
@@ -2714,12 +4339,25 @@ protected theorem ClosedComplemented.isClosed [TopologicalAddGroup M] [T1Space M
have : ker (id R M - p.subtypeL.comp f) = p := LinearMap.ker_id_sub_eq_of_proj hf
exact this ▸ is_closed_ker _
#align submodule.closed_complemented.is_closed Submodule.ClosedComplemented.isClosed
+-/
+/- warning: submodule.closed_complemented_bot -> Submodule.closedComplemented_bot is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)], Submodule.ClosedComplemented.{u1, u2} R _inst_1 M _inst_2 _inst_3 _inst_4 (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.hasBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))
+but is expected to have type
+ forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {M : Type.{u1}} [_inst_2 : TopologicalSpace.{u1} M] [_inst_3 : AddCommGroup.{u1} M] [_inst_4 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3)], Submodule.ClosedComplemented.{u2, u1} R _inst_1 M _inst_2 _inst_3 _inst_4 (Bot.bot.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_4) (Submodule.instBotSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_4))
+Case conversion may be inaccurate. Consider using '#align submodule.closed_complemented_bot Submodule.closedComplemented_botₓ'. -/
@[simp]
theorem closedComplemented_bot : ClosedComplemented (⊥ : Submodule R M) :=
⟨0, fun x => by simp only [zero_apply, eq_zero_of_bot_submodule x]⟩
#align submodule.closed_complemented_bot Submodule.closedComplemented_bot
+/- warning: submodule.closed_complemented_top -> Submodule.closedComplemented_top is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)], Submodule.ClosedComplemented.{u1, u2} R _inst_1 M _inst_2 _inst_3 _inst_4 (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))
+but is expected to have type
+ forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {M : Type.{u1}} [_inst_2 : TopologicalSpace.{u1} M] [_inst_3 : AddCommGroup.{u1} M] [_inst_4 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3)], Submodule.ClosedComplemented.{u2, u1} R _inst_1 M _inst_2 _inst_3 _inst_4 (Top.top.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_4) (Submodule.instTopSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_4))
+Case conversion may be inaccurate. Consider using '#align submodule.closed_complemented_top Submodule.closedComplemented_topₓ'. -/
@[simp]
theorem closedComplemented_top : ClosedComplemented (⊤ : Submodule R M) :=
⟨(id R M).codRestrict ⊤ fun x => trivial, fun x => Subtype.ext_iff_val.2 <| by simp⟩
@@ -2727,6 +4365,12 @@ theorem closedComplemented_top : ClosedComplemented (⊤ : Submodule R M) :=
end Submodule
+/- warning: continuous_linear_map.closed_complemented_ker_of_right_inverse -> ContinuousLinearMap.closedComplemented_ker_of_rightInverse is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommGroup.{u2} M] {M₂ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} M₂] [_inst_5 : AddCommGroup.{u3} M₂] [_inst_6 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] [_inst_7 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5)] [_inst_8 : TopologicalAddGroup.{u2} M _inst_2 (AddCommGroup.toAddGroup.{u2} M _inst_3)] (f₁ : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_7) (f₂ : ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6), (Function.RightInverse.{succ u2, succ u3} M M₂ (coeFn.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6) (fun (_x : ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6) => M₂ -> M) 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(Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 _inst_7)) f₁))
+but is expected to have type
+ forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {M : Type.{u2}} [_inst_2 : TopologicalSpace.{u2} M] [_inst_3 : AddCommGroup.{u2} M] {M₂ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} M₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] [_inst_7 : Module.{u3, u1} R M₂ (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] [_inst_8 : TopologicalAddGroup.{u2} M _inst_2 (AddCommGroup.toAddGroup.{u2} M _inst_3)] (f₁ : ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7) (f₂ : ContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6), (Function.RightInverse.{succ u2, succ u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (ContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M₂) => M) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u1, u2} (ContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6) M₂ M _inst_4 _inst_2 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u3, u1, u2} (ContinuousLinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_7 _inst_6))) f₂) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M) => M₂) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7) M M₂ _inst_2 _inst_4 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7))) f₁)) -> (Submodule.ClosedComplemented.{u3, u2} R _inst_1 M _inst_2 _inst_3 _inst_6 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M₂ (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7) (ContinuousSemilinearMapClass.toSemilinearMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7) R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7 (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) M₂ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 _inst_7)) f₁))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.closed_complemented_ker_of_right_inverse ContinuousLinearMap.closedComplemented_ker_of_rightInverseₓ'. -/
theorem ContinuousLinearMap.closedComplemented_ker_of_rightInverse {R : Type _} [Ring R]
{M : Type _} [TopologicalSpace M] [AddCommGroup M] {M₂ : Type _} [TopologicalSpace M₂]
[AddCommGroup M₂] [Module R M] [Module R M₂] [TopologicalAddGroup M] (f₁ : M →L[R] M₂)
@@ -2741,14 +4385,23 @@ namespace Submodule
variable {R M : Type _} [Ring R] [AddCommGroup M] [Module R M] [TopologicalSpace M]
(S : Submodule R M)
+/- warning: submodule.is_open_map_mkq -> Submodule.isOpenMap_mkQ is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : TopologicalSpace.{u2} M] (S : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : TopologicalAddGroup.{u2} M _inst_4 (AddCommGroup.toAddGroup.{u2} M _inst_2)], IsOpenMap.{u2, u2} M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) _inst_4 (Quotient.topologicalSpace.{u2} M (Submodule.quotientRel.{u1, u2} R M _inst_1 _inst_2 _inst_3 S) _inst_4) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) => M -> (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 S))
+but is expected to have type
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : TopologicalSpace.{u2} M] (S : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : TopologicalAddGroup.{u2} M _inst_4 (AddCommGroup.toAddGroup.{u2} M _inst_2)], IsOpenMap.{u2, u2} M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) _inst_4 (QuotientModule.Quotient.topologicalSpace.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 S) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M _inst_1 _inst_2 _inst_3) S) (Submodule.Quotient.addCommGroup.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) _inst_3 (Submodule.Quotient.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 S) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.mkQ.{u1, u2} R M _inst_1 _inst_2 _inst_3 S))
+Case conversion may be inaccurate. Consider using '#align submodule.is_open_map_mkq Submodule.isOpenMap_mkQₓ'. -/
theorem isOpenMap_mkQ [TopologicalAddGroup M] : IsOpenMap S.mkQ :=
QuotientAddGroup.isOpenMap_coe S.toAddSubgroup
#align submodule.is_open_map_mkq Submodule.isOpenMap_mkQ
+#print Submodule.topologicalAddGroup_quotient /-
instance topologicalAddGroup_quotient [TopologicalAddGroup M] : TopologicalAddGroup (M ⧸ S) :=
topologicalAddGroup_quotient S.toAddSubgroup
#align submodule.topological_add_group_quotient Submodule.topologicalAddGroup_quotient
+-/
+#print Submodule.continuousSMul_quotient /-
instance continuousSMul_quotient [TopologicalSpace R] [TopologicalAddGroup M] [ContinuousSMul R M] :
ContinuousSMul R (M ⧸ S) := by
constructor
@@ -2759,11 +4412,14 @@ instance continuousSMul_quotient [TopologicalSpace R] [TopologicalAddGroup M] [C
rw [quot.continuous_iff]
exact continuous_quot_mk.comp continuous_smul
#align submodule.has_continuous_smul_quotient Submodule.continuousSMul_quotient
+-/
+#print Submodule.t3_quotient_of_isClosed /-
instance t3_quotient_of_isClosed [TopologicalAddGroup M] [IsClosed (S : Set M)] : T3Space (M ⧸ S) :=
letI : IsClosed (S.to_add_subgroup : Set M) := ‹_›
S.to_add_subgroup.t3_quotient_of_is_closed
#align submodule.t3_quotient_of_is_closed Submodule.t3_quotient_of_isClosed
+-/
end Submodule
mathlib commit https://github.com/leanprover-community/mathlib/commit/1f4705ccdfe1e557fc54a0ce081a05e33d2e6240
@@ -5,7 +5,7 @@ Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov, Fréd
Heather Macbeth
! This file was ported from Lean 3 source module topology.algebra.module.basic
-! leanprover-community/mathlib commit 9a59dcb7a2d06bf55da57b9030169219980660cd
+! leanprover-community/mathlib commit f430769b562e0cedef59ee1ed968d67e0e0c86ba
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -17,7 +17,6 @@ import Mathbin.Topology.UniformSpace.UniformEmbedding
import Mathbin.Algebra.Algebra.Basic
import Mathbin.LinearAlgebra.Projection
import Mathbin.LinearAlgebra.Pi
-import Mathbin.RingTheory.SimpleModule
/-!
# Theory of topological modules and continuous linear maps.
@@ -185,9 +184,8 @@ end Submodule
section closure
-variable {R R' : Type u} {M M' : Type v} [Semiring R] [TopologicalSpace R] [Ring R']
- [TopologicalSpace R'] [TopologicalSpace M] [AddCommMonoid M] [TopologicalSpace M']
- [AddCommGroup M'] [Module R M] [ContinuousSMul R M] [Module R' M'] [ContinuousSMul R' M']
+variable {R : Type u} {M : Type v} [Semiring R] [TopologicalSpace R] [TopologicalSpace M]
+ [AddCommMonoid M] [Module R M] [ContinuousSMul R M]
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -278,16 +276,6 @@ theorem Submodule.isClosed_or_dense_of_isCoatom (s : Submodule R M) (hs : IsCoat
Submodule.dense_iff_topologicalClosure_eq_top.mpr
#align submodule.is_closed_or_dense_of_is_coatom Submodule.isClosed_or_dense_of_isCoatom
-theorem LinearMap.isClosed_or_dense_ker [ContinuousAdd M'] [IsSimpleModule R' R']
- (l : M' →ₗ[R'] R') : IsClosed (l.ker : Set M') ∨ Dense (l.ker : Set M') :=
- by
- rcases l.surjective_or_eq_zero with (hl | rfl)
- · refine' l.ker.is_closed_or_dense_of_is_coatom (LinearMap.isCoatom_ker_of_surjective hl)
- · rw [LinearMap.ker_zero]
- left
- exact isClosed_univ
-#align linear_map.is_closed_or_dense_ker LinearMap.isClosed_or_dense_ker
-
end closure
section Pi
mathlib commit https://github.com/leanprover-community/mathlib/commit/62e8311c791f02c47451bf14aa2501048e7c2f33
@@ -5,11 +5,11 @@ Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov, Fréd
Heather Macbeth
! This file was ported from Lean 3 source module topology.algebra.module.basic
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 9a59dcb7a2d06bf55da57b9030169219980660cd
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
-import Mathbin.Topology.Algebra.Ring
+import Mathbin.Topology.Algebra.Ring.Basic
import Mathbin.Topology.Algebra.MulAction
import Mathbin.Topology.Algebra.UniformGroup
import Mathbin.Topology.ContinuousFunction.Basic
mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442
@@ -200,7 +200,7 @@ theorem Submodule.closure_smul_self_subset (s : Submodule R M) :
(fun p : R × M => p.1 • p.2) '' closure (Set.univ ×ˢ s) :=
by simp [closure_prod_eq]
_ ⊆ closure ((fun p : R × M => p.1 • p.2) '' Set.univ ×ˢ s) :=
- image_closure_subset_closure_image continuous_smul
+ (image_closure_subset_closure_image continuous_smul)
_ = closure s := by
congr
ext x
mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee
@@ -532,7 +532,7 @@ protected theorem continuous (f : M₁ →SL[σ₁₂] M₂) : Continuous f :=
protected theorem uniformContinuous {E₁ E₂ : Type _} [UniformSpace E₁] [UniformSpace E₂]
[AddCommGroup E₁] [AddCommGroup E₂] [Module R₁ E₁] [Module R₂ E₂] [UniformAddGroup E₁]
[UniformAddGroup E₂] (f : E₁ →SL[σ₁₂] E₂) : UniformContinuous f :=
- uniform_continuous_add_monoid_hom_of_continuous f.Continuous
+ uniformContinuous_addMonoidHom_of_continuous f.Continuous
#align continuous_linear_map.uniform_continuous ContinuousLinearMap.uniformContinuous
@[simp, norm_cast]
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -1566,7 +1566,7 @@ section DivisionMonoid
variable {R M : Type _}
/-- A nonzero continuous linear functional is open. -/
-protected theorem isOpenMap_of_ne_zero [TopologicalSpace R] [DivisionRing R] [HasContinuousSub R]
+protected theorem isOpenMap_of_ne_zero [TopologicalSpace R] [DivisionRing R] [ContinuousSub R]
[AddCommGroup M] [TopologicalSpace M] [ContinuousAdd M] [Module R M] [ContinuousSMul R M]
(f : M →L[R] R) (hf : f ≠ 0) : IsOpenMap f :=
let ⟨x, hx⟩ := exists_ne_zero hf
@@ -2754,11 +2754,11 @@ variable {R M : Type _} [Ring R] [AddCommGroup M] [Module R M] [TopologicalSpace
(S : Submodule R M)
theorem isOpenMap_mkQ [TopologicalAddGroup M] : IsOpenMap S.mkQ :=
- quotientAddGroup.isOpenMap_coe S.toAddSubgroup
+ QuotientAddGroup.isOpenMap_coe S.toAddSubgroup
#align submodule.is_open_map_mkq Submodule.isOpenMap_mkQ
instance topologicalAddGroup_quotient [TopologicalAddGroup M] : TopologicalAddGroup (M ⧸ S) :=
- topological_add_group_quotient S.toAddSubgroup
+ topologicalAddGroup_quotient S.toAddSubgroup
#align submodule.topological_add_group_quotient Submodule.topologicalAddGroup_quotient
instance continuousSMul_quotient [TopologicalSpace R] [TopologicalAddGroup M] [ContinuousSMul R M] :
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Splits Algebra.Algebra.Defs
off Algebra.Algebra.Basic
. Most imports only need the Defs file, which has significantly smaller imports. The remaining Algebra.Algebra.Basic
is now a grab-bag of unrelated results, and should probably be split further or rehomed.
This is mostly motivated by the wasted effort during minimization upon encountering Algebra.Algebra.Basic.
Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>
@@ -9,7 +9,7 @@ import Mathlib.Topology.Algebra.MulAction
import Mathlib.Topology.Algebra.UniformGroup
import Mathlib.Topology.ContinuousFunction.Basic
import Mathlib.Topology.UniformSpace.UniformEmbedding
-import Mathlib.Algebra.Algebra.Basic
+import Mathlib.Algebra.Algebra.Defs
import Mathlib.LinearAlgebra.Projection
import Mathlib.LinearAlgebra.Pi
import Mathlib.LinearAlgebra.Finsupp
There is a technical issue: I need to register two local instances to be even able to state the norm estimates. The issue is typeclass inference getting stuck in complicated types of linear maps...
@@ -1351,6 +1351,17 @@ theorem iInf_ker_proj : (⨅ i, ker (proj i : (∀ i, φ i) →L[R] φ i) : Subm
variable (R φ)
+/-- Given a function `f : α → ι`, it induces a continuous linear function by right composition on
+product types. For `f = Subtype.val`, this corresponds to forgetting some set of variables. -/
+def _root_.Pi.compRightL {α : Type*} (f : α → ι) : ((i : ι) → φ i) →L[R] ((i : α) → φ (f i)) where
+ toFun := fun v i ↦ v (f i)
+ map_add' := by intros; ext; simp
+ map_smul' := by intros; ext; simp
+ cont := by continuity
+
+@[simp] lemma _root_.Pi.compRightL_apply {α : Type*} (f : α → ι) (v : (i : ι) → φ i) (i : α) :
+ Pi.compRightL R φ f v i = v (f i) := rfl
+
/-- If `I` and `J` are complementary index sets, the product of the kernels of the `J`th projections
of `φ` is linearly equivalent to the product over `I`. -/
def iInfKerProjEquiv {I J : Set ι} [DecidablePred fun i => i ∈ I] (hd : Disjoint I J)
@@ -269,7 +269,7 @@ class ContinuousSemilinearMapClass (F : Type*) {R S : outParam (Type*)} [Semirin
#align continuous_semilinear_map_class ContinuousSemilinearMapClass
-- `σ`, `R` and `S` become metavariables, but they are all outparams so it's OK
--- Porting note: was attribute [nolint dangerous_instance]
+-- Porting note(#12094): removed nolint; dangerous_instance linter not ported yet
-- attribute [nolint dangerous_instance] ContinuousSemilinearMapClass.toContinuousMapClass
/-- `ContinuousLinearMapClass F R M M₂` asserts `F` is a type of bundled continuous
@@ -284,7 +284,7 @@ abbrev ContinuousLinearMapClass (F : Type*) (R : outParam (Type*)) [Semiring R]
/-- Continuous linear equivalences between modules. We only put the type classes that are necessary
for the definition, although in applications `M` and `M₂` will be topological modules over the
topological semiring `R`. -/
--- Porting note (#11215): TODO: was @[nolint has_nonempty_instance]
+-- Porting note (#5171): linter not ported yet; was @[nolint has_nonempty_instance]
structure ContinuousLinearEquiv {R : Type*} {S : Type*} [Semiring R] [Semiring S] (σ : R →+* S)
{σ' : S →+* R} [RingHomInvPair σ σ'] [RingHomInvPair σ' σ] (M : Type*) [TopologicalSpace M]
[AddCommMonoid M] (M₂ : Type*) [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M]
Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.
@@ -888,7 +888,7 @@ instance semiring [ContinuousAdd M₁] : Semiring (M₁ →L[R₁] M₁) where
natCast_succ n := AddMonoid.nsmul_succ n (1 : M₁ →L[R₁] M₁)
#align continuous_linear_map.semiring ContinuousLinearMap.semiring
-/-- `ContinuousLinearMap.toLinearMap` as a `RingHom`.-/
+/-- `ContinuousLinearMap.toLinearMap` as a `RingHom`. -/
@[simps]
def toLinearMapRingHom [ContinuousAdd M₁] : (M₁ →L[R₁] M₁) →+* M₁ →ₗ[R₁] M₁ where
toFun := toLinearMap
@@ -1258,7 +1258,7 @@ variable (R₁)
variable [ContinuousSMul R₁ M₁]
/-- Given an element `x` of a topological space `M` over a semiring `R`, the natural continuous
-linear map from `R` to `M` by taking multiples of `x`.-/
+linear map from `R` to `M` by taking multiples of `x`. -/
def toSpanSingleton (x : M₁) : R₁ →L[R₁] M₁
where
toLinearMap := LinearMap.toSpanSingleton R₁ M₁ x
We change the following field in the definition of an additive commutative monoid:
nsmul_succ : ∀ (n : ℕ) (x : G),
- AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+ AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x
where the latter is more natural
We adjust the definitions of ^
in monoids, groups, etc.
Originally there was a warning comment about why this natural order was preferred
use
x * npowRec n x
and notnpowRec n x * x
in the definition to make sure that definitional unfolding ofnpowRec
is blocked, to avoid deep recursion issues.
but it seems to no longer apply.
Remarks on the PR :
pow_succ
and pow_succ'
have switched their meanings.Ideal.IsPrime.mul_mem_pow
which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul
.@@ -757,7 +757,7 @@ instance addCommMonoid : AddCommMonoid (M₁ →SL[σ₁₂] M₂) where
simp
nsmul_succ n f := by
ext
- simp [Nat.add_comm n 1, add_smul]
+ simp [add_smul]
#align continuous_linear_map.add_comm_monoid ContinuousLinearMap.addCommMonoid
@[simp, norm_cast]
@@ -885,7 +885,7 @@ instance semiring [ContinuousAdd M₁] : Semiring (M₁ →L[R₁] M₁) where
right_distrib _ _ _ := ext fun _ => LinearMap.add_apply _ _ _
toNatCast := instNatCast
natCast_zero := zero_smul ℕ (1 : M₁ →L[R₁] M₁)
- natCast_succ n := (AddMonoid.nsmul_succ n (1 : M₁ →L[R₁] M₁)).trans (add_comm _ _)
+ natCast_succ n := AddMonoid.nsmul_succ n (1 : M₁ →L[R₁] M₁)
#align continuous_linear_map.semiring ContinuousLinearMap.semiring
/-- `ContinuousLinearMap.toLinearMap` as a `RingHom`.-/
smul
(#11331)
We want to avoid making Lean unfold smul
during unification. A separate instance does helps at the cost of some elaboration failures.
@@ -584,8 +584,10 @@ variable {S₂ T₂ : Type*} [Monoid S₂] [Monoid T₂]
variable [DistribMulAction S₂ M₂] [SMulCommClass R₂ S₂ M₂] [ContinuousConstSMul S₂ M₂]
variable [DistribMulAction T₂ M₂] [SMulCommClass R₂ T₂ M₂] [ContinuousConstSMul T₂ M₂]
-instance mulAction : MulAction S₂ (M₁ →SL[σ₁₂] M₂) where
+instance instSMul : SMul S₂ (M₁ →SL[σ₁₂] M₂) where
smul c f := ⟨c • (f : M₁ →ₛₗ[σ₁₂] M₂), (f.2.const_smul _ : Continuous fun x => c • f x)⟩
+
+instance mulAction : MulAction S₂ (M₁ →SL[σ₁₂] M₂) where
one_smul _f := ext fun _x => one_smul _ _
mul_smul _a _b _f := ext fun _x => mul_smul _ _ _
#align continuous_linear_map.mul_action ContinuousLinearMap.mulAction
@@ -733,8 +735,6 @@ theorem coe_add' (f g : M₁ →SL[σ₁₂] M₂) : ⇑(f + g) = f + g :=
#align continuous_linear_map.coe_add' ContinuousLinearMap.coe_add'
instance addCommMonoid : AddCommMonoid (M₁ →SL[σ₁₂] M₂) where
- zero := (0 : M₁ →SL[σ₁₂] M₂)
- add := (· + ·)
zero_add := by
intros
ext
@@ -865,9 +865,6 @@ theorem mul_apply (f g : M₁ →L[R₁] M₁) (x : M₁) : (f * g) x = f (g x)
#align continuous_linear_map.mul_apply ContinuousLinearMap.mul_apply
instance monoidWithZero : MonoidWithZero (M₁ →L[R₁] M₁) where
- mul := (· * ·)
- one := 1
- zero := 0
mul_zero f := ext fun _ => map_zero f
zero_mul _ := ext fun _ => rfl
mul_one _ := ext fun _ => rfl
@@ -878,12 +875,15 @@ instance monoidWithZero : MonoidWithZero (M₁ →L[R₁] M₁) where
theorem coe_pow (f : M₁ →L[R₁] M₁) (n : ℕ) : ⇑(f ^ n) = f^[n] :=
hom_coe_pow _ rfl (fun _ _ ↦ rfl) _ _
+instance instNatCast [ContinuousAdd M₁] : NatCast (M₁ →L[R₁] M₁) where
+ natCast n := n • (1 : M₁ →L[R₁] M₁)
+
instance semiring [ContinuousAdd M₁] : Semiring (M₁ →L[R₁] M₁) where
__ := ContinuousLinearMap.monoidWithZero
__ := ContinuousLinearMap.addCommMonoid
left_distrib f g h := ext fun x => map_add f (g x) (h x)
right_distrib _ _ _ := ext fun _ => LinearMap.add_apply _ _ _
- natCast n := n • (1 : M₁ →L[R₁] M₁)
+ toNatCast := instNatCast
natCast_zero := zero_smul ℕ (1 : M₁ →L[R₁] M₁)
natCast_succ n := (AddMonoid.nsmul_succ n (1 : M₁ →L[R₁] M₁)).trans (add_comm _ _)
#align continuous_linear_map.semiring ContinuousLinearMap.semiring
zpow_coe_nat
to zpow_natCast
(#11528)
... and add a deprecated alias for the old name. This is mostly just me discovering the power of F2
@@ -1518,7 +1518,7 @@ instance ring [TopologicalAddGroup M] : Ring (M →L[R] M) where
__ := ContinuousLinearMap.semiring
__ := ContinuousLinearMap.addCommGroup
intCast z := z • (1 : M →L[R] M)
- intCast_ofNat := coe_nat_zsmul _
+ intCast_ofNat := natCast_zsmul _
intCast_negSucc := negSucc_zsmul _
#align continuous_linear_map.ring ContinuousLinearMap.ring
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)
@@ -581,9 +581,7 @@ theorem _root_.DenseRange.topologicalClosure_map_submodule [RingHomSurjective σ
section SMulMonoid
variable {S₂ T₂ : Type*} [Monoid S₂] [Monoid T₂]
-
variable [DistribMulAction S₂ M₂] [SMulCommClass R₂ S₂ M₂] [ContinuousConstSMul S₂ M₂]
-
variable [DistribMulAction T₂ M₂] [SMulCommClass R₂ T₂ M₂] [ContinuousConstSMul T₂ M₂]
instance mulAction : MulAction S₂ (M₁ →SL[σ₁₂] M₂) where
@@ -1257,7 +1255,6 @@ theorem smulRight_comp [ContinuousMul R₁] {x : M₂} {c : R₁} :
section ToSpanSingleton
variable (R₁)
-
variable [ContinuousSMul R₁ M₁]
/-- Given an element `x` of a topological space `M` over a semiring `R`, the natural continuous
@@ -1611,7 +1608,6 @@ theorem smul_comp (c : S₃) (h : M₂ →SL[σ₂₃] M₃) (f : M →SL[σ₁
#align continuous_linear_map.smul_comp ContinuousLinearMap.smul_comp
variable [DistribMulAction S₃ M₂] [ContinuousConstSMul S₃ M₂] [SMulCommClass R₂ S₃ M₂]
-
variable [DistribMulAction S N₂] [ContinuousConstSMul S N₂] [SMulCommClass R S N₂]
@[simp]
@@ -2599,9 +2595,7 @@ variable {R : Type*} {M : Type*} {M₂ : Type*} [TopologicalSpace M] [Topologica
section
variable [Semiring R]
-
variable [AddCommMonoid M₂] [Module R M₂]
-
variable [AddCommMonoid M] [Module R M]
/-- Introduce a function `inverse` from `M →L[R] M₂` to `M₂ →L[R] M`, which sends `f` to `f.symm` if
@@ -2632,9 +2626,7 @@ end
section
variable [Ring R]
-
variable [AddCommGroup M] [TopologicalAddGroup M] [Module R M]
-
variable [AddCommGroup M₂] [Module R M₂]
@[simp]
@@ -284,7 +284,7 @@ abbrev ContinuousLinearMapClass (F : Type*) (R : outParam (Type*)) [Semiring R]
/-- Continuous linear equivalences between modules. We only put the type classes that are necessary
for the definition, although in applications `M` and `M₂` will be topological modules over the
topological semiring `R`. -/
--- Porting note: todo: was @[nolint has_nonempty_instance]
+-- Porting note (#11215): TODO: was @[nolint has_nonempty_instance]
structure ContinuousLinearEquiv {R : Type*} {S : Type*} [Semiring R] [Semiring S] (σ : R →+* S)
{σ' : S →+* R} [RingHomInvPair σ σ'] [RingHomInvPair σ' σ] (M : Type*) [TopologicalSpace M]
[AddCommMonoid M] (M₂ : Type*) [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M]
open Classical
(#11199)
We remove all but one open Classical
s, instead preferring to use open scoped Classical
. The only real side-effect this led to is moving a couple declarations to use Exists.choose
instead of Classical.choose
.
The first few commits are explicitly labelled regex replaces for ease of review.
@@ -2592,7 +2592,7 @@ end ContinuousLinearEquiv
namespace ContinuousLinearMap
-open Classical
+open scoped Classical
variable {R : Type*} {M : Type*} {M₂ : Type*} [TopologicalSpace M] [TopologicalSpace M₂]
Homogenises porting notes via capitalisation and addition of whitespace.
It makes the following changes:
@@ -269,7 +269,7 @@ class ContinuousSemilinearMapClass (F : Type*) {R S : outParam (Type*)} [Semirin
#align continuous_semilinear_map_class ContinuousSemilinearMapClass
-- `σ`, `R` and `S` become metavariables, but they are all outparams so it's OK
--- porting note: was attribute [nolint dangerous_instance]
+-- Porting note: was attribute [nolint dangerous_instance]
-- attribute [nolint dangerous_instance] ContinuousSemilinearMapClass.toContinuousMapClass
/-- `ContinuousLinearMapClass F R M M₂` asserts `F` is a type of bundled continuous
@@ -284,7 +284,7 @@ abbrev ContinuousLinearMapClass (F : Type*) (R : outParam (Type*)) [Semiring R]
/-- Continuous linear equivalences between modules. We only put the type classes that are necessary
for the definition, although in applications `M` and `M₂` will be topological modules over the
topological semiring `R`. -/
--- porting note: todo: was @[nolint has_nonempty_instance]
+-- Porting note: todo: was @[nolint has_nonempty_instance]
structure ContinuousLinearEquiv {R : Type*} {S : Type*} [Semiring R] [Semiring S] (σ : R →+* S)
{σ' : S →+* R} [RingHomInvPair σ σ'] [RingHomInvPair σ' σ] (M : Type*) [TopologicalSpace M]
[AddCommMonoid M] (M₂ : Type*) [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M]
zpow_ofNat
and ofNat_zsmul
(#10969)
Previously these were syntactically identical to the corresponding zpow_coe_nat
and coe_nat_zsmul
lemmas, now they are about OfNat.ofNat
.
Unfortunately, almost every call site uses the ofNat
name to refer to Nat.cast
, so the downstream proofs had to be adjusted too.
@@ -1521,7 +1521,7 @@ instance ring [TopologicalAddGroup M] : Ring (M →L[R] M) where
__ := ContinuousLinearMap.semiring
__ := ContinuousLinearMap.addCommGroup
intCast z := z • (1 : M →L[R] M)
- intCast_ofNat := ofNat_zsmul _
+ intCast_ofNat := coe_nat_zsmul _
intCast_negSucc := negSucc_zsmul _
#align continuous_linear_map.ring ContinuousLinearMap.ring
@@ -504,12 +504,12 @@ protected theorem map_add (f : M₁ →SL[σ₁₂] M₂) (x y : M₁) : f (x +
map_add f x y
#align continuous_linear_map.map_add ContinuousLinearMap.map_add
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
protected theorem map_smulₛₗ (f : M₁ →SL[σ₁₂] M₂) (c : R₁) (x : M₁) : f (c • x) = σ₁₂ c • f x :=
(toLinearMap _).map_smulₛₗ _ _
#align continuous_linear_map.map_smulₛₗ ContinuousLinearMap.map_smulₛₗ
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
protected theorem map_smul [Module R₁ M₂] (f : M₁ →L[R₁] M₂) (c : R₁) (x : M₁) :
f (c • x) = c • f x := by simp only [RingHom.id_apply, ContinuousLinearMap.map_smulₛₗ]
#align continuous_linear_map.map_smul ContinuousLinearMap.map_smul
@@ -1960,27 +1960,27 @@ theorem map_nhds_eq (e : M₁ ≃SL[σ₁₂] M₂) (x : M₁) : map e (𝓝 x)
#align continuous_linear_equiv.map_nhds_eq ContinuousLinearEquiv.map_nhds_eq
-- Make some straightforward lemmas available to `simp`.
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
theorem map_zero (e : M₁ ≃SL[σ₁₂] M₂) : e (0 : M₁) = 0 :=
(e : M₁ →SL[σ₁₂] M₂).map_zero
#align continuous_linear_equiv.map_zero ContinuousLinearEquiv.map_zero
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
theorem map_add (e : M₁ ≃SL[σ₁₂] M₂) (x y : M₁) : e (x + y) = e x + e y :=
(e : M₁ →SL[σ₁₂] M₂).map_add x y
#align continuous_linear_equiv.map_add ContinuousLinearEquiv.map_add
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
theorem map_smulₛₗ (e : M₁ ≃SL[σ₁₂] M₂) (c : R₁) (x : M₁) : e (c • x) = σ₁₂ c • e x :=
(e : M₁ →SL[σ₁₂] M₂).map_smulₛₗ c x
#align continuous_linear_equiv.map_smulₛₗ ContinuousLinearEquiv.map_smulₛₗ
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
theorem map_smul [Module R₁ M₂] (e : M₁ ≃L[R₁] M₂) (c : R₁) (x : M₁) : e (c • x) = c • e x :=
(e : M₁ →L[R₁] M₂).map_smul c x
#align continuous_linear_equiv.map_smul ContinuousLinearEquiv.map_smul
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
theorem map_eq_zero_iff (e : M₁ ≃SL[σ₁₂] M₂) {x : M₁} : e x = 0 ↔ x = 0 :=
e.toLinearEquiv.map_eq_zero_iff
#align continuous_linear_equiv.map_eq_zero_iff ContinuousLinearEquiv.map_eq_zero_iff
@@ -2394,12 +2394,12 @@ variable {R : Type*} [Ring R] {R₂ : Type*} [Ring R₂] {M : Type*} [Topologica
variable {σ₁₂ : R →+* R₂} {σ₂₁ : R₂ →+* R} [RingHomInvPair σ₁₂ σ₂₁] [RingHomInvPair σ₂₁ σ₁₂]
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
theorem map_sub (e : M ≃SL[σ₁₂] M₂) (x y : M) : e (x - y) = e x - e y :=
(e : M →SL[σ₁₂] M₂).map_sub x y
#align continuous_linear_equiv.map_sub ContinuousLinearEquiv.map_sub
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
theorem map_neg (e : M ≃SL[σ₁₂] M₂) (x : M) : e (-x) = -e x :=
(e : M →SL[σ₁₂] M₂).map_neg x
#align continuous_linear_equiv.map_neg ContinuousLinearEquiv.map_neg
@@ -427,7 +427,7 @@ instance continuousSemilinearMapClass :
/-- Coerce continuous linear maps to functions. -/
--instance toFun' : CoeFun (M₁ →SL[σ₁₂] M₂) fun _ => M₁ → M₂ := ⟨DFunLike.coe⟩
--- porting note: was `simp`, now `simp only` proves it
+-- porting note (#10618): was `simp`, now `simp only` proves it
theorem coe_mk (f : M₁ →ₛₗ[σ₁₂] M₂) (h) : (mk f h : M₁ →ₛₗ[σ₁₂] M₂) = f :=
rfl
#align continuous_linear_map.coe_mk ContinuousLinearMap.coe_mk
have
, replace
and suffices
(#10640)
No changes to tactic file, it's just boring fixes throughout the library.
This follows on from #6964.
Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
@@ -86,7 +86,7 @@ One can also use `haveI := Module.punctured_nhds_neBot R M` in a proof.
theorem Module.punctured_nhds_neBot [Nontrivial M] [NeBot (𝓝[≠] (0 : R))] [NoZeroSMulDivisors R M]
(x : M) : NeBot (𝓝[≠] x) := by
rcases exists_ne (0 : M) with ⟨y, hy⟩
- suffices : Tendsto (fun c : R => x + c • y) (𝓝[≠] 0) (𝓝[≠] x); exact this.neBot
+ suffices Tendsto (fun c : R => x + c • y) (𝓝[≠] 0) (𝓝[≠] x) from this.neBot
refine' Tendsto.inf _ (tendsto_principal_principal.2 <| _)
· convert tendsto_const_nhds.add ((@tendsto_id R _).smul_const y)
rw [zero_smul, add_zero]
IsSeparable
API (#10286)
isSeparable_iUnion
to an Iff
lemma, restore the original version as IsSeparable.iUnion
;isSeparable_union
and isSeparable_closure
;isSeparable_pi
from [Finite ι]
to [Countable ι]
, add IsSeparable.univ_pi
version;Dense.isSeparable_iff
and isSeparable_range
;isSeparable_of_separableSpace_subtype
to IsSeparable.of_subtype
;isSeparable_of_separableSpace
to IsSeparable.of_separableSpace
.@@ -115,12 +115,10 @@ lemma TopologicalSpace.IsSeparable.span {R M : Type*} [AddCommMonoid M] [Semirin
[ContinuousAdd M] [ContinuousSMul R M] {s : Set M} (hs : IsSeparable s) :
IsSeparable (Submodule.span R s : Set M) := by
rw [span_eq_iUnion_nat]
- apply isSeparable_iUnion (fun n ↦ ?_)
- apply IsSeparable.image
+ refine .iUnion fun n ↦ .image ?_ ?_
· have : IsSeparable {f : Fin n → R × M | ∀ (i : Fin n), f i ∈ Set.univ ×ˢ s} := by
- apply isSeparable_pi (fun i ↦ (isSeparable_of_separableSpace Set.univ).prod hs)
- convert this
- simp
+ apply isSeparable_pi (fun i ↦ .prod (.of_separableSpace Set.univ) hs)
+ rwa [Set.univ_prod] at this
· apply continuous_finset_sum _ (fun i _ ↦ ?_)
exact (continuous_fst.comp (continuous_apply i)).smul (continuous_snd.comp (continuous_apply i))
The FunLike hierarchy is very big and gets scanned through each time we need a coercion (via the CoeFun
instance). It looks like unbundled inheritance suits Lean 4 better here. The only class that still extends FunLike
is EquivLike
, since that has a custom coe_injective'
field that is easier to implement. All other classes should take FunLike
or EquivLike
as a parameter.
Previously, morphism classes would be Type
-valued and extend FunLike
:
/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
extends FunLike F A B :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))
After this PR, they should be Prop
-valued and take FunLike
as a parameter:
/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
[FunLike F A B] : Prop :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))
(Note that A B
stay marked as outParam
even though they are not purely required to be so due to the FunLike
parameter already filling them in. This is required to see through type synonyms, which is important in the category theory library. Also, I think keeping them as outParam
is slightly faster.)
Similarly, MyEquivClass
should take EquivLike
as a parameter.
As a result, every mention of [MyHomClass F A B]
should become [FunLike F A B] [MyHomClass F A B]
.
While overall this gives some great speedups, there are some cases that are noticeably slower. In particular, a failing application of a lemma such as map_mul
is more expensive. This is due to suboptimal processing of arguments. For example:
variable [FunLike F M N] [Mul M] [Mul N] (f : F) (x : M) (y : M)
theorem map_mul [MulHomClass F M N] : f (x * y) = f x * f y
example [AddHomClass F A B] : f (x * y) = f x * f y := map_mul f _ _
Before this PR, applying map_mul f
gives the goals [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]
. Since M
and N
are out_param
s, [MulHomClass F ?M ?N]
is synthesized first, supplies values for ?M
and ?N
and then the Mul M
and Mul N
instances can be found.
After this PR, the goals become [FunLike F ?M ?N] [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]
. Now [FunLike F ?M ?N]
is synthesized first, supplies values for ?M
and ?N
and then the Mul M
and Mul N
instances can be found, before trying MulHomClass F M N
which fails. Since the Mul
hierarchy is very big, this can be slow to fail, especially when there is no such Mul
instance.
A long-term but harder to achieve solution would be to specify the order in which instance goals get solved. For example, we'd like to change the arguments to map_mul
to look like [FunLike F M N] [Mul M] [Mul N] [highPriority <| MulHomClass F M N]
because MulHomClass
fails or succeeds much faster than the others.
As a consequence, the simpNF
linter is much slower since by design it tries and fails to apply many map_
lemmas. The same issue occurs a few times in existing calls to simp [map_mul]
, where map_mul
is tried "too soon" and fails. Thanks to the speedup of leanprover/lean4#2478 the impact is very limited, only in files that already were close to the timeout.
simp
not firing sometimesThis affects map_smulₛₗ
and related definitions. For simp
lemmas Lean apparently uses a slightly different mechanism to find instances, so that rw
can find every argument to map_smulₛₗ
successfully but simp
can't: leanprover/lean4#3701.
Especially in the category theory library, we might sometimes have a type A
which is also accessible as a synonym (Bundled A hA).1
. Instance synthesis doesn't always work if we have f : A →* B
but x * y : (Bundled A hA).1
or vice versa. This seems to be mostly fixed by keeping A B
as outParam
s in MulHomClass F A B
. (Presumably because Lean will do a definitional check A =?= (Bundled A hA).1
instead of using the syntax in the discrimination tree.)
The timeouts can be worked around for now by specifying which map_mul
we mean, either as map_mul f
for some explicit f
, or as e.g. MonoidHomClass.map_mul
.
map_smulₛₗ
not firing as simp
lemma can be worked around by going back to the pre-FunLike situation and making LinearMap.map_smulₛₗ
a simp
lemma instead of the generic map_smulₛₗ
. Writing simp [map_smulₛₗ _]
also works.
Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
@@ -266,7 +266,8 @@ and `f (c • x) = (σ c) • f x`. -/
class ContinuousSemilinearMapClass (F : Type*) {R S : outParam (Type*)} [Semiring R] [Semiring S]
(σ : outParam <| R →+* S) (M : outParam (Type*)) [TopologicalSpace M] [AddCommMonoid M]
(M₂ : outParam (Type*)) [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M]
- [Module S M₂] extends SemilinearMapClass F σ M M₂, ContinuousMapClass F M M₂
+ [Module S M₂] [FunLike F M M₂]
+ extends SemilinearMapClass F σ M M₂, ContinuousMapClass F M M₂ : Prop
#align continuous_semilinear_map_class ContinuousSemilinearMapClass
-- `σ`, `R` and `S` become metavariables, but they are all outparams so it's OK
@@ -278,7 +279,7 @@ class ContinuousSemilinearMapClass (F : Type*) {R S : outParam (Type*)} [Semirin
`ContinuousSemilinearMapClass F (RingHom.id R) M M₂`. -/
abbrev ContinuousLinearMapClass (F : Type*) (R : outParam (Type*)) [Semiring R]
(M : outParam (Type*)) [TopologicalSpace M] [AddCommMonoid M] (M₂ : outParam (Type*))
- [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M] [Module R M₂] :=
+ [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M] [Module R M₂] [FunLike F M M₂] :=
ContinuousSemilinearMapClass F (RingHom.id R) M M₂
#align continuous_linear_map_class ContinuousLinearMapClass
@@ -315,9 +316,9 @@ class ContinuousSemilinearEquivClass (F : Type*) {R : outParam (Type*)} {S : out
[Semiring R] [Semiring S] (σ : outParam <| R →+* S) {σ' : outParam <| S →+* R}
[RingHomInvPair σ σ'] [RingHomInvPair σ' σ] (M : outParam (Type*)) [TopologicalSpace M]
[AddCommMonoid M] (M₂ : outParam (Type*)) [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M]
- [Module S M₂] extends SemilinearEquivClass F σ M M₂ where
+ [Module S M₂] [EquivLike F M M₂] extends SemilinearEquivClass F σ M M₂ : Prop where
map_continuous : ∀ f : F, Continuous f := by continuity
- inv_continuous : ∀ f : F, Continuous (inv f) := by continuity
+ inv_continuous : ∀ f : F, Continuous (EquivLike.inv f) := by continuity
#align continuous_semilinear_equiv_class ContinuousSemilinearEquivClass
attribute [inherit_doc ContinuousSemilinearEquivClass]
@@ -329,7 +330,7 @@ ContinuousSemilinearEquivClass.inv_continuous
`ContinuousSemilinearEquivClass F (RingHom.id R) M M₂`. -/
abbrev ContinuousLinearEquivClass (F : Type*) (R : outParam (Type*)) [Semiring R]
(M : outParam (Type*)) [TopologicalSpace M] [AddCommMonoid M] (M₂ : outParam (Type*))
- [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M] [Module R M₂] :=
+ [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M] [Module R M₂] [EquivLike F M M₂] :=
ContinuousSemilinearEquivClass F (RingHom.id R) M M₂
#align continuous_linear_equiv_class ContinuousLinearEquivClass
@@ -342,11 +343,9 @@ variable (F : Type*) {R : Type*} {S : Type*} [Semiring R] [Semiring S] (σ : R
[Module R M] [Module S M₂]
-- `σ'` becomes a metavariable, but it's OK since it's an outparam
-instance (priority := 100) continuousSemilinearMapClass
+instance (priority := 100) continuousSemilinearMapClass [EquivLike F M M₂]
[s : ContinuousSemilinearEquivClass F σ M M₂] : ContinuousSemilinearMapClass F σ M M₂ :=
- { s with
- coe := ((↑) : F → M → M₂)
- coe_injective' := @DFunLike.coe_injective F _ _ _ }
+ { s with }
#align continuous_semilinear_equiv_class.continuous_semilinear_map_class ContinuousSemilinearEquivClass.continuousSemilinearMapClass
end ContinuousSemilinearEquivClass
@@ -363,8 +362,7 @@ closure of the set of linear maps. -/
@[simps (config := .asFn)]
def linearMapOfMemClosureRangeCoe (f : M₁ → M₂)
(hf : f ∈ closure (Set.range ((↑) : (M₁ →ₛₗ[σ] M₂) → M₁ → M₂))) : M₁ →ₛₗ[σ] M₂ :=
- { @addMonoidHomOfMemClosureRangeCoe M₁ M₂ _ _ _ _ _ (M₁ →ₛₗ[σ] M₂)
- (SemilinearMapClass.addMonoidHomClass _) f hf with
+ { addMonoidHomOfMemClosureRangeCoe f hf with
map_smul' := (isClosed_setOf_map_smul M₁ M₂ σ).closure_subset_iff.2
(Set.range_subset_iff.2 LinearMap.map_smulₛₗ) hf }
#align linear_map_of_mem_closure_range_coe linearMapOfMemClosureRangeCoe
@@ -416,10 +414,12 @@ theorem coe_injective : Function.Injective ((↑) : (M₁ →SL[σ₁₂] M₂)
congr
#align continuous_linear_map.coe_injective ContinuousLinearMap.coe_injective
-instance continuousSemilinearMapClass :
- ContinuousSemilinearMapClass (M₁ →SL[σ₁₂] M₂) σ₁₂ M₁ M₂ where
+instance funLike : FunLike (M₁ →SL[σ₁₂] M₂) M₁ M₂ where
coe f := f.toLinearMap
coe_injective' _ _ h := coe_injective (DFunLike.coe_injective h)
+
+instance continuousSemilinearMapClass :
+ ContinuousSemilinearMapClass (M₁ →SL[σ₁₂] M₂) σ₁₂ M₁ M₂ where
map_add f := map_add f.toLinearMap
map_continuous f := f.2
map_smulₛₗ f := f.toLinearMap.map_smul'
@@ -1003,25 +1003,29 @@ theorem coe_inr [Module R₁ M₂] : (inr R₁ M₁ M₂ : M₂ →ₗ[R₁] M
rfl
#align continuous_linear_map.coe_inr ContinuousLinearMap.coe_inr
-theorem isClosed_ker [T1Space M₂] [ContinuousSemilinearMapClass F σ₁₂ M₁ M₂] (f : F) :
+theorem isClosed_ker [T1Space M₂] [FunLike F M₁ M₂] [ContinuousSemilinearMapClass F σ₁₂ M₁ M₂]
+ (f : F) :
IsClosed (ker f : Set M₁) :=
continuous_iff_isClosed.1 (map_continuous f) _ isClosed_singleton
#align continuous_linear_map.is_closed_ker ContinuousLinearMap.isClosed_ker
theorem isComplete_ker {M' : Type*} [UniformSpace M'] [CompleteSpace M'] [AddCommMonoid M']
- [Module R₁ M'] [T1Space M₂] [ContinuousSemilinearMapClass F σ₁₂ M' M₂] (f : F) :
+ [Module R₁ M'] [T1Space M₂] [FunLike F M' M₂] [ContinuousSemilinearMapClass F σ₁₂ M' M₂]
+ (f : F) :
IsComplete (ker f : Set M') :=
(isClosed_ker f).isComplete
#align continuous_linear_map.is_complete_ker ContinuousLinearMap.isComplete_ker
instance completeSpace_ker {M' : Type*} [UniformSpace M'] [CompleteSpace M']
- [AddCommMonoid M'] [Module R₁ M'] [T1Space M₂] [ContinuousSemilinearMapClass F σ₁₂ M' M₂]
+ [AddCommMonoid M'] [Module R₁ M'] [T1Space M₂]
+ [FunLike F M' M₂] [ContinuousSemilinearMapClass F σ₁₂ M' M₂]
(f : F) : CompleteSpace (ker f) :=
(isComplete_ker f).completeSpace_coe
#align continuous_linear_map.complete_space_ker ContinuousLinearMap.completeSpace_ker
instance completeSpace_eqLocus {M' : Type*} [UniformSpace M'] [CompleteSpace M']
- [AddCommMonoid M'] [Module R₁ M'] [T2Space M₂] [ContinuousSemilinearMapClass F σ₁₂ M' M₂]
+ [AddCommMonoid M'] [Module R₁ M'] [T2Space M₂]
+ [FunLike F M' M₂] [ContinuousSemilinearMapClass F σ₁₂ M' M₂]
(f g : F) : CompleteSpace (LinearMap.eqLocus f g) :=
IsClosed.completeSpace_coe <| isClosed_eq (map_continuous f) (map_continuous g)
@@ -1864,8 +1868,8 @@ instance ContinuousLinearMap.coe : Coe (M₁ ≃SL[σ₁₂] M₂) (M₁ →SL[
⟨toContinuousLinearMap⟩
#align continuous_linear_equiv.continuous_linear_map.has_coe ContinuousLinearEquiv.ContinuousLinearMap.coe
-instance continuousSemilinearEquivClass :
- ContinuousSemilinearEquivClass (M₁ ≃SL[σ₁₂] M₂) σ₁₂ M₁ M₂ where
+instance equivLike :
+ EquivLike (M₁ ≃SL[σ₁₂] M₂) M₁ M₂ where
coe f := f.toFun
inv f := f.invFun
coe_injective' f g h₁ h₂ := by
@@ -1876,6 +1880,9 @@ instance continuousSemilinearEquivClass :
congr
left_inv f := f.left_inv
right_inv f := f.right_inv
+
+instance continuousSemilinearEquivClass :
+ ContinuousSemilinearEquivClass (M₁ ≃SL[σ₁₂] M₂) σ₁₂ M₁ M₂ where
map_add f := f.map_add'
map_smulₛₗ f := f.map_smul'
map_continuous := continuous_toFun
FunLike
to DFunLike
(#9785)
This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.
This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:
sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
@@ -346,7 +346,7 @@ instance (priority := 100) continuousSemilinearMapClass
[s : ContinuousSemilinearEquivClass F σ M M₂] : ContinuousSemilinearMapClass F σ M M₂ :=
{ s with
coe := ((↑) : F → M → M₂)
- coe_injective' := @FunLike.coe_injective F _ _ _ }
+ coe_injective' := @DFunLike.coe_injective F _ _ _ }
#align continuous_semilinear_equiv_class.continuous_semilinear_map_class ContinuousSemilinearEquivClass.continuousSemilinearMapClass
end ContinuousSemilinearEquivClass
@@ -419,7 +419,7 @@ theorem coe_injective : Function.Injective ((↑) : (M₁ →SL[σ₁₂] M₂)
instance continuousSemilinearMapClass :
ContinuousSemilinearMapClass (M₁ →SL[σ₁₂] M₂) σ₁₂ M₁ M₂ where
coe f := f.toLinearMap
- coe_injective' _ _ h := coe_injective (FunLike.coe_injective h)
+ coe_injective' _ _ h := coe_injective (DFunLike.coe_injective h)
map_add f := map_add f.toLinearMap
map_continuous f := f.2
map_smulₛₗ f := f.toLinearMap.map_smul'
@@ -427,7 +427,7 @@ instance continuousSemilinearMapClass :
-- see Note [function coercion]
/-- Coerce continuous linear maps to functions. -/
---instance toFun' : CoeFun (M₁ →SL[σ₁₂] M₂) fun _ => M₁ → M₂ := ⟨FunLike.coe⟩
+--instance toFun' : CoeFun (M₁ →SL[σ₁₂] M₂) fun _ => M₁ → M₂ := ⟨DFunLike.coe⟩
-- porting note: was `simp`, now `simp only` proves it
theorem coe_mk (f : M₁ →ₛₗ[σ₁₂] M₂) (h) : (mk f h : M₁ →ₛₗ[σ₁₂] M₂) = f :=
@@ -456,7 +456,7 @@ theorem coe_inj {f g : M₁ →SL[σ₁₂] M₂} : (f : M₁ →ₛₗ[σ₁₂
#align continuous_linear_map.coe_inj ContinuousLinearMap.coe_inj
theorem coeFn_injective : @Function.Injective (M₁ →SL[σ₁₂] M₂) (M₁ → M₂) (↑) :=
- FunLike.coe_injective
+ DFunLike.coe_injective
#align continuous_linear_map.coe_fn_injective ContinuousLinearMap.coeFn_injective
/-- See Note [custom simps projection]. We need to specify this projection explicitly in this case,
@@ -474,11 +474,11 @@ initialize_simps_projections ContinuousLinearMap (toLinearMap_toFun → apply, t
@[ext]
theorem ext {f g : M₁ →SL[σ₁₂] M₂} (h : ∀ x, f x = g x) : f = g :=
- FunLike.ext f g h
+ DFunLike.ext f g h
#align continuous_linear_map.ext ContinuousLinearMap.ext
theorem ext_iff {f g : M₁ →SL[σ₁₂] M₂} : f = g ↔ ∀ x, f x = g x :=
- FunLike.ext_iff
+ DFunLike.ext_iff
#align continuous_linear_map.ext_iff ContinuousLinearMap.ext_iff
/-- Copy of a `ContinuousLinearMap` with a new `toFun` equal to the old one. Useful to fix
@@ -494,7 +494,7 @@ theorem coe_copy (f : M₁ →SL[σ₁₂] M₂) (f' : M₁ → M₂) (h : f' =
#align continuous_linear_map.coe_copy ContinuousLinearMap.coe_copy
theorem copy_eq (f : M₁ →SL[σ₁₂] M₂) (f' : M₁ → M₂) (h : f' = ⇑f) : f.copy f' h = f :=
- FunLike.ext' h
+ DFunLike.ext' h
#align continuous_linear_map.copy_eq ContinuousLinearMap.copy_eq
-- make some straightforward lemmas available to `simp`.
@@ -710,7 +710,8 @@ theorem one_apply (x : M₁) : (1 : M₁ →L[R₁] M₁) x = x :=
#align continuous_linear_map.one_apply ContinuousLinearMap.one_apply
instance [Nontrivial M₁] : Nontrivial (M₁ →L[R₁] M₁) :=
- ⟨0, 1, fun e ↦ have ⟨x, hx⟩ := exists_ne (0 : M₁); hx (by simpa using FunLike.congr_fun e.symm x)⟩
+ ⟨0, 1, fun e ↦
+ have ⟨x, hx⟩ := exists_ne (0 : M₁); hx (by simpa using DFunLike.congr_fun e.symm x)⟩
section Add
Added analogue of LinearEquiv.ofInjective but for ContinuousLinearEquiv
on Banach spaces.
Added analogue of LinearMap.rangeRestrict but for ContinuousLinearMap
.
Also I updated a docstring that had the old name of a theorem.
Co-authored-by: Jireh Loreaux <loreaujy@gmail.com>
@@ -1055,6 +1055,16 @@ theorem ker_codRestrict (f : M₁ →SL[σ₁₂] M₂) (p : Submodule R₂ M₂
(f : M₁ →ₛₗ[σ₁₂] M₂).ker_codRestrict p h
#align continuous_linear_map.ker_cod_restrict ContinuousLinearMap.ker_codRestrict
+/-- Restrict the codomain of a continuous linear map `f` to `f.range`. -/
+@[reducible]
+def rangeRestrict [RingHomSurjective σ₁₂] (f : M₁ →SL[σ₁₂] M₂) :=
+ f.codRestrict (LinearMap.range f) (LinearMap.mem_range_self f)
+
+@[simp]
+theorem coe_rangeRestrict [RingHomSurjective σ₁₂] (f : M₁ →SL[σ₁₂] M₂) :
+ (f.rangeRestrict : M₁ →ₛₗ[σ₁₂] LinearMap.range f) = (f : M₁ →ₛₗ[σ₁₂] M₂).rangeRestrict :=
+ rfl
+
/-- `Submodule.subtype` as a `ContinuousLinearMap`. -/
def _root_.Submodule.subtypeL (p : Submodule R₁ M₁) : p →L[R₁] M₁ where
cont := continuous_subtype_val
Inducing.continuousSMul
(#9713)
Inducing.continuousSMul
and Inducing.continuousVAdd
;Units.continuousSMul
and Inducing.continuousMul
;Submonoid.continuousSMul
from a submonoid of a group
to a submonoid of a monoid;Submonoid.continuousSMul
in Subgroup.continuousSMul
.@@ -102,11 +102,9 @@ variable {ι R M₁ M₂ : Type*} [Semiring R] [AddCommMonoid M₁] [AddCommMono
[Module R M₂] [u : TopologicalSpace R] {t : TopologicalSpace M₂} [ContinuousSMul R M₂]
(f : M₁ →ₗ[R] M₂)
-theorem continuousSMul_induced : @ContinuousSMul R M₁ _ u (t.induced f) := by
+theorem continuousSMul_induced : @ContinuousSMul R M₁ _ u (t.induced f) :=
let _ : TopologicalSpace M₁ := t.induced f
- refine' ⟨continuous_induced_rng.2 _⟩
- simp_rw [Function.comp, f.map_smul]
- exact continuous_fst.smul (continuous_induced_dom.comp continuous_snd)
+ Inducing.continuousSMul ⟨rfl⟩ continuous_id (map_smul f _ _)
#align has_continuous_smul_induced continuousSMul_induced
end LatticeOps
@@ -130,10 +128,7 @@ namespace Submodule
variable {α β : Type*} [TopologicalSpace β]
-instance continuousSMul [TopologicalSpace α] [Semiring α] [AddCommMonoid β] [Module α β]
- [ContinuousSMul α β] (S : Submodule α β) : ContinuousSMul α S :=
- continuousSMul_induced S.subtype
-#align submodule.has_continuous_smul Submodule.continuousSMul
+#align submodule.has_continuous_smul SMulMemClass.continuousSMul
instance topologicalAddGroup [Ring α] [AddCommGroup β] [Module α β] [TopologicalAddGroup β]
(S : Submodule α β) : TopologicalAddGroup S :=
finrank
to rings. (#8912)
A portion of results in Mathlib/LinearAlgebra/FiniteDimensional.lean
were generalized to rings and moved to Mathlib/LinearAlgebra/FreeModule/Finite/Rank.lean
. Most API lemmas for FiniteDimensional
are kept but replaced with one lemma proofs. Definitions and niche lemmas are replaced by the generalized version completely.
Co-authored-by: erd1 <the.erd.one@gmail.com> Co-authored-by: Andrew Yang <the.erd.one@gmail.com>
@@ -714,6 +714,9 @@ theorem one_apply (x : M₁) : (1 : M₁ →L[R₁] M₁) x = x :=
rfl
#align continuous_linear_map.one_apply ContinuousLinearMap.one_apply
+instance [Nontrivial M₁] : Nontrivial (M₁ →L[R₁] M₁) :=
+ ⟨0, 1, fun e ↦ have ⟨x, hx⟩ := exists_ne (0 : M₁); hx (by simpa using FunLike.congr_fun e.symm x)⟩
+
section Add
variable [ContinuousAdd M₂]
And
instead of Exists
;Subspace
to Submodule
namespace;ClosedComplemented.exists_submodule_equiv_prod
.@@ -2672,11 +2672,11 @@ def ClosedComplemented (p : Submodule R M) : Prop :=
∃ f : M →L[R] p, ∀ x : p, f x = x
#align submodule.closed_complemented Submodule.ClosedComplemented
-theorem ClosedComplemented.has_closed_complement {p : Submodule R M} [T1Space p]
+theorem ClosedComplemented.exists_isClosed_isCompl {p : Submodule R M} [T1Space p]
(h : ClosedComplemented p) :
- ∃ (q : Submodule R M) (_ : IsClosed (q : Set M)), IsCompl p q :=
+ ∃ q : Submodule R M, IsClosed (q : Set M) ∧ IsCompl p q :=
Exists.elim h fun f hf => ⟨ker f, isClosed_ker f, LinearMap.isCompl_of_proj hf⟩
-#align submodule.closed_complemented.has_closed_complement Submodule.ClosedComplemented.has_closed_complement
+#align submodule.closed_complemented.has_closed_complement Submodule.ClosedComplemented.exists_isClosed_isCompl
protected theorem ClosedComplemented.isClosed [TopologicalAddGroup M] [T1Space M]
{p : Submodule R M} (h : ClosedComplemented p) : IsClosed (p : Set M) := by
@@ -2695,6 +2695,20 @@ theorem closedComplemented_top : ClosedComplemented (⊤ : Submodule R M) :=
⟨(id R M).codRestrict ⊤ fun _x => trivial, fun x => Subtype.ext_iff_val.2 <| by simp⟩
#align submodule.closed_complemented_top Submodule.closedComplemented_top
+/-- If `p` is a closed complemented submodule,
+then there exists a submodule `q` and a continuous linear equivalence `M ≃L[R] (p × q)` such that
+`e (x : p) = (x, 0)`, `e (y : q) = (0, y)`, and `e.symm x = x.1 + x.2`.
+
+In fact, the properties of `e` imply the properties of `e.symm` and vice versa,
+but we provide both for convenience. -/
+lemma ClosedComplemented.exists_submodule_equiv_prod [TopologicalAddGroup M]
+ {p : Submodule R M} (hp : p.ClosedComplemented) :
+ ∃ (q : Submodule R M) (e : M ≃L[R] (p × q)),
+ (∀ x : p, e x = (x, 0)) ∧ (∀ y : q, e y = (0, y)) ∧ (∀ x, e.symm x = x.1 + x.2) :=
+ let ⟨f, hf⟩ := hp
+ ⟨LinearMap.ker f, .equivOfRightInverse _ p.subtypeL hf,
+ fun _ ↦ by ext <;> simp [hf], fun _ ↦ by ext <;> simp [hf], fun _ ↦ rfl⟩
+
end Submodule
theorem ContinuousLinearMap.closedComplemented_ker_of_rightInverse {R : Type*} [Ring R]
@@ -768,7 +768,7 @@ instance addCommMonoid : AddCommMonoid (M₁ →SL[σ₁₂] M₂) where
@[simp, norm_cast]
theorem coe_sum {ι : Type*} (t : Finset ι) (f : ι → M₁ →SL[σ₁₂] M₂) :
↑(∑ d in t, f d) = (∑ d in t, f d : M₁ →ₛₗ[σ₁₂] M₂) :=
- (AddMonoidHom.mk ⟨((↑) : (M₁ →SL[σ₁₂] M₂) → M₁ →ₛₗ[σ₁₂] M₂), rfl⟩ fun _ _ => rfl).map_sum _ _
+ map_sum (AddMonoidHom.mk ⟨((↑) : (M₁ →SL[σ₁₂] M₂) → M₁ →ₛₗ[σ₁₂] M₂), rfl⟩ fun _ _ => rfl) _ _
#align continuous_linear_map.coe_sum ContinuousLinearMap.coe_sum
@[simp, norm_cast]
@@ -667,7 +667,7 @@ instance uniqueOfRight [Subsingleton M₂] : Unique (M₁ →SL[σ₁₂] M₂)
#align continuous_linear_map.unique_of_right ContinuousLinearMap.uniqueOfRight
theorem exists_ne_zero {f : M₁ →SL[σ₁₂] M₂} (hf : f ≠ 0) : ∃ x, f x ≠ 0 := by
- by_contra' h
+ by_contra! h
exact hf (ContinuousLinearMap.ext h)
#align continuous_linear_map.exists_ne_zero ContinuousLinearMap.exists_ne_zero
ContinuousLinearMap
(#8725)
Move parts of the proof of "two uniformities are equal" up while generalizing it.
Also add a ContinuousConstSMul
instance that needs less assumptions than ContinuousSMul
.
@@ -942,9 +942,9 @@ instance applySMulCommClass' : SMulCommClass (M₁ →L[R₁] M₁) R₁ M₁ wh
smul_comm := ContinuousLinearMap.map_smul
#align continuous_linear_map.apply_smul_comm_class' ContinuousLinearMap.applySMulCommClass'
-instance continuousConstSMul : ContinuousConstSMul (M₁ →L[R₁] M₁) M₁ :=
+instance continuousConstSMul_apply : ContinuousConstSMul (M₁ →L[R₁] M₁) M₁ :=
⟨ContinuousLinearMap.continuous⟩
-#align continuous_linear_map.has_continuous_const_smul ContinuousLinearMap.continuousConstSMul
+#align continuous_linear_map.has_continuous_const_smul ContinuousLinearMap.continuousConstSMul_apply
end ApplyAction
exact_mod_cast
tactic with mod_cast
elaborator where possible (#8404)
We still have the exact_mod_cast
tactic, used in a few places, which somehow (?) works a little bit harder to prevent the expected type influencing the elaboration of the term. I would like to get to the bottom of this, and it will be easier once the only usages of exact_mod_cast
are the ones that don't work using the term elaborator by itself.
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
@@ -2604,7 +2604,7 @@ theorem inverse_equiv (e : M ≃L[R] M₂) : inverse (e : M →L[R] M₂) = e.sy
have h : ∃ e' : M ≃L[R] M₂, (e' : M →L[R] M₂) = ↑e := ⟨e, rfl⟩
simp only [inverse, dif_pos h]
congr
- exact_mod_cast Classical.choose_spec h
+ exact mod_cast Classical.choose_spec h
#align continuous_linear_map.inverse_equiv ContinuousLinearMap.inverse_equiv
/-- By definition, if `f` is not invertible then `inverse f = 0`. -/
This is the supremum of
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.
In particular this includes adjustments for the Lean PRs
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).
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})
.
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:
(config := { unfoldPartialApp := true })
in some places, to recover the old behaviour@[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>
@@ -605,13 +605,13 @@ theorem smul_apply (c : S₂) (f : M₁ →SL[σ₁₂] M₂) (x : M₁) : (c
@[simp, norm_cast]
theorem coe_smul (c : S₂) (f : M₁ →SL[σ₁₂] M₂) :
- (c • f : M₁ →ₛₗ[σ₁₂] M₂) = c • (f : M₁ →ₛₗ[σ₁₂] M₂) :=
+ ↑(c • f) = c • (f : M₁ →ₛₗ[σ₁₂] M₂) :=
rfl
#align continuous_linear_map.coe_smul ContinuousLinearMap.coe_smul
@[simp, norm_cast]
theorem coe_smul' (c : S₂) (f : M₁ →SL[σ₁₂] M₂) :
- (c • f : M₁ → M₂) = c • (f : M₁ → M₂) :=
+ ↑(c • f) = c • (f : M₁ → M₂) :=
rfl
#align continuous_linear_map.coe_smul' ContinuousLinearMap.coe_smul'
@@ -1198,8 +1198,8 @@ theorem comp_fst_add_comp_snd [Module R₁ M₂] [Module R₁ M₃] [ContinuousA
theorem coprod_inl_inr [ContinuousAdd M₁] [ContinuousAdd M'₁] :
(ContinuousLinearMap.inl R₁ M₁ M'₁).coprod (ContinuousLinearMap.inr R₁ M₁ M'₁) =
- ContinuousLinearMap.id R₁ (M₁ × M'₁) :=
- by apply coe_injective; apply LinearMap.coprod_inl_inr
+ ContinuousLinearMap.id R₁ (M₁ × M'₁) := by
+ apply coe_injective; apply LinearMap.coprod_inl_inr
#align continuous_linear_map.coprod_inl_inr ContinuousLinearMap.coprod_inl_inr
section
@@ -1268,8 +1268,8 @@ theorem toSpanSingleton_add [ContinuousAdd M₁] (x y : M₁) :
theorem toSpanSingleton_smul' {α} [Monoid α] [DistribMulAction α M₁] [ContinuousConstSMul α M₁]
[SMulCommClass R₁ α M₁] (c : α) (x : M₁) :
- toSpanSingleton R₁ (c • x) = c • toSpanSingleton R₁ x :=
- by ext1; rw [toSpanSingleton_apply, smul_apply, toSpanSingleton_apply, smul_comm]
+ toSpanSingleton R₁ (c • x) = c • toSpanSingleton R₁ x := by
+ ext1; rw [toSpanSingleton_apply, smul_apply, toSpanSingleton_apply, smul_comm]
#align continuous_linear_map.to_span_singleton_smul' ContinuousLinearMap.toSpanSingleton_smul'
/-- A special case of `to_span_singleton_smul'` for when `R` is commutative. -/
Use .asFn
and .lemmasOnly
as simps
configuration options.
For reference, these are defined here:
@@ -2556,7 +2556,7 @@ variable (R M)
/-- Continuous linear equivalence between dependent functions `(i : Fin 2) → M i` and `M 0 × M 1`.
-/
-@[simps! (config := { fullyApplied := false }) apply symm_apply]
+@[simps! (config := .asFn) apply symm_apply]
def piFinTwo (M : Fin 2 → Type*) [∀ i, AddCommMonoid (M i)] [∀ i, Module R (M i)]
[∀ i, TopologicalSpace (M i)] : ((i : _) → M i) ≃L[R] M 0 × M 1 :=
{ Homeomorph.piFinTwo M with toLinearEquiv := LinearEquiv.piFinTwo R M }
@@ -2565,7 +2565,7 @@ def piFinTwo (M : Fin 2 → Type*) [∀ i, AddCommMonoid (M i)] [∀ i, Module R
#align continuous_linear_equiv.pi_fin_two_symm_apply ContinuousLinearEquiv.piFinTwo_symm_apply
/-- Continuous linear equivalence between vectors in `M² = Fin 2 → M` and `M × M`. -/
-@[simps! (config := { fullyApplied := false }) apply symm_apply]
+@[simps! (config := .asFn) apply symm_apply]
def finTwoArrow : (Fin 2 → M) ≃L[R] M × M :=
{ piFinTwo R fun _ => M with toLinearEquiv := LinearEquiv.finTwoArrow R M }
#align continuous_linear_equiv.fin_two_arrow ContinuousLinearEquiv.finTwoArrow
@@ -883,11 +883,14 @@ instance monoidWithZero : MonoidWithZero (M₁ →L[R₁] M₁) where
theorem coe_pow (f : M₁ →L[R₁] M₁) (n : ℕ) : ⇑(f ^ n) = f^[n] :=
hom_coe_pow _ rfl (fun _ _ ↦ rfl) _ _
-instance semiring [ContinuousAdd M₁] : Semiring (M₁ →L[R₁] M₁) :=
- { ContinuousLinearMap.monoidWithZero,
- ContinuousLinearMap.addCommMonoid with
- left_distrib := fun f g h => ext fun x => map_add f (g x) (h x)
- right_distrib := fun _ _ _ => ext fun _ => LinearMap.add_apply _ _ _ }
+instance semiring [ContinuousAdd M₁] : Semiring (M₁ →L[R₁] M₁) where
+ __ := ContinuousLinearMap.monoidWithZero
+ __ := ContinuousLinearMap.addCommMonoid
+ left_distrib f g h := ext fun x => map_add f (g x) (h x)
+ right_distrib _ _ _ := ext fun _ => LinearMap.add_apply _ _ _
+ natCast n := n • (1 : M₁ →L[R₁] M₁)
+ natCast_zero := zero_smul ℕ (1 : M₁ →L[R₁] M₁)
+ natCast_succ n := (AddMonoid.nsmul_succ n (1 : M₁ →L[R₁] M₁)).trans (add_comm _ _)
#align continuous_linear_map.semiring ContinuousLinearMap.semiring
/-- `ContinuousLinearMap.toLinearMap` as a `RingHom`.-/
@@ -901,6 +904,15 @@ def toLinearMapRingHom [ContinuousAdd M₁] : (M₁ →L[R₁] M₁) →+* M₁
#align continuous_linear_map.to_linear_map_ring_hom ContinuousLinearMap.toLinearMapRingHom
#align continuous_linear_map.to_linear_map_ring_hom_apply ContinuousLinearMap.toLinearMapRingHom_apply
+@[simp]
+theorem natCast_apply [ContinuousAdd M₁] (n : ℕ) (m : M₁) : (↑n : M₁ →L[R₁] M₁) m = n • m :=
+ rfl
+
+@[simp]
+theorem ofNat_apply [ContinuousAdd M₁] (n : ℕ) [n.AtLeastTwo] (m : M₁) :
+ ((no_index (OfNat.ofNat n) : M₁ →L[R₁] M₁)) m = OfNat.ofNat n • m :=
+ rfl
+
section ApplyAction
variable [ContinuousAdd M₁]
@@ -1494,11 +1506,18 @@ theorem sub_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddG
simp
#align continuous_linear_map.sub_comp ContinuousLinearMap.sub_comp
-instance ring [TopologicalAddGroup M] : Ring (M →L[R] M) :=
- { ContinuousLinearMap.semiring,
- ContinuousLinearMap.addCommGroup with }
+instance ring [TopologicalAddGroup M] : Ring (M →L[R] M) where
+ __ := ContinuousLinearMap.semiring
+ __ := ContinuousLinearMap.addCommGroup
+ intCast z := z • (1 : M →L[R] M)
+ intCast_ofNat := ofNat_zsmul _
+ intCast_negSucc := negSucc_zsmul _
#align continuous_linear_map.ring ContinuousLinearMap.ring
+@[simp]
+theorem intCast_apply [TopologicalAddGroup M] (z : ℤ) (m : M) : (↑z : M →L[R] M) m = z • m :=
+ rfl
+
theorem smulRight_one_pow [TopologicalSpace R] [TopologicalRing R] (c : R) (n : ℕ) :
smulRight (1 : R →L[R] R) c ^ n = smulRight (1 : R →L[R] R) (c ^ n) := by
induction' n with n ihn
@@ -1727,6 +1746,8 @@ instance algebra : Algebra R (M₂ →L[R] M₂) :=
Algebra.ofModule smul_comp fun _ _ _ => comp_smul _ _ _
#align continuous_linear_map.algebra ContinuousLinearMap.algebra
+@[simp] theorem algebraMap_apply (r : R) (m : M₂) : algebraMap R (M₂ →L[R] M₂) r m = r • m := rfl
+
end CommRing
section RestrictScalars
CompleteSpace
assumptions (#7691)
Also add completeSpace_prod
, integrable_prod
.
@@ -2087,6 +2087,19 @@ theorem prod_symm [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e :
rfl
#align continuous_linear_equiv.prod_symm ContinuousLinearEquiv.prod_symm
+variable (R₁ M₁ M₂)
+
+/-- Product of modules is commutative up to continuous linear isomorphism. -/
+@[simps! apply toLinearEquiv]
+def prodComm [Module R₁ M₂] : (M₁ × M₂) ≃L[R₁] M₂ × M₁ :=
+ { LinearEquiv.prodComm R₁ M₁ M₂ with
+ continuous_toFun := continuous_swap
+ continuous_invFun := continuous_swap }
+
+@[simp] lemma prodComm_symm [Module R₁ M₂] : (prodComm R₁ M₁ M₂).symm = prodComm R₁ M₂ M₁ := rfl
+
+variable {R₁ M₁ M₂}
+
protected theorem bijective (e : M₁ ≃SL[σ₁₂] M₂) : Function.Bijective e :=
e.toLinearEquiv.toEquiv.bijective
#align continuous_linear_equiv.bijective ContinuousLinearEquiv.bijective
_root_.map_sum
more consistently (#7189)
Also _root_.map_smul
when in the neighbourhood.
@@ -528,9 +528,10 @@ theorem map_smul_of_tower {R S : Type*} [Semiring S] [SMul R M₁] [Module S M
LinearMap.CompatibleSMul.map_smul (f : M₁ →ₗ[S] M₂) c x
#align continuous_linear_map.map_smul_of_tower ContinuousLinearMap.map_smul_of_tower
+@[deprecated _root_.map_sum]
protected theorem map_sum {ι : Type*} (f : M₁ →SL[σ₁₂] M₂) (s : Finset ι) (g : ι → M₁) :
f (∑ i in s, g i) = ∑ i in s, f (g i) :=
- f.toLinearMap.map_sum
+ map_sum ..
#align continuous_linear_map.map_sum ContinuousLinearMap.map_sum
@[simp, norm_cast]
This removes redundant field values of the form add := add
for smaller terms and less unfolding during unification.
A list of all files containing a structure instance of the form { a1, ... with x1 := val, ... }
where some xi
is a field of some aj
was generated by modifying the structure instance elaboration algorithm to print such overlaps to stdout in a custom toolchain.
Using that toolchain, I went through each file on the list and attempted to remove algebraic fields that overlapped and were redundant, eg add := add
and not toFun
(though some other ones did creep in). If things broke (which was the case in a couple of cases), I did not push further and reverted.
It is possible that pushing harder and trying to remove all redundant overlaps will yield further improvements.
@@ -163,7 +163,6 @@ variable [ContinuousAdd M]
a submodule. -/
def Submodule.topologicalClosure (s : Submodule R M) : Submodule R M :=
{ s.toAddSubmonoid.topologicalClosure with
- carrier := closure (s : Set M)
smul_mem' := s.mapsTo_smul_closure }
#align submodule.topological_closure Submodule.topologicalClosure
@@ -371,7 +370,6 @@ def linearMapOfMemClosureRangeCoe (f : M₁ → M₂)
(hf : f ∈ closure (Set.range ((↑) : (M₁ →ₛₗ[σ] M₂) → M₁ → M₂))) : M₁ →ₛₗ[σ] M₂ :=
{ @addMonoidHomOfMemClosureRangeCoe M₁ M₂ _ _ _ _ _ (M₁ →ₛₗ[σ] M₂)
(SemilinearMapClass.addMonoidHomClass _) f hf with
- toFun := f
map_smul' := (isClosed_setOf_map_smul M₁ M₂ σ).closure_subset_iff.2
(Set.range_subset_iff.2 LinearMap.map_smulₛₗ) hf }
#align linear_map_of_mem_closure_range_coe linearMapOfMemClosureRangeCoe
@@ -887,8 +885,6 @@ theorem coe_pow (f : M₁ →L[R₁] M₁) (n : ℕ) : ⇑(f ^ n) = f^[n] :=
instance semiring [ContinuousAdd M₁] : Semiring (M₁ →L[R₁] M₁) :=
{ ContinuousLinearMap.monoidWithZero,
ContinuousLinearMap.addCommMonoid with
- mul := (· * ·)
- one := 1
left_distrib := fun f g h => ext fun x => map_add f (g x) (h x)
right_distrib := fun _ _ _ => ext fun _ => LinearMap.add_apply _ _ _ }
#align continuous_linear_map.semiring ContinuousLinearMap.semiring
@@ -1439,8 +1435,6 @@ instance sub : Sub (M →SL[σ₁₂] M₂) :=
instance addCommGroup : AddCommGroup (M →SL[σ₁₂] M₂) := by
refine'
{ ContinuousLinearMap.addCommMonoid with
- zero := 0
- add := (· + ·)
neg := (-·)
sub := (· - ·)
sub_eq_add_neg := _
@@ -1501,9 +1495,7 @@ theorem sub_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddG
instance ring [TopologicalAddGroup M] : Ring (M →L[R] M) :=
{ ContinuousLinearMap.semiring,
- ContinuousLinearMap.addCommGroup with
- mul := (· * ·)
- one := 1 }
+ ContinuousLinearMap.addCommGroup with }
#align continuous_linear_map.ring ContinuousLinearMap.ring
theorem smulRight_one_pow [TopologicalSpace R] [TopologicalRing R] (c : R) (n : ℕ) :
@@ -2236,7 +2228,6 @@ inverse of each other. -/
def equivOfInverse (f₁ : M₁ →SL[σ₁₂] M₂) (f₂ : M₂ →SL[σ₂₁] M₁) (h₁ : Function.LeftInverse f₂ f₁)
(h₂ : Function.RightInverse f₂ f₁) : M₁ ≃SL[σ₁₂] M₂ :=
{ f₁ with
- toFun := f₁
continuous_toFun := f₁.continuous
invFun := f₂
continuous_invFun := f₂.continuous
@@ -12,6 +12,7 @@ import Mathlib.Topology.UniformSpace.UniformEmbedding
import Mathlib.Algebra.Algebra.Basic
import Mathlib.LinearAlgebra.Projection
import Mathlib.LinearAlgebra.Pi
+import Mathlib.LinearAlgebra.Finsupp
#align_import topology.algebra.module.basic from "leanprover-community/mathlib"@"6285167a053ad0990fc88e56c48ccd9fae6550eb"
@@ -110,6 +111,21 @@ theorem continuousSMul_induced : @ContinuousSMul R M₁ _ u (t.induced f) := by
end LatticeOps
+/-- The span of a separable subset with respect to a separable scalar ring is again separable. -/
+lemma TopologicalSpace.IsSeparable.span {R M : Type*} [AddCommMonoid M] [Semiring R] [Module R M]
+ [TopologicalSpace M] [TopologicalSpace R] [SeparableSpace R]
+ [ContinuousAdd M] [ContinuousSMul R M] {s : Set M} (hs : IsSeparable s) :
+ IsSeparable (Submodule.span R s : Set M) := by
+ rw [span_eq_iUnion_nat]
+ apply isSeparable_iUnion (fun n ↦ ?_)
+ apply IsSeparable.image
+ · have : IsSeparable {f : Fin n → R × M | ∀ (i : Fin n), f i ∈ Set.univ ×ˢ s} := by
+ apply isSeparable_pi (fun i ↦ (isSeparable_of_separableSpace Set.univ).prod hs)
+ convert this
+ simp
+ · apply continuous_finset_sum _ (fun i _ ↦ ?_)
+ exact (continuous_fst.comp (continuous_apply i)).smul (continuous_snd.comp (continuous_apply i))
+
namespace Submodule
variable {α β : Type*} [TopologicalSpace β]
@@ -161,6 +177,11 @@ theorem Submodule.le_topologicalClosure (s : Submodule R M) : s ≤ s.topologica
subset_closure
#align submodule.le_topological_closure Submodule.le_topologicalClosure
+theorem Submodule.closure_subset_topologicalClosure_span (s : Set M) :
+ closure s ⊆ (span R s).topologicalClosure := by
+ rw [Submodule.topologicalClosure_coe]
+ exact closure_mono subset_span
+
theorem Submodule.isClosed_topologicalClosure (s : Submodule R M) :
IsClosed (s.topologicalClosure : Set M) := isClosed_closure
#align submodule.is_closed_topological_closure Submodule.isClosed_topologicalClosure
We prove some lemmas that will be useful in following PRs #6832 and #7037, mainly:
theorem Basis.addHaar_eq {b : Basis ι ℝ E} {b' : Basis ι' ℝ E} :
b.addHaar = b'.addHaar ↔ b.addHaar b'.parallelepiped = 1
theorem Basis.parallelepiped_eq_map (b : Basis ι ℝ E) :
b.parallelepiped = (TopologicalSpace.PositiveCompacts.piIcc01 ι).map b.equivFun.symm
b.equivFunL.symm.continuous
theorem Basis.addHaar_map (b : Basis ι ℝ E) (f : E ≃L[ℝ] F) :
map f b.addHaar = (b.map f.toLinearEquiv).addHaar
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
@@ -1890,6 +1890,9 @@ theorem coe_toHomeomorph (e : M₁ ≃SL[σ₁₂] M₂) : ⇑e.toHomeomorph = e
rfl
#align continuous_linear_equiv.coe_to_homeomorph ContinuousLinearEquiv.coe_toHomeomorph
+theorem isOpenMap (e : M₁ ≃SL[σ₁₂] M₂) : IsOpenMap e :=
+ (ContinuousLinearEquiv.toHomeomorph e).isOpenMap
+
theorem image_closure (e : M₁ ≃SL[σ₁₂] M₂) (s : Set M₁) : e '' closure s = closure (e '' s) :=
e.toHomeomorph.image_closure s
#align continuous_linear_equiv.image_closure ContinuousLinearEquiv.image_closure
The names are all over the place, leading me to believe that ULift.moduleEquiv
didn't exist. Cross-linking to the other equivs (via code and comments) makes them easier to find.
@@ -2257,11 +2257,11 @@ variable {M₁} {R₄ : Type*} [Semiring R₄] [Module R₄ M₄] {σ₃₄ : R
[RingHomInvPair σ₃₄ σ₄₃] [RingHomInvPair σ₄₃ σ₃₄] {σ₂₄ : R₂ →+* R₄} {σ₁₄ : R₁ →+* R₄}
[RingHomCompTriple σ₂₁ σ₁₄ σ₂₄] [RingHomCompTriple σ₂₄ σ₄₃ σ₂₃] [RingHomCompTriple σ₁₃ σ₃₄ σ₁₄]
-/-- The continuous linear equivalence between `ULift M₁` and `M₁`. -/
+/-- The continuous linear equivalence between `ULift M₁` and `M₁`.
+
+This is a continuous version of `ULift.moduleEquiv`. -/
def ulift : ULift M₁ ≃L[R₁] M₁ :=
- { Equiv.ulift with
- map_add' := fun _x _y => rfl
- map_smul' := fun _c _x => rfl
+ { ULift.moduleEquiv with
continuous_toFun := continuous_uLift_down
continuous_invFun := continuous_uLift_up }
#align continuous_linear_equiv.ulift ContinuousLinearEquiv.ulift
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -35,7 +35,7 @@ universe u v w u'
section
-variable {R : Type _} {M : Type _} [Ring R] [TopologicalSpace R] [TopologicalSpace M]
+variable {R : Type*} {M : Type*} [Ring R] [TopologicalSpace R] [TopologicalSpace M]
[AddCommGroup M] [Module R M]
theorem ContinuousSMul.of_nhds_zero [TopologicalRing R] [TopologicalAddGroup M]
@@ -51,7 +51,7 @@ end
section
-variable {R : Type _} {M : Type _} [Ring R] [TopologicalSpace R] [TopologicalSpace M]
+variable {R : Type*} {M : Type*} [Ring R] [TopologicalSpace R] [TopologicalSpace M]
[AddCommGroup M] [ContinuousAdd M] [Module R M] [ContinuousSMul R M]
/-- If `M` is a topological module over `R` and `0` is a limit of invertible elements of `R`, then
@@ -97,7 +97,7 @@ end
section LatticeOps
-variable {ι R M₁ M₂ : Type _} [Semiring R] [AddCommMonoid M₁] [AddCommMonoid M₂] [Module R M₁]
+variable {ι R M₁ M₂ : Type*} [Semiring R] [AddCommMonoid M₁] [AddCommMonoid M₂] [Module R M₁]
[Module R M₂] [u : TopologicalSpace R] {t : TopologicalSpace M₂} [ContinuousSMul R M₂]
(f : M₁ →ₗ[R] M₂)
@@ -112,7 +112,7 @@ end LatticeOps
namespace Submodule
-variable {α β : Type _} [TopologicalSpace β]
+variable {α β : Type*} [TopologicalSpace β]
instance continuousSMul [TopologicalSpace α] [Semiring α] [AddCommMonoid β] [Module α β]
[ContinuousSMul α β] (S : Submodule α β) : ContinuousSMul α S :=
@@ -188,7 +188,7 @@ theorem Submodule.dense_iff_topologicalClosure_eq_top {s : Submodule R M} :
simp
#align submodule.dense_iff_topological_closure_eq_top Submodule.dense_iff_topologicalClosure_eq_top
-instance Submodule.topologicalClosure.completeSpace {M' : Type _} [AddCommMonoid M'] [Module R M']
+instance Submodule.topologicalClosure.completeSpace {M' : Type*} [AddCommMonoid M'] [Module R M']
[UniformSpace M'] [ContinuousAdd M'] [ContinuousConstSMul R M'] [CompleteSpace M']
(U : Submodule R M') : CompleteSpace U.topologicalClosure :=
isClosed_closure.completeSpace_coe
@@ -206,7 +206,7 @@ end closure
section Pi
-theorem LinearMap.continuous_on_pi {ι : Type _} {R : Type _} {M : Type _} [Finite ι] [Semiring R]
+theorem LinearMap.continuous_on_pi {ι : Type*} {R : Type*} {M : Type*} [Finite ι] [Semiring R]
[TopologicalSpace R] [AddCommMonoid M] [Module R M] [TopologicalSpace M] [ContinuousAdd M]
[ContinuousSMul R M] (f : (ι → R) →ₗ[R] M) : Continuous f := by
cases nonempty_fintype ι
@@ -226,8 +226,8 @@ end Pi
/-- Continuous linear maps between modules. We only put the type classes that are necessary for the
definition, although in applications `M` and `M₂` will be topological modules over the topological
ring `R`. -/
-structure ContinuousLinearMap {R : Type _} {S : Type _} [Semiring R] [Semiring S] (σ : R →+* S)
- (M : Type _) [TopologicalSpace M] [AddCommMonoid M] (M₂ : Type _) [TopologicalSpace M₂]
+structure ContinuousLinearMap {R : Type*} {S : Type*} [Semiring R] [Semiring S] (σ : R →+* S)
+ (M : Type*) [TopologicalSpace M] [AddCommMonoid M] (M₂ : Type*) [TopologicalSpace M₂]
[AddCommMonoid M₂] [Module R M] [Module S M₂] extends M →ₛₗ[σ] M₂ where
cont : Continuous toFun := by continuity
#align continuous_linear_map ContinuousLinearMap
@@ -248,9 +248,9 @@ notation:25 M " →L⋆[" R "] " M₂ => ContinuousLinearMap (starRingEnd R) M M
`σ` is the identity map on `R`. A map `f` between an `R`-module and an `S`-module over a ring
homomorphism `σ : R →+* S` is semilinear if it satisfies the two properties `f (x + y) = f x + f y`
and `f (c • x) = (σ c) • f x`. -/
-class ContinuousSemilinearMapClass (F : Type _) {R S : outParam (Type _)} [Semiring R] [Semiring S]
- (σ : outParam <| R →+* S) (M : outParam (Type _)) [TopologicalSpace M] [AddCommMonoid M]
- (M₂ : outParam (Type _)) [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M]
+class ContinuousSemilinearMapClass (F : Type*) {R S : outParam (Type*)} [Semiring R] [Semiring S]
+ (σ : outParam <| R →+* S) (M : outParam (Type*)) [TopologicalSpace M] [AddCommMonoid M]
+ (M₂ : outParam (Type*)) [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M]
[Module S M₂] extends SemilinearMapClass F σ M M₂, ContinuousMapClass F M M₂
#align continuous_semilinear_map_class ContinuousSemilinearMapClass
@@ -261,8 +261,8 @@ class ContinuousSemilinearMapClass (F : Type _) {R S : outParam (Type _)} [Semir
/-- `ContinuousLinearMapClass F R M M₂` asserts `F` is a type of bundled continuous
`R`-linear maps `M → M₂`. This is an abbreviation for
`ContinuousSemilinearMapClass F (RingHom.id R) M M₂`. -/
-abbrev ContinuousLinearMapClass (F : Type _) (R : outParam (Type _)) [Semiring R]
- (M : outParam (Type _)) [TopologicalSpace M] [AddCommMonoid M] (M₂ : outParam (Type _))
+abbrev ContinuousLinearMapClass (F : Type*) (R : outParam (Type*)) [Semiring R]
+ (M : outParam (Type*)) [TopologicalSpace M] [AddCommMonoid M] (M₂ : outParam (Type*))
[TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M] [Module R M₂] :=
ContinuousSemilinearMapClass F (RingHom.id R) M M₂
#align continuous_linear_map_class ContinuousLinearMapClass
@@ -271,9 +271,9 @@ abbrev ContinuousLinearMapClass (F : Type _) (R : outParam (Type _)) [Semiring R
for the definition, although in applications `M` and `M₂` will be topological modules over the
topological semiring `R`. -/
-- porting note: todo: was @[nolint has_nonempty_instance]
-structure ContinuousLinearEquiv {R : Type _} {S : Type _} [Semiring R] [Semiring S] (σ : R →+* S)
- {σ' : S →+* R} [RingHomInvPair σ σ'] [RingHomInvPair σ' σ] (M : Type _) [TopologicalSpace M]
- [AddCommMonoid M] (M₂ : Type _) [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M]
+structure ContinuousLinearEquiv {R : Type*} {S : Type*} [Semiring R] [Semiring S] (σ : R →+* S)
+ {σ' : S →+* R} [RingHomInvPair σ σ'] [RingHomInvPair σ' σ] (M : Type*) [TopologicalSpace M]
+ [AddCommMonoid M] (M₂ : Type*) [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M]
[Module S M₂] extends M ≃ₛₗ[σ] M₂ where
continuous_toFun : Continuous toFun := by continuity
continuous_invFun : Continuous invFun := by continuity
@@ -296,10 +296,10 @@ notation:50 M " ≃L⋆[" R "] " M₂ => ContinuousLinearEquiv (starRingEnd R) M
where `σ` is the identity map on `R`. A map `f` between an `R`-module and an `S`-module over a ring
homomorphism `σ : R →+* S` is semilinear if it satisfies the two properties `f (x + y) = f x + f y`
and `f (c • x) = (σ c) • f x`. -/
-class ContinuousSemilinearEquivClass (F : Type _) {R : outParam (Type _)} {S : outParam (Type _)}
+class ContinuousSemilinearEquivClass (F : Type*) {R : outParam (Type*)} {S : outParam (Type*)}
[Semiring R] [Semiring S] (σ : outParam <| R →+* S) {σ' : outParam <| S →+* R}
- [RingHomInvPair σ σ'] [RingHomInvPair σ' σ] (M : outParam (Type _)) [TopologicalSpace M]
- [AddCommMonoid M] (M₂ : outParam (Type _)) [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M]
+ [RingHomInvPair σ σ'] [RingHomInvPair σ' σ] (M : outParam (Type*)) [TopologicalSpace M]
+ [AddCommMonoid M] (M₂ : outParam (Type*)) [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M]
[Module S M₂] extends SemilinearEquivClass F σ M M₂ where
map_continuous : ∀ f : F, Continuous f := by continuity
inv_continuous : ∀ f : F, Continuous (inv f) := by continuity
@@ -312,18 +312,18 @@ ContinuousSemilinearEquivClass.inv_continuous
/-- `ContinuousLinearEquivClass F σ M M₂` asserts `F` is a type of bundled continuous
`R`-linear equivs `M → M₂`. This is an abbreviation for
`ContinuousSemilinearEquivClass F (RingHom.id R) M M₂`. -/
-abbrev ContinuousLinearEquivClass (F : Type _) (R : outParam (Type _)) [Semiring R]
- (M : outParam (Type _)) [TopologicalSpace M] [AddCommMonoid M] (M₂ : outParam (Type _))
+abbrev ContinuousLinearEquivClass (F : Type*) (R : outParam (Type*)) [Semiring R]
+ (M : outParam (Type*)) [TopologicalSpace M] [AddCommMonoid M] (M₂ : outParam (Type*))
[TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M] [Module R M₂] :=
ContinuousSemilinearEquivClass F (RingHom.id R) M M₂
#align continuous_linear_equiv_class ContinuousLinearEquivClass
namespace ContinuousSemilinearEquivClass
-variable (F : Type _) {R : Type _} {S : Type _} [Semiring R] [Semiring S] (σ : R →+* S)
+variable (F : Type*) {R : Type*} {S : Type*} [Semiring R] [Semiring S] (σ : R →+* S)
{σ' : S →+* R} [RingHomInvPair σ σ'] [RingHomInvPair σ' σ]
- (M : Type _) [TopologicalSpace M] [AddCommMonoid M]
- (M₂ : Type _) [TopologicalSpace M₂] [AddCommMonoid M₂]
+ (M : Type*) [TopologicalSpace M] [AddCommMonoid M]
+ (M₂ : Type*) [TopologicalSpace M₂] [AddCommMonoid M₂]
[Module R M] [Module S M₂]
-- `σ'` becomes a metavariable, but it's OK since it's an outparam
@@ -338,7 +338,7 @@ end ContinuousSemilinearEquivClass
section PointwiseLimits
-variable {M₁ M₂ α R S : Type _} [TopologicalSpace M₂] [T2Space M₂] [Semiring R] [Semiring S]
+variable {M₁ M₂ α R S : Type*} [TopologicalSpace M₂] [T2Space M₂] [Semiring R] [Semiring S]
[AddCommMonoid M₁] [AddCommMonoid M₂] [Module R M₁] [Module S M₂] [ContinuousConstSMul S M₂]
variable [ContinuousAdd M₂] {σ : R →+* S} {l : Filter α}
@@ -381,11 +381,11 @@ section Semiring
### Properties that hold for non-necessarily commutative semirings.
-/
-variable {R₁ : Type _} {R₂ : Type _} {R₃ : Type _} [Semiring R₁] [Semiring R₂] [Semiring R₃]
- {σ₁₂ : R₁ →+* R₂} {σ₂₃ : R₂ →+* R₃} {σ₁₃ : R₁ →+* R₃} {M₁ : Type _} [TopologicalSpace M₁]
- [AddCommMonoid M₁] {M'₁ : Type _} [TopologicalSpace M'₁] [AddCommMonoid M'₁] {M₂ : Type _}
- [TopologicalSpace M₂] [AddCommMonoid M₂] {M₃ : Type _} [TopologicalSpace M₃] [AddCommMonoid M₃]
- {M₄ : Type _} [TopologicalSpace M₄] [AddCommMonoid M₄] [Module R₁ M₁] [Module R₁ M'₁]
+variable {R₁ : Type*} {R₂ : Type*} {R₃ : Type*} [Semiring R₁] [Semiring R₂] [Semiring R₃]
+ {σ₁₂ : R₁ →+* R₂} {σ₂₃ : R₂ →+* R₃} {σ₁₃ : R₁ →+* R₃} {M₁ : Type*} [TopologicalSpace M₁]
+ [AddCommMonoid M₁] {M'₁ : Type*} [TopologicalSpace M'₁] [AddCommMonoid M'₁] {M₂ : Type*}
+ [TopologicalSpace M₂] [AddCommMonoid M₂] {M₃ : Type*} [TopologicalSpace M₃] [AddCommMonoid M₃]
+ {M₄ : Type*} [TopologicalSpace M₄] [AddCommMonoid M₄] [Module R₁ M₁] [Module R₁ M'₁]
[Module R₂ M₂] [Module R₃ M₃]
attribute [coe] ContinuousLinearMap.toLinearMap
@@ -430,7 +430,7 @@ protected theorem continuous (f : M₁ →SL[σ₁₂] M₂) : Continuous f :=
f.2
#align continuous_linear_map.continuous ContinuousLinearMap.continuous
-protected theorem uniformContinuous {E₁ E₂ : Type _} [UniformSpace E₁] [UniformSpace E₂]
+protected theorem uniformContinuous {E₁ E₂ : Type*} [UniformSpace E₁] [UniformSpace E₂]
[AddCommGroup E₁] [AddCommGroup E₂] [Module R₁ E₁] [Module R₂ E₂] [UniformAddGroup E₁]
[UniformAddGroup E₂] (f : E₁ →SL[σ₁₂] E₂) : UniformContinuous f :=
uniformContinuous_addMonoidHom_of_continuous f.continuous
@@ -503,13 +503,13 @@ protected theorem map_smul [Module R₁ M₂] (f : M₁ →L[R₁] M₂) (c : R
#align continuous_linear_map.map_smul ContinuousLinearMap.map_smul
@[simp]
-theorem map_smul_of_tower {R S : Type _} [Semiring S] [SMul R M₁] [Module S M₁] [SMul R M₂]
+theorem map_smul_of_tower {R S : Type*} [Semiring S] [SMul R M₁] [Module S M₁] [SMul R M₂]
[Module S M₂] [LinearMap.CompatibleSMul M₁ M₂ R S] (f : M₁ →L[S] M₂) (c : R) (x : M₁) :
f (c • x) = c • f x :=
LinearMap.CompatibleSMul.map_smul (f : M₁ →ₗ[S] M₂) c x
#align continuous_linear_map.map_smul_of_tower ContinuousLinearMap.map_smul_of_tower
-protected theorem map_sum {ι : Type _} (f : M₁ →SL[σ₁₂] M₂) (s : Finset ι) (g : ι → M₁) :
+protected theorem map_sum {ι : Type*} (f : M₁ →SL[σ₁₂] M₂) (s : Finset ι) (g : ι → M₁) :
f (∑ i in s, g i) = ∑ i in s, f (g i) :=
f.toLinearMap.map_sum
#align continuous_linear_map.map_sum ContinuousLinearMap.map_sum
@@ -567,7 +567,7 @@ theorem _root_.DenseRange.topologicalClosure_map_submodule [RingHomSurjective σ
section SMulMonoid
-variable {S₂ T₂ : Type _} [Monoid S₂] [Monoid T₂]
+variable {S₂ T₂ : Type*} [Monoid S₂] [Monoid T₂]
variable [DistribMulAction S₂ M₂] [SMulCommClass R₂ S₂ M₂] [ContinuousConstSMul S₂ M₂]
@@ -746,17 +746,17 @@ instance addCommMonoid : AddCommMonoid (M₁ →SL[σ₁₂] M₂) where
#align continuous_linear_map.add_comm_monoid ContinuousLinearMap.addCommMonoid
@[simp, norm_cast]
-theorem coe_sum {ι : Type _} (t : Finset ι) (f : ι → M₁ →SL[σ₁₂] M₂) :
+theorem coe_sum {ι : Type*} (t : Finset ι) (f : ι → M₁ →SL[σ₁₂] M₂) :
↑(∑ d in t, f d) = (∑ d in t, f d : M₁ →ₛₗ[σ₁₂] M₂) :=
(AddMonoidHom.mk ⟨((↑) : (M₁ →SL[σ₁₂] M₂) → M₁ →ₛₗ[σ₁₂] M₂), rfl⟩ fun _ _ => rfl).map_sum _ _
#align continuous_linear_map.coe_sum ContinuousLinearMap.coe_sum
@[simp, norm_cast]
-theorem coe_sum' {ι : Type _} (t : Finset ι) (f : ι → M₁ →SL[σ₁₂] M₂) :
+theorem coe_sum' {ι : Type*} (t : Finset ι) (f : ι → M₁ →SL[σ₁₂] M₂) :
⇑(∑ d in t, f d) = ∑ d in t, ⇑(f d) := by simp only [← coe_coe, coe_sum, LinearMap.coeFn_sum]
#align continuous_linear_map.coe_sum' ContinuousLinearMap.coe_sum'
-theorem sum_apply {ι : Type _} (t : Finset ι) (f : ι → M₁ →SL[σ₁₂] M₂) (b : M₁) :
+theorem sum_apply {ι : Type*} (t : Finset ι) (f : ι → M₁ →SL[σ₁₂] M₂) (b : M₁) :
(∑ d in t, f d) b = ∑ d in t, f d b := by simp only [coe_sum', Finset.sum_apply]
#align continuous_linear_map.sum_apply ContinuousLinearMap.sum_apply
@@ -825,7 +825,7 @@ theorem add_comp [ContinuousAdd M₃] (g₁ g₂ : M₂ →SL[σ₂₃] M₃) (f
simp
#align continuous_linear_map.add_comp ContinuousLinearMap.add_comp
-theorem comp_assoc {R₄ : Type _} [Semiring R₄] [Module R₄ M₄] {σ₁₄ : R₁ →+* R₄} {σ₂₄ : R₂ →+* R₄}
+theorem comp_assoc {R₄ : Type*} [Semiring R₄] [Module R₄ M₄] {σ₁₄ : R₁ →+* R₄} {σ₂₄ : R₂ →+* R₄}
{σ₃₄ : R₃ →+* R₄} [RingHomCompTriple σ₁₃ σ₃₄ σ₁₄] [RingHomCompTriple σ₂₃ σ₃₄ σ₂₄]
[RingHomCompTriple σ₁₂ σ₂₄ σ₁₄] (h : M₃ →SL[σ₃₄] M₄) (g : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) :
(h.comp g).comp f = h.comp (g.comp f) :=
@@ -952,7 +952,7 @@ def inr [Module R₁ M₂] : M₂ →L[R₁] M₁ × M₂ :=
end
-variable {F : Type _}
+variable {F : Type*}
@[simp]
theorem inl_apply [Module R₁ M₂] (x : M₁) : inl R₁ M₁ M₂ x = (x, 0) :=
@@ -979,19 +979,19 @@ theorem isClosed_ker [T1Space M₂] [ContinuousSemilinearMapClass F σ₁₂ M
continuous_iff_isClosed.1 (map_continuous f) _ isClosed_singleton
#align continuous_linear_map.is_closed_ker ContinuousLinearMap.isClosed_ker
-theorem isComplete_ker {M' : Type _} [UniformSpace M'] [CompleteSpace M'] [AddCommMonoid M']
+theorem isComplete_ker {M' : Type*} [UniformSpace M'] [CompleteSpace M'] [AddCommMonoid M']
[Module R₁ M'] [T1Space M₂] [ContinuousSemilinearMapClass F σ₁₂ M' M₂] (f : F) :
IsComplete (ker f : Set M') :=
(isClosed_ker f).isComplete
#align continuous_linear_map.is_complete_ker ContinuousLinearMap.isComplete_ker
-instance completeSpace_ker {M' : Type _} [UniformSpace M'] [CompleteSpace M']
+instance completeSpace_ker {M' : Type*} [UniformSpace M'] [CompleteSpace M']
[AddCommMonoid M'] [Module R₁ M'] [T1Space M₂] [ContinuousSemilinearMapClass F σ₁₂ M' M₂]
(f : F) : CompleteSpace (ker f) :=
(isComplete_ker f).completeSpace_coe
#align continuous_linear_map.complete_space_ker ContinuousLinearMap.completeSpace_ker
-instance completeSpace_eqLocus {M' : Type _} [UniformSpace M'] [CompleteSpace M']
+instance completeSpace_eqLocus {M' : Type*} [UniformSpace M'] [CompleteSpace M']
[AddCommMonoid M'] [Module R₁ M'] [T2Space M₂] [ContinuousSemilinearMapClass F σ₁₂ M' M₂]
(f g : F) : CompleteSpace (LinearMap.eqLocus f g) :=
IsClosed.completeSpace_coe <| isClosed_eq (map_continuous f) (map_continuous g)
@@ -1174,7 +1174,7 @@ theorem coprod_inl_inr [ContinuousAdd M₁] [ContinuousAdd M'₁] :
section
-variable {R S : Type _} [Semiring R] [Semiring S] [Module R M₁] [Module R M₂] [Module R S]
+variable {R S : Type*} [Semiring R] [Semiring S] [Module R M₁] [Module R M₂] [Module R S]
[Module S M₂] [IsScalarTower R S M₂] [TopologicalSpace S] [ContinuousSMul S M₂]
/-- The linear map `fun x => c x • f`. Associates to a scalar-valued linear map and an element of
@@ -1255,8 +1255,8 @@ end Semiring
section Pi
-variable {R : Type _} [Semiring R] {M : Type _} [TopologicalSpace M] [AddCommMonoid M] [Module R M]
- {M₂ : Type _} [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M₂] {ι : Type _} {φ : ι → Type _}
+variable {R : Type*} [Semiring R] {M : Type*} [TopologicalSpace M] [AddCommMonoid M] [Module R M]
+ {M₂ : Type*} [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R M₂] {ι : Type*} {φ : ι → Type*}
[∀ i, TopologicalSpace (φ i)] [∀ i, AddCommMonoid (φ i)] [∀ i, Module R (φ i)]
/-- `pi` construction for continuous linear functions. From a family of continuous linear functions
@@ -1343,9 +1343,9 @@ end Pi
section Ring
-variable {R : Type _} [Ring R] {R₂ : Type _} [Ring R₂] {R₃ : Type _} [Ring R₃] {M : Type _}
- [TopologicalSpace M] [AddCommGroup M] {M₂ : Type _} [TopologicalSpace M₂] [AddCommGroup M₂]
- {M₃ : Type _} [TopologicalSpace M₃] [AddCommGroup M₃] {M₄ : Type _} [TopologicalSpace M₄]
+variable {R : Type*} [Ring R] {R₂ : Type*} [Ring R₂] {R₃ : Type*} [Ring R₃] {M : Type*}
+ [TopologicalSpace M] [AddCommGroup M] {M₂ : Type*} [TopologicalSpace M₂] [AddCommGroup M₂]
+ {M₃ : Type*} [TopologicalSpace M₃] [AddCommGroup M₃] {M₄ : Type*} [TopologicalSpace M₄]
[AddCommGroup M₄] [Module R M] [Module R₂ M₂] [Module R₃ M₃] {σ₁₂ : R →+* R₂} {σ₂₃ : R₂ →+* R₃}
{σ₁₃ : R →+* R₃}
@@ -1534,7 +1534,7 @@ end Ring
section DivisionMonoid
-variable {R M : Type _}
+variable {R M : Type*}
/-- A nonzero continuous linear functional is open. -/
protected theorem isOpenMap_of_ne_zero [TopologicalSpace R] [DivisionRing R] [ContinuousSub R]
@@ -1551,11 +1551,11 @@ end DivisionMonoid
section SMulMonoid
-- The M's are used for semilinear maps, and the N's for plain linear maps
-variable {R R₂ R₃ S S₃ : Type _} [Semiring R] [Semiring R₂] [Semiring R₃] [Monoid S] [Monoid S₃]
- {M : Type _} [TopologicalSpace M] [AddCommMonoid M] [Module R M] {M₂ : Type _}
- [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R₂ M₂] {M₃ : Type _} [TopologicalSpace M₃]
- [AddCommMonoid M₃] [Module R₃ M₃] {N₂ : Type _} [TopologicalSpace N₂] [AddCommMonoid N₂]
- [Module R N₂] {N₃ : Type _} [TopologicalSpace N₃] [AddCommMonoid N₃] [Module R N₃]
+variable {R R₂ R₃ S S₃ : Type*} [Semiring R] [Semiring R₂] [Semiring R₃] [Monoid S] [Monoid S₃]
+ {M : Type*} [TopologicalSpace M] [AddCommMonoid M] [Module R M] {M₂ : Type*}
+ [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R₂ M₂] {M₃ : Type*} [TopologicalSpace M₃]
+ [AddCommMonoid M₃] [Module R₃ M₃] {N₂ : Type*} [TopologicalSpace N₂] [AddCommMonoid N₂]
+ [Module R N₂] {N₃ : Type*} [TopologicalSpace N₃] [AddCommMonoid N₃] [Module R N₃]
[DistribMulAction S₃ M₃] [SMulCommClass R₃ S₃ M₃] [ContinuousConstSMul S₃ M₃]
[DistribMulAction S N₃] [SMulCommClass R S N₃] [ContinuousConstSMul S N₃] {σ₁₂ : R →+* R₂}
{σ₂₃ : R₂ →+* R₃} {σ₁₃ : R →+* R₃} [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃]
@@ -1596,11 +1596,11 @@ end SMulMonoid
section SMul
-- The M's are used for semilinear maps, and the N's for plain linear maps
-variable {R R₂ R₃ S S₃ : Type _} [Semiring R] [Semiring R₂] [Semiring R₃] [Semiring S] [Semiring S₃]
- {M : Type _} [TopologicalSpace M] [AddCommMonoid M] [Module R M] {M₂ : Type _}
- [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R₂ M₂] {M₃ : Type _} [TopologicalSpace M₃]
- [AddCommMonoid M₃] [Module R₃ M₃] {N₂ : Type _} [TopologicalSpace N₂] [AddCommMonoid N₂]
- [Module R N₂] {N₃ : Type _} [TopologicalSpace N₃] [AddCommMonoid N₃] [Module R N₃] [Module S₃ M₃]
+variable {R R₂ R₃ S S₃ : Type*} [Semiring R] [Semiring R₂] [Semiring R₃] [Semiring S] [Semiring S₃]
+ {M : Type*} [TopologicalSpace M] [AddCommMonoid M] [Module R M] {M₂ : Type*}
+ [TopologicalSpace M₂] [AddCommMonoid M₂] [Module R₂ M₂] {M₃ : Type*} [TopologicalSpace M₃]
+ [AddCommMonoid M₃] [Module R₃ M₃] {N₂ : Type*} [TopologicalSpace N₂] [AddCommMonoid N₂]
+ [Module R N₂] {N₃ : Type*} [TopologicalSpace N₃] [AddCommMonoid N₃] [Module R N₃] [Module S₃ M₃]
[SMulCommClass R₃ S₃ M₃] [ContinuousConstSMul S₃ M₃] [Module S N₂] [ContinuousConstSMul S N₂]
[SMulCommClass R S N₂] [Module S N₃] [SMulCommClass R S N₃] [ContinuousConstSMul S N₃]
{σ₁₂ : R →+* R₂} {σ₂₃ : R₂ →+* R₃} {σ₁₃ : R →+* R₃} [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] (c : S)
@@ -1675,7 +1675,7 @@ end SMul
section SMulRightₗ
-variable {R S T M M₂ : Type _} [Semiring R] [Semiring S] [Semiring T] [Module R S]
+variable {R S T M M₂ : Type*} [Semiring R] [Semiring S] [Semiring T] [Module R S]
[AddCommMonoid M₂] [Module R M₂] [Module S M₂] [IsScalarTower R S M₂] [TopologicalSpace S]
[TopologicalSpace M₂] [ContinuousSMul S M₂] [TopologicalSpace M] [AddCommMonoid M] [Module R M]
[ContinuousAdd M₂] [Module T M₂] [ContinuousConstSMul T M₂] [SMulCommClass R T M₂]
@@ -1703,8 +1703,8 @@ end SMulRightₗ
section CommRing
-variable {R : Type _} [CommRing R] {M : Type _} [TopologicalSpace M] [AddCommGroup M] {M₂ : Type _}
- [TopologicalSpace M₂] [AddCommGroup M₂] {M₃ : Type _} [TopologicalSpace M₃] [AddCommGroup M₃]
+variable {R : Type*} [CommRing R] {M : Type*} [TopologicalSpace M] [AddCommGroup M] {M₂ : Type*}
+ [TopologicalSpace M₂] [AddCommGroup M₂] {M₃ : Type*} [TopologicalSpace M₃] [AddCommGroup M₃]
[Module R M] [Module R M₂] [Module R M₃] [ContinuousConstSMul R M₃]
variable [TopologicalAddGroup M₂] [ContinuousConstSMul R M₂]
@@ -1717,8 +1717,8 @@ end CommRing
section RestrictScalars
-variable {A M M₂ : Type _} [Ring A] [AddCommGroup M] [AddCommGroup M₂] [Module A M] [Module A M₂]
- [TopologicalSpace M] [TopologicalSpace M₂] (R : Type _) [Ring R] [Module R M] [Module R M₂]
+variable {A M M₂ : Type*} [Ring A] [AddCommGroup M] [AddCommGroup M₂] [Module A M] [Module A M₂]
+ [TopologicalSpace M] [TopologicalSpace M₂] (R : Type*) [Ring R] [Module R M] [Module R M₂]
[LinearMap.CompatibleSMul M M₂ R A]
/-- If `A` is an `R`-algebra, then a continuous `A`-linear map can be interpreted as a continuous
@@ -1763,7 +1763,7 @@ theorem restrictScalars_neg (f : M →L[A] M₂) : (-f).restrictScalars R = -f.r
end
-variable {S : Type _}
+variable {S : Type*}
variable [Ring S] [Module S M₂] [ContinuousConstSMul S M₂] [SMulCommClass A S M₂]
[SMulCommClass R S M₂]
@@ -1799,14 +1799,14 @@ namespace ContinuousLinearEquiv
section AddCommMonoid
-variable {R₁ : Type _} {R₂ : Type _} {R₃ : Type _} [Semiring R₁] [Semiring R₂] [Semiring R₃]
+variable {R₁ : Type*} {R₂ : Type*} {R₃ : Type*} [Semiring R₁] [Semiring R₂] [Semiring R₃]
{σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁} [RingHomInvPair σ₁₂ σ₂₁] [RingHomInvPair σ₂₁ σ₁₂]
{σ₂₃ : R₂ →+* R₃} {σ₃₂ : R₃ →+* R₂} [RingHomInvPair σ₂₃ σ₃₂] [RingHomInvPair σ₃₂ σ₂₃]
{σ₁₃ : R₁ →+* R₃} {σ₃₁ : R₃ →+* R₁} [RingHomInvPair σ₁₃ σ₃₁] [RingHomInvPair σ₃₁ σ₁₃]
- [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [RingHomCompTriple σ₃₂ σ₂₁ σ₃₁] {M₁ : Type _}
- [TopologicalSpace M₁] [AddCommMonoid M₁] {M'₁ : Type _} [TopologicalSpace M'₁] [AddCommMonoid M'₁]
- {M₂ : Type _} [TopologicalSpace M₂] [AddCommMonoid M₂] {M₃ : Type _} [TopologicalSpace M₃]
- [AddCommMonoid M₃] {M₄ : Type _} [TopologicalSpace M₄] [AddCommMonoid M₄] [Module R₁ M₁]
+ [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [RingHomCompTriple σ₃₂ σ₂₁ σ₃₁] {M₁ : Type*}
+ [TopologicalSpace M₁] [AddCommMonoid M₁] {M'₁ : Type*} [TopologicalSpace M'₁] [AddCommMonoid M'₁]
+ {M₂ : Type*} [TopologicalSpace M₂] [AddCommMonoid M₂] {M₃ : Type*} [TopologicalSpace M₃]
+ [AddCommMonoid M₃] {M₄ : Type*} [TopologicalSpace M₄] [AddCommMonoid M₄] [Module R₁ M₁]
[Module R₁ M'₁] [Module R₂ M₂] [Module R₃ M₃]
/-- A continuous linear equivalence induces a continuous linear map. -/
@@ -1954,12 +1954,12 @@ protected theorem continuousWithinAt (e : M₁ ≃SL[σ₁₂] M₂) {s : Set M
e.continuous.continuousWithinAt
#align continuous_linear_equiv.continuous_within_at ContinuousLinearEquiv.continuousWithinAt
-theorem comp_continuousOn_iff {α : Type _} [TopologicalSpace α] (e : M₁ ≃SL[σ₁₂] M₂) {f : α → M₁}
+theorem comp_continuousOn_iff {α : Type*} [TopologicalSpace α] (e : M₁ ≃SL[σ₁₂] M₂) {f : α → M₁}
{s : Set α} : ContinuousOn (e ∘ f) s ↔ ContinuousOn f s :=
e.toHomeomorph.comp_continuousOn_iff _ _
#align continuous_linear_equiv.comp_continuous_on_iff ContinuousLinearEquiv.comp_continuousOn_iff
-theorem comp_continuous_iff {α : Type _} [TopologicalSpace α] (e : M₁ ≃SL[σ₁₂] M₂) {f : α → M₁} :
+theorem comp_continuous_iff {α : Type*} [TopologicalSpace α] (e : M₁ ≃SL[σ₁₂] M₂) {f : α → M₁} :
Continuous (e ∘ f) ↔ Continuous f :=
e.toHomeomorph.comp_continuous_iff
#align continuous_linear_equiv.comp_continuous_iff ContinuousLinearEquiv.comp_continuous_iff
@@ -2189,14 +2189,14 @@ protected theorem preimage_symm_preimage (e : M₁ ≃SL[σ₁₂] M₂) (s : Se
e.symm.symm_preimage_preimage s
#align continuous_linear_equiv.preimage_symm_preimage ContinuousLinearEquiv.preimage_symm_preimage
-protected theorem uniformEmbedding {E₁ E₂ : Type _} [UniformSpace E₁] [UniformSpace E₂]
+protected theorem uniformEmbedding {E₁ E₂ : Type*} [UniformSpace E₁] [UniformSpace E₂]
[AddCommGroup E₁] [AddCommGroup E₂] [Module R₁ E₁] [Module R₂ E₂] [UniformAddGroup E₁]
[UniformAddGroup E₂] (e : E₁ ≃SL[σ₁₂] E₂) : UniformEmbedding e :=
e.toLinearEquiv.toEquiv.uniformEmbedding e.toContinuousLinearMap.uniformContinuous
e.symm.toContinuousLinearMap.uniformContinuous
#align continuous_linear_equiv.uniform_embedding ContinuousLinearEquiv.uniformEmbedding
-protected theorem _root_.LinearEquiv.uniformEmbedding {E₁ E₂ : Type _} [UniformSpace E₁]
+protected theorem _root_.LinearEquiv.uniformEmbedding {E₁ E₂ : Type*} [UniformSpace E₁]
[UniformSpace E₂] [AddCommGroup E₁] [AddCommGroup E₂] [Module R₁ E₁] [Module R₂ E₂]
[UniformAddGroup E₁] [UniformAddGroup E₂] (e : E₁ ≃ₛₗ[σ₁₂] E₂)
(h₁ : Continuous e) (h₂ : Continuous e.symm) : UniformEmbedding e :=
@@ -2253,7 +2253,7 @@ instance automorphismGroup : Group (M₁ ≃L[R₁] M₁) where
exact f.left_inv x
#align continuous_linear_equiv.automorphism_group ContinuousLinearEquiv.automorphismGroup
-variable {M₁} {R₄ : Type _} [Semiring R₄] [Module R₄ M₄] {σ₃₄ : R₃ →+* R₄} {σ₄₃ : R₄ →+* R₃}
+variable {M₁} {R₄ : Type*} [Semiring R₄] [Module R₄ M₄] {σ₃₄ : R₃ →+* R₄} {σ₄₃ : R₄ →+* R₃}
[RingHomInvPair σ₃₄ σ₄₃] [RingHomInvPair σ₄₃ σ₃₄] {σ₂₄ : R₂ →+* R₄} {σ₁₄ : R₁ →+* R₄}
[RingHomCompTriple σ₂₁ σ₁₄ σ₂₄] [RingHomCompTriple σ₂₄ σ₄₃ σ₂₃] [RingHomCompTriple σ₁₃ σ₃₄ σ₁₄]
@@ -2287,9 +2287,9 @@ end AddCommMonoid
section AddCommGroup
-variable {R : Type _} [Semiring R] {M : Type _} [TopologicalSpace M] [AddCommGroup M] {M₂ : Type _}
- [TopologicalSpace M₂] [AddCommGroup M₂] {M₃ : Type _} [TopologicalSpace M₃] [AddCommGroup M₃]
- {M₄ : Type _} [TopologicalSpace M₄] [AddCommGroup M₄] [Module R M] [Module R M₂] [Module R M₃]
+variable {R : Type*} [Semiring R] {M : Type*} [TopologicalSpace M] [AddCommGroup M] {M₂ : Type*}
+ [TopologicalSpace M₂] [AddCommGroup M₂] {M₃ : Type*} [TopologicalSpace M₃] [AddCommGroup M₃]
+ {M₄ : Type*} [TopologicalSpace M₄] [AddCommGroup M₄] [Module R M] [Module R M₂] [Module R M₃]
[Module R M₄]
variable [TopologicalAddGroup M₄]
@@ -2325,8 +2325,8 @@ end AddCommGroup
section Ring
-variable {R : Type _} [Ring R] {R₂ : Type _} [Ring R₂] {M : Type _} [TopologicalSpace M]
- [AddCommGroup M] [Module R M] {M₂ : Type _} [TopologicalSpace M₂] [AddCommGroup M₂] [Module R₂ M₂]
+variable {R : Type*} [Ring R] {R₂ : Type*} [Ring R₂] {M : Type*} [TopologicalSpace M]
+ [AddCommGroup M] [Module R M] {M₂ : Type*} [TopologicalSpace M₂] [AddCommGroup M₂] [Module R₂ M₂]
variable {σ₁₂ : R →+* R₂} {σ₂₁ : R₂ →+* R} [RingHomInvPair σ₁₂ σ₂₁] [RingHomInvPair σ₂₁ σ₁₂]
@@ -2482,7 +2482,7 @@ end Ring
section
-variable (ι R M : Type _) [Unique ι] [Semiring R] [AddCommMonoid M] [Module R M]
+variable (ι R M : Type*) [Unique ι] [Semiring R] [AddCommMonoid M] [Module R M]
[TopologicalSpace M]
/-- If `ι` has a unique element, then `ι → M` is continuously linear equivalent to `M`. -/
@@ -2507,7 +2507,7 @@ variable (R M)
/-- Continuous linear equivalence between dependent functions `(i : Fin 2) → M i` and `M 0 × M 1`.
-/
@[simps! (config := { fullyApplied := false }) apply symm_apply]
-def piFinTwo (M : Fin 2 → Type _) [∀ i, AddCommMonoid (M i)] [∀ i, Module R (M i)]
+def piFinTwo (M : Fin 2 → Type*) [∀ i, AddCommMonoid (M i)] [∀ i, Module R (M i)]
[∀ i, TopologicalSpace (M i)] : ((i : _) → M i) ≃L[R] M 0 × M 1 :=
{ Homeomorph.piFinTwo M with toLinearEquiv := LinearEquiv.piFinTwo R M }
#align continuous_linear_equiv.pi_fin_two ContinuousLinearEquiv.piFinTwo
@@ -2530,7 +2530,7 @@ namespace ContinuousLinearMap
open Classical
-variable {R : Type _} {M : Type _} {M₂ : Type _} [TopologicalSpace M] [TopologicalSpace M₂]
+variable {R : Type*} {M : Type*} {M₂ : Type*} [TopologicalSpace M] [TopologicalSpace M₂]
section
@@ -2612,8 +2612,8 @@ end ContinuousLinearMap
namespace Submodule
-variable {R : Type _} [Ring R] {M : Type _} [TopologicalSpace M] [AddCommGroup M] [Module R M]
- {M₂ : Type _} [TopologicalSpace M₂] [AddCommGroup M₂] [Module R M₂]
+variable {R : Type*} [Ring R] {M : Type*} [TopologicalSpace M] [AddCommGroup M] [Module R M]
+ {M₂ : Type*} [TopologicalSpace M₂] [AddCommGroup M₂] [Module R M₂]
open ContinuousLinearMap
@@ -2647,8 +2647,8 @@ theorem closedComplemented_top : ClosedComplemented (⊤ : Submodule R M) :=
end Submodule
-theorem ContinuousLinearMap.closedComplemented_ker_of_rightInverse {R : Type _} [Ring R]
- {M : Type _} [TopologicalSpace M] [AddCommGroup M] {M₂ : Type _} [TopologicalSpace M₂]
+theorem ContinuousLinearMap.closedComplemented_ker_of_rightInverse {R : Type*} [Ring R]
+ {M : Type*} [TopologicalSpace M] [AddCommGroup M] {M₂ : Type*} [TopologicalSpace M₂]
[AddCommGroup M₂] [Module R M] [Module R M₂] [TopologicalAddGroup M] (f₁ : M →L[R] M₂)
(f₂ : M₂ →L[R] M) (h : Function.RightInverse f₂ f₁) : (ker f₁).ClosedComplemented :=
⟨f₁.projKerOfRightInverse f₂ h, f₁.projKerOfRightInverse_apply_idem f₂ h⟩
@@ -2658,7 +2658,7 @@ section Quotient
namespace Submodule
-variable {R M : Type _} [Ring R] [AddCommGroup M] [Module R M] [TopologicalSpace M]
+variable {R M : Type*} [Ring R] [AddCommGroup M] [Module R M] [TopologicalSpace M]
(S : Submodule R M)
-- Porting note: This is required in Lean4.
completeSpace_eqLocus
(#6132)
LinearMap.eqLocus f g
is a complete space.priority := 100
in completeSpace_ker
: this is the main way to prove that the kernel is a complete space.@@ -985,12 +985,17 @@ theorem isComplete_ker {M' : Type _} [UniformSpace M'] [CompleteSpace M'] [AddCo
(isClosed_ker f).isComplete
#align continuous_linear_map.is_complete_ker ContinuousLinearMap.isComplete_ker
-instance (priority := 100) completeSpace_ker {M' : Type _} [UniformSpace M'] [CompleteSpace M']
+instance completeSpace_ker {M' : Type _} [UniformSpace M'] [CompleteSpace M']
[AddCommMonoid M'] [Module R₁ M'] [T1Space M₂] [ContinuousSemilinearMapClass F σ₁₂ M' M₂]
(f : F) : CompleteSpace (ker f) :=
- (isClosed_ker f).completeSpace_coe
+ (isComplete_ker f).completeSpace_coe
#align continuous_linear_map.complete_space_ker ContinuousLinearMap.completeSpace_ker
+instance completeSpace_eqLocus {M' : Type _} [UniformSpace M'] [CompleteSpace M']
+ [AddCommMonoid M'] [Module R₁ M'] [T2Space M₂] [ContinuousSemilinearMapClass F σ₁₂ M' M₂]
+ (f g : F) : CompleteSpace (LinearMap.eqLocus f g) :=
+ IsClosed.completeSpace_coe <| isClosed_eq (map_continuous f) (map_continuous g)
+
@[simp]
theorem ker_prod [Module R₁ M₂] [Module R₁ M₃] (f : M₁ →L[R₁] M₂) (g : M₁ →L[R₁] M₃) :
ker (f.prod g) = ker f ⊓ ker g :=
@@ -860,6 +860,9 @@ instance monoidWithZero : MonoidWithZero (M₁ →L[R₁] M₁) where
mul_assoc _ _ _ := ext fun _ => rfl
#align continuous_linear_map.monoid_with_zero ContinuousLinearMap.monoidWithZero
+theorem coe_pow (f : M₁ →L[R₁] M₁) (n : ℕ) : ⇑(f ^ n) = f^[n] :=
+ hom_coe_pow _ rfl (fun _ _ ↦ rfl) _ _
+
instance semiring [ContinuousAdd M₁] : Semiring (M₁ →L[R₁] M₁) :=
{ ContinuousLinearMap.monoidWithZero,
ContinuousLinearMap.addCommMonoid with
@@ -3,11 +3,6 @@ Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov, Frédéric Dupuis,
Heather Macbeth
-
-! This file was ported from Lean 3 source module topology.algebra.module.basic
-! leanprover-community/mathlib commit 6285167a053ad0990fc88e56c48ccd9fae6550eb
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Topology.Algebra.Ring.Basic
import Mathlib.Topology.Algebra.MulAction
@@ -18,6 +13,8 @@ import Mathlib.Algebra.Algebra.Basic
import Mathlib.LinearAlgebra.Projection
import Mathlib.LinearAlgebra.Pi
+#align_import topology.algebra.module.basic from "leanprover-community/mathlib"@"6285167a053ad0990fc88e56c48ccd9fae6550eb"
+
/-!
# Theory of topological modules and continuous linear maps.
@@ -5,7 +5,7 @@ Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov, Fréd
Heather Macbeth
! This file was ported from Lean 3 source module topology.algebra.module.basic
-! leanprover-community/mathlib commit e354e865255654389cc46e6032160238df2e0f40
+! leanprover-community/mathlib commit 6285167a053ad0990fc88e56c48ccd9fae6550eb
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -1208,6 +1208,44 @@ theorem smulRight_comp [ContinuousMul R₁] {x : M₂} {c : R₁} :
simp [mul_smul]
#align continuous_linear_map.smul_right_comp ContinuousLinearMap.smulRight_comp
+section ToSpanSingleton
+
+variable (R₁)
+
+variable [ContinuousSMul R₁ M₁]
+
+/-- Given an element `x` of a topological space `M` over a semiring `R`, the natural continuous
+linear map from `R` to `M` by taking multiples of `x`.-/
+def toSpanSingleton (x : M₁) : R₁ →L[R₁] M₁
+ where
+ toLinearMap := LinearMap.toSpanSingleton R₁ M₁ x
+ cont := continuous_id.smul continuous_const
+#align continuous_linear_map.to_span_singleton ContinuousLinearMap.toSpanSingleton
+
+theorem toSpanSingleton_apply (x : M₁) (r : R₁) : toSpanSingleton R₁ x r = r • x :=
+ rfl
+#align continuous_linear_map.to_span_singleton_apply ContinuousLinearMap.toSpanSingleton_apply
+
+theorem toSpanSingleton_add [ContinuousAdd M₁] (x y : M₁) :
+ toSpanSingleton R₁ (x + y) = toSpanSingleton R₁ x + toSpanSingleton R₁ y := by
+ ext1; simp [toSpanSingleton_apply]
+#align continuous_linear_map.to_span_singleton_add ContinuousLinearMap.toSpanSingleton_add
+
+theorem toSpanSingleton_smul' {α} [Monoid α] [DistribMulAction α M₁] [ContinuousConstSMul α M₁]
+ [SMulCommClass R₁ α M₁] (c : α) (x : M₁) :
+ toSpanSingleton R₁ (c • x) = c • toSpanSingleton R₁ x :=
+ by ext1; rw [toSpanSingleton_apply, smul_apply, toSpanSingleton_apply, smul_comm]
+#align continuous_linear_map.to_span_singleton_smul' ContinuousLinearMap.toSpanSingleton_smul'
+
+/-- A special case of `to_span_singleton_smul'` for when `R` is commutative. -/
+theorem toSpanSingleton_smul (R) {M₁} [CommSemiring R] [AddCommMonoid M₁] [Module R M₁]
+ [TopologicalSpace R] [TopologicalSpace M₁] [ContinuousSMul R M₁] (c : R) (x : M₁) :
+ toSpanSingleton R (c • x) = c • toSpanSingleton R x :=
+ toSpanSingleton_smul' R c x
+#align continuous_linear_map.to_span_singleton_smul ContinuousLinearMap.toSpanSingleton_smul
+
+end ToSpanSingleton
+
end Semiring
section Pi
at
and goals (#5387)
Changes are of the form
some_tactic at h⊢
-> some_tactic at h ⊢
some_tactic at h
-> some_tactic at h
@@ -563,8 +563,8 @@ theorem _root_.DenseRange.topologicalClosure_map_submodule [RingHomSurjective σ
[ContinuousSMul R₂ M₂] [ContinuousAdd M₂] {f : M₁ →SL[σ₁₂] M₂} (hf' : DenseRange f)
{s : Submodule R₁ M₁} (hs : s.topologicalClosure = ⊤) :
(s.map (f : M₁ →ₛₗ[σ₁₂] M₂)).topologicalClosure = ⊤ := by
- rw [SetLike.ext'_iff] at hs⊢
- simp only [Submodule.topologicalClosure_coe, Submodule.top_coe, ← dense_iff_closure_eq] at hs⊢
+ rw [SetLike.ext'_iff] at hs ⊢
+ simp only [Submodule.topologicalClosure_coe, Submodule.top_coe, ← dense_iff_closure_eq] at hs ⊢
exact hf'.dense_image f.continuous hs
#align dense_range.topological_closure_map_submodule DenseRange.topologicalClosure_map_submodule
@@ -5,7 +5,7 @@ Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov, Fréd
Heather Macbeth
! This file was ported from Lean 3 source module topology.algebra.module.basic
-! leanprover-community/mathlib commit f430769b562e0cedef59ee1ed968d67e0e0c86ba
+! leanprover-community/mathlib commit e354e865255654389cc46e6032160238df2e0f40
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -1154,6 +1154,19 @@ theorem range_coprod [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃]
LinearMap.range_coprod _ _
#align continuous_linear_map.range_coprod ContinuousLinearMap.range_coprod
+theorem comp_fst_add_comp_snd [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃] (f : M₁ →L[R₁] M₃)
+ (g : M₂ →L[R₁] M₃) :
+ f.comp (ContinuousLinearMap.fst R₁ M₁ M₂) + g.comp (ContinuousLinearMap.snd R₁ M₁ M₂) =
+ f.coprod g :=
+ rfl
+#align continuous_linear_map.comp_fst_add_comp_snd ContinuousLinearMap.comp_fst_add_comp_snd
+
+theorem coprod_inl_inr [ContinuousAdd M₁] [ContinuousAdd M'₁] :
+ (ContinuousLinearMap.inl R₁ M₁ M'₁).coprod (ContinuousLinearMap.inr R₁ M₁ M'₁) =
+ ContinuousLinearMap.id R₁ (M₁ × M'₁) :=
+ by apply coe_injective; apply LinearMap.coprod_inl_inr
+#align continuous_linear_map.coprod_inl_inr ContinuousLinearMap.coprod_inl_inr
+
section
variable {R S : Type _} [Semiring R] [Semiring S] [Module R M₁] [Module R M₂] [Module R S]
@@ -1674,7 +1674,7 @@ def restrictScalars (f : M →L[A] M₂) : M →L[R] M₂ :=
variable {R}
-@[simp] -- @[norm_cast] -- Porting note: This theorem can't be an `norm_cast` theorem.
+@[simp] -- @[norm_cast] -- Porting note: This theorem can't be a `norm_cast` theorem.
theorem coe_restrictScalars (f : M →L[A] M₂) :
(f.restrictScalars R : M →ₗ[R] M₂) = (f : M →ₗ[A] M₂).restrictScalars R :=
rfl
Tracking down porting notes mentioning lean4#2210.
Some removals of nolint simpNF
may need to be reverted; let's see what CI says.
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
@@ -1360,8 +1360,6 @@ instance sub : Sub (M →SL[σ₁₂] M₂) :=
#align continuous_linear_map.has_sub ContinuousLinearMap.sub
instance addCommGroup : AddCommGroup (M →SL[σ₁₂] M₂) := by
- -- Porting note: Original proofs were `simp`s, but they timeout.
- -- Check this again during lean4#2210 cleanup
refine'
{ ContinuousLinearMap.addCommMonoid with
zero := 0
@@ -1371,26 +1369,13 @@ instance addCommGroup : AddCommGroup (M →SL[σ₁₂] M₂) := by
sub_eq_add_neg := _
nsmul := (· • ·)
zsmul := (· • ·)
- zsmul_zero' := fun f => by
- ext
- dsimp only []
- rw [coe_smul', Pi.smul_apply, zero_zsmul, zero_apply]
- zsmul_succ' := fun n f => by
- ext
- dsimp only []
- rw [coe_smul', Nat.succ_eq_one_add, Pi.smul_apply, Int.ofNat_eq_cast,
- Int.ofNat_eq_cast, Nat.cast_add, add_smul, Nat.cast_one, one_smul, coe_add',
- Pi.add_apply, coe_smul', Pi.smul_apply]
- zsmul_neg' := fun n f => by
- ext
- dsimp only []
- rw [Nat.succ_eq_add_one, coe_smul', Pi.smul_apply, negSucc_zsmul, add_smul,
- one_nsmul, neg_add_rev, Nat.cast_add, Nat.cast_one, neg_apply, coe_smul',
- add_smul, coe_nat_zsmul, one_zsmul, Pi.add_apply, neg_add_rev, Pi.smul_apply]
+ zsmul_zero' := fun f => by ext; simp
+ zsmul_succ' := fun n f => by ext; simp [add_smul, add_comm]
+ zsmul_neg' := fun n f => by ext; simp [Nat.succ_eq_add_one, add_smul]
.. } <;>
- intros <;>
- ext <;>
- apply_rules [zero_add, add_assoc, add_zero, add_left_neg, add_comm, sub_eq_add_neg]
+ { intros
+ ext
+ apply_rules [zero_add, add_assoc, add_zero, add_left_neg, add_comm, sub_eq_add_neg] }
#align continuous_linear_map.add_comm_group ContinuousLinearMap.addCommGroup
theorem sub_apply (f g : M →SL[σ₁₂] M₂) (x : M) : (f - g) x = f x - g x :=
@@ -1409,36 +1394,28 @@ theorem coe_sub' (f g : M →SL[σ₁₂] M₂) : ⇑(f - g) = f - g :=
end
--- Porting note: checked that lack of eta causes simp to fail, otherwise works
--- This can probably be removed during lean4#2210 cleanup.
-@[simp, nolint simpNF]
+@[simp]
theorem comp_neg [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₂] [TopologicalAddGroup M₃]
(g : M₂ →SL[σ₂₃] M₃) (f : M →SL[σ₁₂] M₂) : g.comp (-f) = -g.comp f := by
ext x
simp
#align continuous_linear_map.comp_neg ContinuousLinearMap.comp_neg
--- Porting note: checked that lack of eta causes simp to fail, otherwise works
--- This can probably be removed during lean4#2210 cleanup.
-@[simp, nolint simpNF]
+@[simp]
theorem neg_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₃] (g : M₂ →SL[σ₂₃] M₃)
(f : M →SL[σ₁₂] M₂) : (-g).comp f = -g.comp f := by
ext
simp
#align continuous_linear_map.neg_comp ContinuousLinearMap.neg_comp
--- Porting note: checked that lack of eta causes simp to fail, otherwise works
--- This can probably be removed during lean4#2210 cleanup.
-@[simp, nolint simpNF]
+@[simp]
theorem comp_sub [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₂] [TopologicalAddGroup M₃]
(g : M₂ →SL[σ₂₃] M₃) (f₁ f₂ : M →SL[σ₁₂] M₂) : g.comp (f₁ - f₂) = g.comp f₁ - g.comp f₂ := by
ext
simp
#align continuous_linear_map.comp_sub ContinuousLinearMap.comp_sub
--- Porting note: checked that lack of eta causes simp to fail, otherwise works
--- This can probably be removed during lean4#2210 cleanup.
-@[simp, nolint simpNF]
+@[simp]
theorem sub_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₃] (g₁ g₂ : M₂ →SL[σ₂₃] M₃)
(f : M →SL[σ₁₂] M₂) : (g₁ - g₂).comp f = g₁.comp f - g₂.comp f := by
ext
@@ -1676,10 +1653,8 @@ variable {R : Type _} [CommRing R] {M : Type _} [TopologicalSpace M] [AddCommGro
variable [TopologicalAddGroup M₂] [ContinuousConstSMul R M₂]
--- Porting note: Instances should be specified, or timeouts.
--- Check this again during lean4#2210 cleanup.
instance algebra : Algebra R (M₂ →L[R] M₂) :=
- @Algebra.ofModule _ _ _ _ ContinuousLinearMap.module smul_comp fun _ _ _ => comp_smul _ _ _
+ Algebra.ofModule smul_comp fun _ _ _ => comp_smul _ _ _
#align continuous_linear_map.algebra ContinuousLinearMap.algebra
end CommRing
Forward-port leanprover-community/mathlib#19107
@@ -1992,8 +1992,7 @@ def Simps.symm_apply (h : M₁ ≃SL[σ₁₂] M₂) : M₂ → M₁ :=
h.symm
#align continuous_linear_equiv.simps.symm_apply ContinuousLinearEquiv.Simps.symm_apply
-initialize_simps_projections ContinuousLinearEquiv
- (toLinearEquiv_toFun → apply, toLinearEquiv_invFun → symm_apply)
+initialize_simps_projections ContinuousLinearEquiv (toFun → apply, invFun → symm_apply)
theorem symm_map_nhds_eq (e : M₁ ≃SL[σ₁₂] M₂) (x : M₁) : map e.symm (𝓝 (e x)) = 𝓝 x :=
e.toHomeomorph.symm_map_nhds_eq x
SProd
to implement overloaded notation · ×ˢ ·
(#4200)
Currently, the following notations are changed from · ×ˢ ·
because Lean 4 can't deal with ambiguous notations.
| Definition | Notation |
| :
Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Chris Hughes <chrishughes24@gmail.com>
@@ -42,7 +42,7 @@ variable {R : Type _} {M : Type _} [Ring R] [TopologicalSpace R] [TopologicalSpa
[AddCommGroup M] [Module R M]
theorem ContinuousSMul.of_nhds_zero [TopologicalRing R] [TopologicalAddGroup M]
- (hmul : Tendsto (fun p : R × M => p.1 • p.2) (𝓝 0 ×ᶠ 𝓝 0) (𝓝 0))
+ (hmul : Tendsto (fun p : R × M => p.1 • p.2) (𝓝 0 ×ˢ 𝓝 0) (𝓝 0))
(hmulleft : ∀ m : M, Tendsto (fun a : R => a • m) (𝓝 0) (𝓝 0))
(hmulright : ∀ a : R, Tendsto (fun m : M => a • m) (𝓝 0) (𝓝 0)) : ContinuousSMul R M where
continuous_smul := by
@@ -568,7 +568,7 @@ theorem _root_.DenseRange.topologicalClosure_map_submodule [RingHomSurjective σ
exact hf'.dense_image f.continuous hs
#align dense_range.topological_closure_map_submodule DenseRange.topologicalClosure_map_submodule
-section SmulMonoid
+section SMulMonoid
variable {S₂ T₂ : Type _} [Monoid S₂] [Monoid T₂]
@@ -607,7 +607,7 @@ instance smulCommClass [SMulCommClass S₂ T₂ M₂] : SMulCommClass S₂ T₂
⟨fun a b f => ext fun x => smul_comm a b (f x)⟩
#align continuous_linear_map.smul_comm_class ContinuousLinearMap.smulCommClass
-end SmulMonoid
+end SMulMonoid
/-- The continuous map that is constantly zero. -/
instance zero : Zero (M₁ →SL[σ₁₂] M₂) :=
@@ -745,11 +745,7 @@ instance addCommMonoid : AddCommMonoid (M₁ →SL[σ₁₂] M₂) where
simp
nsmul_succ n f := by
ext
- -- Porting note: `simp [Nat.add_comm n 1, add_smul]` timeouts.
- -- Check this again during lean4#2210 cleanup
- dsimp only []
- rw [Nat.add_comm n 1, coe_smul', Pi.smul_apply, add_smul, one_smul, add_apply,
- coe_smul', Pi.smul_apply]
+ simp [Nat.add_comm n 1, add_smul]
#align continuous_linear_map.add_comm_monoid ContinuousLinearMap.addCommMonoid
@[simp, norm_cast]
@@ -908,12 +904,12 @@ instance applyFaithfulSMul : FaithfulSMul (M₁ →L[R₁] M₁) M₁ :=
⟨fun {_ _} => ContinuousLinearMap.ext⟩
#align continuous_linear_map.apply_has_faithful_smul ContinuousLinearMap.applyFaithfulSMul
-instance applySMulCommClass : SMulCommClass R₁ (M₁ →L[R₁] M₁) M₁
- where smul_comm r e m := (e.map_smul r m).symm
+instance applySMulCommClass : SMulCommClass R₁ (M₁ →L[R₁] M₁) M₁ where
+ smul_comm r e m := (e.map_smul r m).symm
#align continuous_linear_map.apply_smul_comm_class ContinuousLinearMap.applySMulCommClass
-instance applySMulCommClass' : SMulCommClass (M₁ →L[R₁] M₁) R₁ M₁
- where smul_comm := ContinuousLinearMap.map_smul
+instance applySMulCommClass' : SMulCommClass (M₁ →L[R₁] M₁) R₁ M₁ where
+ smul_comm := ContinuousLinearMap.map_smul
#align continuous_linear_map.apply_smul_comm_class' ContinuousLinearMap.applySMulCommClass'
instance continuousConstSMul : ContinuousConstSMul (M₁ →L[R₁] M₁) M₁ :=
@@ -1341,11 +1337,7 @@ section
variable [TopologicalAddGroup M₂]
instance neg : Neg (M →SL[σ₁₂] M₂) :=
- -- Porting note: The explicit instance should be specified, or it timeouts.
- -- We hope these problem will be resolved by
- -- https://github.com/leanprover/lean4/issues/2055.
- ⟨fun f => ⟨-(f : M →ₛₗ[σ₁₂] M₂),
- @Continuous.neg _ _ _ _ (TopologicalAddGroup.toContinuousNeg) _ _ f.2⟩⟩
+ ⟨fun f => ⟨-f, f.2.neg⟩⟩
#align continuous_linear_map.has_neg ContinuousLinearMap.neg
@[simp]
@@ -1378,9 +1370,7 @@ instance addCommGroup : AddCommGroup (M →SL[σ₁₂] M₂) := by
sub := (· - ·)
sub_eq_add_neg := _
nsmul := (· • ·)
- -- Porting note: Instances should be specified, or it timeouts.
- zsmul := @HSMul.hSMul _ _ _ (@instHSMul _ _
- (@MulAction.toSMul _ _ _ ContinuousLinearMap.mulAction))
+ zsmul := (· • ·)
zsmul_zero' := fun f => by
ext
dsimp only []
@@ -1494,12 +1484,8 @@ theorem coe_projKerOfRightInverse_apply [TopologicalAddGroup M] (f₁ : M →SL[
theorem projKerOfRightInverse_apply_idem [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂)
(f₂ : M₂ →SL[σ₂₁] M) (h : Function.RightInverse f₂ f₁) (x : LinearMap.ker f₁) :
f₁.projKerOfRightInverse f₂ h x = x := by
- -- porting note: should be `ext1; simp` but TC search fails
- -- check this during post lean4#2210 cleanup
ext1
- refine sub_eq_self.2 ?_
- calc f₂ (f₁ x) = f₂ 0 := by rw [x.2.out]
- _ = 0 := f₂.map_zero
+ simp
#align continuous_linear_map.proj_ker_of_right_inverse_apply_idem ContinuousLinearMap.projKerOfRightInverse_apply_idem
@[simp]
@@ -1529,12 +1515,7 @@ protected theorem isOpenMap_of_ne_zero [TopologicalSpace R] [DivisionRing R] [Co
end DivisionMonoid
-section SmulMonoid
-
--- Porting note: This is required to prevent timeouts.
--- Check this again during lean4#2210 cleanup.
-local infixr:73 " •SL " => @HSMul.hSMul _ _ _ (@instHSMul _ _ (@MulAction.toSMul _ _ _
- (@ContinuousLinearMap.mulAction _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _)))
+section SMulMonoid
-- The M's are used for semilinear maps, and the N's for plain linear maps
variable {R R₂ R₃ S S₃ : Type _} [Semiring R] [Semiring R₂] [Semiring R₃] [Monoid S] [Monoid S₃]
@@ -1548,7 +1529,7 @@ variable {R R₂ R₃ S S₃ : Type _} [Semiring R] [Semiring R₂] [Semiring R
@[simp]
theorem smul_comp (c : S₃) (h : M₂ →SL[σ₂₃] M₃) (f : M →SL[σ₁₂] M₂) :
- (c •SL h).comp f = c •SL h.comp f :=
+ (c • h).comp f = c • h.comp f :=
rfl
#align continuous_linear_map.smul_comp ContinuousLinearMap.smul_comp
@@ -1558,7 +1539,7 @@ variable [DistribMulAction S N₂] [ContinuousConstSMul S N₂] [SMulCommClass R
@[simp]
theorem comp_smul [LinearMap.CompatibleSMul N₂ N₃ S R] (hₗ : N₂ →L[R] N₃) (c : S)
- (fₗ : M →L[R] N₂) : hₗ.comp (c •SL fₗ) = c •SL hₗ.comp fₗ := by
+ (fₗ : M →L[R] N₂) : hₗ.comp (c • fₗ) = c • hₗ.comp fₗ := by
ext x
exact hₗ.map_smul_of_tower c (fₗ x)
#align continuous_linear_map.comp_smul ContinuousLinearMap.comp_smul
@@ -1566,7 +1547,7 @@ theorem comp_smul [LinearMap.CompatibleSMul N₂ N₃ S R] (hₗ : N₂ →L[R]
@[simp]
theorem comp_smulₛₗ [SMulCommClass R₂ R₂ M₂] [SMulCommClass R₃ R₃ M₃] [ContinuousConstSMul R₂ M₂]
[ContinuousConstSMul R₃ M₃] (h : M₂ →SL[σ₂₃] M₃) (c : R₂) (f : M →SL[σ₁₂] M₂) :
- h.comp (c •SL f) = σ₂₃ c •SL h.comp f := by
+ h.comp (c • f) = σ₂₃ c • h.comp f := by
ext x
simp only [coe_smul', coe_comp', Function.comp_apply, Pi.smul_apply,
ContinuousLinearMap.map_smulₛₗ]
@@ -1577,9 +1558,9 @@ instance distribMulAction [ContinuousAdd M₂] : DistribMulAction S₃ (M →SL[
smul_zero _a := ext fun _x => smul_zero _
#align continuous_linear_map.distrib_mul_action ContinuousLinearMap.distribMulAction
-end SmulMonoid
+end SMulMonoid
-section Smul
+section SMul
-- The M's are used for semilinear maps, and the N's for plain linear maps
variable {R R₂ R₃ S S₃ : Type _} [Semiring R] [Semiring R₂] [Semiring R₃] [Semiring S] [Semiring S₃]
@@ -1621,26 +1602,9 @@ instance module : Module S₃ (M →SL[σ₁₃] M₃) where
add_smul _ _ _ := ext fun _ => add_smul _ _ _
#align continuous_linear_map.module ContinuousLinearMap.module
--- Porting note: Instances should be specified, or timeouts.
--- Check this again during lean4#2210 cleanup.
instance isCentralScalar [Module S₃ᵐᵒᵖ M₃] [IsCentralScalar S₃ M₃] :
- @IsCentralScalar S₃ (M →SL[σ₁₃] M₃)
- (@SMulZeroClass.toSMul _ _ _ (@SMulWithZero.toSMulZeroClass _ _ _ _
- (@MulActionWithZero.toSMulWithZero _ _ _ _ (@Module.toMulActionWithZero _ _ _ _
- ContinuousLinearMap.module))))
- (@SMulZeroClass.toSMul _ _ _ (@SMulWithZero.toSMulZeroClass _ _ _ _
- (@MulActionWithZero.toSMulWithZero _ _ _ _ (@Module.toMulActionWithZero _ _ _ _
- (@ContinuousLinearMap.module _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
- (@SMulCommClass.op_right _ _ _ _ _ _ _ _) _ _ _))))) :=
- @IsCentralScalar.mk S₃ (M →SL[σ₁₃] M₃)
- (@SMulZeroClass.toSMul _ _ _ (@SMulWithZero.toSMulZeroClass _ _ _ _
- (@MulActionWithZero.toSMulWithZero _ _ _ _ (@Module.toMulActionWithZero _ _ _ _
- ContinuousLinearMap.module))))
- (@SMulZeroClass.toSMul _ _ _ (@SMulWithZero.toSMulZeroClass _ _ _ _
- (@MulActionWithZero.toSMulWithZero _ _ _ _ (@Module.toMulActionWithZero _ _ _ _
- (@ContinuousLinearMap.module _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
- (@SMulCommClass.op_right _ _ _ _ _ _ _ _) _ _ _)))))
- fun _ _ => ext fun _ => op_smul_eq_smul _ _
+ IsCentralScalar S₃ (M →SL[σ₁₃] M₃) where
+ op_smul_eq_smul _ _ := ext fun _ => op_smul_eq_smul _ _
#align continuous_linear_map.is_central_scalar ContinuousLinearMap.isCentralScalar
variable (S) [ContinuousAdd N₃]
@@ -1674,11 +1638,9 @@ def coeLMₛₗ : (M →SL[σ₁₃] M₃) →ₗ[S₃] M →ₛₗ[σ₁₃] M
#align continuous_linear_map.coe_lmₛₗ ContinuousLinearMap.coeLMₛₗ
#align continuous_linear_map.coe_lmₛₗ_apply ContinuousLinearMap.coeLMₛₗ_apply
-variable {σ₁₃}
-
-end Smul
+end SMul
-section SmulRightₗ
+section SMulRightₗ
variable {R S T M M₂ : Type _} [Semiring R] [Semiring S] [Semiring T] [Module R S]
[AddCommMonoid M₂] [Module R M₂] [Module S M₂] [IsScalarTower R S M₂] [TopologicalSpace S]
@@ -1704,7 +1666,7 @@ theorem coe_smulRightₗ (c : M →L[R] S) : ⇑(smulRightₗ c : M₂ →ₗ[T]
rfl
#align continuous_linear_map.coe_smul_rightₗ ContinuousLinearMap.coe_smulRightₗ
-end SmulRightₗ
+end SMulRightₗ
section CommRing
@@ -1724,9 +1686,6 @@ end CommRing
section RestrictScalars
-local infixr:73 " •SL " => @HSMul.hSMul _ _ _ (@instHSMul _ _ (@MulAction.toSMul _ _ _
- (@ContinuousLinearMap.mulAction _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _)))
-
variable {A M M₂ : Type _} [Ring A] [AddCommGroup M] [AddCommGroup M₂] [Module A M] [Module A M₂]
[TopologicalSpace M] [TopologicalSpace M₂] (R : Type _) [Ring R] [Module R M] [Module R M₂]
[LinearMap.CompatibleSMul M M₂ R A]
@@ -1779,7 +1738,7 @@ variable [Ring S] [Module S M₂] [ContinuousConstSMul S M₂] [SMulCommClass A
@[simp]
theorem restrictScalars_smul (c : S) (f : M →L[A] M₂) :
- (c •SL f).restrictScalars R = c •SL f.restrictScalars R :=
+ (c • f).restrictScalars R = c • f.restrictScalars R :=
rfl
#align continuous_linear_map.restrict_scalars_smul ContinuousLinearMap.restrictScalars_smul
fix-comments.py
on all files.@@ -2055,7 +2055,7 @@ theorem trans_toLinearEquiv (e₁ : M₁ ≃SL[σ₁₂] M₂) (e₂ : M₂ ≃S
rfl
#align continuous_linear_equiv.trans_to_linear_equiv ContinuousLinearEquiv.trans_toLinearEquiv
-/-- Product of two continuous linear equivalences. The map comes from `equiv.prod_congr`. -/
+/-- Product of two continuous linear equivalences. The map comes from `Equiv.prodCongr`. -/
def prod [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (e : M₁ ≃L[R₁] M₂) (e' : M₃ ≃L[R₁] M₄) :
(M₁ × M₃) ≃L[R₁] M₂ × M₄ :=
{ e.toLinearEquiv.prod e'.toLinearEquiv with
The main breaking change is that tac <;> [t1, t2]
is now written tac <;> [t1; t2]
, to avoid clashing with tactics like cases
and use
that take comma-separated lists.
@@ -1283,7 +1283,7 @@ def iInfKerProjEquiv {I J : Set ι} [DecidablePred fun i => i ∈ I] (hd : Disjo
Continuous (⇑(if h : i ∈ I then LinearMap.proj (R := R) (ι := ↥I)
(φ := fun i : ↥I => φ i) ⟨i, h⟩ else
(0 : ((i : I) → φ i) →ₗ[R] φ i)))
- split_ifs <;> [apply continuous_apply, exact continuous_zero])
+ split_ifs <;> [apply continuous_apply; exact continuous_zero])
_
#align continuous_linear_map.infi_ker_proj_equiv ContinuousLinearMap.iInfKerProjEquiv
Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Arien Malec <arien.malec@gmail.com> Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Mauricio Collares <mauricio@collares.org> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>
@@ -839,9 +839,9 @@ theorem comp_assoc {R₄ : Type _} [Semiring R₄] [Module R₄ M₄] {σ₁₄
rfl
#align continuous_linear_map.comp_assoc ContinuousLinearMap.comp_assoc
-instance mul : Mul (M₁ →L[R₁] M₁) :=
+instance instMul : Mul (M₁ →L[R₁] M₁) :=
⟨comp⟩
-#align continuous_linear_map.has_mul ContinuousLinearMap.mul
+#align continuous_linear_map.has_mul ContinuousLinearMap.instMul
theorem mul_def (f g : M₁ →L[R₁] M₁) : f * g = f.comp g :=
rfl
Now that leanprover/lean4#2210 has been merged, this PR:
set_option synthInstance.etaExperiment true
commands (and some etaExperiment%
term elaborators)set_option maxHeartbeats
commandsCo-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>
@@ -31,9 +31,6 @@ Plain linear maps are denoted by `M →L[R] M₂` and star-linear maps by `M →
The corresponding notation for equivalences is `M ≃SL[σ] M₂`, `M ≃L[R] M₂` and `M ≃L⋆[R] M₂`.
-/
--- Porting note: TODO Erase this line. Needed because we don't have η for classes. (lean4#2074)
--- set_option synthInstance.etaExperiment true
-
open LinearMap (ker range)
open Topology BigOperators Filter Pointwise
@@ -723,8 +720,6 @@ theorem coe_add' (f g : M₁ →SL[σ₁₂] M₂) : ⇑(f + g) = f + g :=
rfl
#align continuous_linear_map.coe_add' ContinuousLinearMap.coe_add'
--- Porting note: Without this line, this timeouts.
-set_option synthInstance.etaExperiment false in
instance addCommMonoid : AddCommMonoid (M₁ →SL[σ₁₂] M₂) where
zero := (0 : M₁ →SL[σ₁₂] M₂)
add := (· + ·)
@@ -751,6 +746,7 @@ instance addCommMonoid : AddCommMonoid (M₁ →SL[σ₁₂] M₂) where
nsmul_succ n f := by
ext
-- Porting note: `simp [Nat.add_comm n 1, add_smul]` timeouts.
+ -- Check this again during lean4#2210 cleanup
dsimp only []
rw [Nat.add_comm n 1, coe_smul', Pi.smul_apply, add_smul, one_smul, add_apply,
coe_smul', Pi.smul_apply]
@@ -1303,20 +1299,14 @@ variable {R : Type _} [Ring R] {R₂ : Type _} [Ring R₂] {R₃ : Type _} [Ring
section
--- Porting note: cannot synth →SL and AddHomMonoidClass
-set_option synthInstance.etaExperiment true in
protected theorem map_neg (f : M →SL[σ₁₂] M₂) (x : M) : f (-x) = -f x := by
exact map_neg f x
#align continuous_linear_map.map_neg ContinuousLinearMap.map_neg
--- Porting note: cannot synth →SL and AddHomMonoidClass
-set_option synthInstance.etaExperiment true in
protected theorem map_sub (f : M →SL[σ₁₂] M₂) (x y : M) : f (x - y) = f x - f y := by
exact map_sub f x y
#align continuous_linear_map.map_sub ContinuousLinearMap.map_sub
--- Porting note: cannot synth →SL and AddHomMonoidClass
-set_option synthInstance.etaExperiment true in
@[simp]
theorem sub_apply' (f g : M →SL[σ₁₂] M₂) (x : M) : ((f : M →ₛₗ[σ₁₂] M₂) - g) x = f x - g x :=
rfl
@@ -1328,22 +1318,16 @@ section
variable [Module R M₂] [Module R M₃] [Module R M₄]
--- Porting note: cannot synth →L
-set_option synthInstance.etaExperiment true in
theorem range_prod_eq {f : M →L[R] M₂} {g : M →L[R] M₃} (h : ker f ⊔ ker g = ⊤) :
range (f.prod g) = (range f).prod (range g) :=
LinearMap.range_prod_eq h
#align continuous_linear_map.range_prod_eq ContinuousLinearMap.range_prod_eq
--- Porting note: cannot synth →L
-set_option synthInstance.etaExperiment true in
theorem ker_prod_ker_le_ker_coprod [ContinuousAdd M₃] (f : M →L[R] M₃) (g : M₂ →L[R] M₃) :
(LinearMap.ker f).prod (LinearMap.ker g) ≤ LinearMap.ker (f.coprod g) :=
LinearMap.ker_prod_ker_le_ker_coprod f.toLinearMap g.toLinearMap
#align continuous_linear_map.ker_prod_ker_le_ker_coprod ContinuousLinearMap.ker_prod_ker_le_ker_coprod
--- Porting note: cannot synth →L
-set_option synthInstance.etaExperiment true in
theorem ker_coprod_of_disjoint_range [ContinuousAdd M₃] (f : M →L[R] M₃) (g : M₂ →L[R] M₃)
(hd : Disjoint (range f) (range g)) :
LinearMap.ker (f.coprod g) = (LinearMap.ker f).prod (LinearMap.ker g) :=
@@ -1356,8 +1340,6 @@ section
variable [TopologicalAddGroup M₂]
--- Porting note: mismatch between →ₛₗ and →SL
-set_option synthInstance.etaExperiment true in
instance neg : Neg (M →SL[σ₁₂] M₂) :=
-- Porting note: The explicit instance should be specified, or it timeouts.
-- We hope these problem will be resolved by
@@ -1366,37 +1348,28 @@ instance neg : Neg (M →SL[σ₁₂] M₂) :=
@Continuous.neg _ _ _ _ (TopologicalAddGroup.toContinuousNeg) _ _ f.2⟩⟩
#align continuous_linear_map.has_neg ContinuousLinearMap.neg
--- Porting note: cannot synth →SL
-set_option synthInstance.etaExperiment true in
@[simp]
theorem neg_apply (f : M →SL[σ₁₂] M₂) (x : M) : (-f) x = -f x :=
rfl
#align continuous_linear_map.neg_apply ContinuousLinearMap.neg_apply
--- Porting note: mismatch between →ₛₗ and →SL
-set_option synthInstance.etaExperiment true in
@[simp, norm_cast]
theorem coe_neg (f : M →SL[σ₁₂] M₂) : (↑(-f) : M →ₛₗ[σ₁₂] M₂) = -f :=
rfl
#align continuous_linear_map.coe_neg ContinuousLinearMap.coe_neg
--- Porting note: cannot coerce to function
-set_option synthInstance.etaExperiment true in
@[norm_cast]
theorem coe_neg' (f : M →SL[σ₁₂] M₂) : ⇑(-f) = -f :=
rfl
#align continuous_linear_map.coe_neg' ContinuousLinearMap.coe_neg'
--- Porting note: cannot synth HSub
-set_option synthInstance.etaExperiment true in
instance sub : Sub (M →SL[σ₁₂] M₂) :=
⟨fun f g => ⟨f - g, f.2.sub g.2⟩⟩
#align continuous_linear_map.has_sub ContinuousLinearMap.sub
--- Porting note: cannot synth continuous semilinear map class
-set_option synthInstance.etaExperiment true in
instance addCommGroup : AddCommGroup (M →SL[σ₁₂] M₂) := by
-- Porting note: Original proofs were `simp`s, but they timeout.
+ -- Check this again during lean4#2210 cleanup
refine'
{ ContinuousLinearMap.addCommMonoid with
zero := 0
@@ -1430,21 +1403,15 @@ instance addCommGroup : AddCommGroup (M →SL[σ₁₂] M₂) := by
apply_rules [zero_add, add_assoc, add_zero, add_left_neg, add_comm, sub_eq_add_neg]
#align continuous_linear_map.add_comm_group ContinuousLinearMap.addCommGroup
--- Porting note: mismatched types
-set_option synthInstance.etaExperiment true in
theorem sub_apply (f g : M →SL[σ₁₂] M₂) (x : M) : (f - g) x = f x - g x :=
rfl
#align continuous_linear_map.sub_apply ContinuousLinearMap.sub_apply
--- Porting note: cannot synth HSub and diamond with Ring.toNonAssocRing
-set_option synthInstance.etaExperiment true in
@[simp, norm_cast]
theorem coe_sub (f g : M →SL[σ₁₂] M₂) : (↑(f - g) : M →ₛₗ[σ₁₂] M₂) = f - g :=
rfl
#align continuous_linear_map.coe_sub ContinuousLinearMap.coe_sub
--- Porting note: cannot synth HSub and diamond with Ring.toNonAssocRing
-set_option synthInstance.etaExperiment true in
@[simp, norm_cast]
theorem coe_sub' (f g : M →SL[σ₁₂] M₂) : ⇑(f - g) = f - g :=
rfl
@@ -1452,9 +1419,8 @@ theorem coe_sub' (f g : M →SL[σ₁₂] M₂) : ⇑(f - g) = f - g :=
end
--- Porting note: cannot synth RingHomCompTriple
-set_option synthInstance.etaExperiment true in
-- Porting note: checked that lack of eta causes simp to fail, otherwise works
+-- This can probably be removed during lean4#2210 cleanup.
@[simp, nolint simpNF]
theorem comp_neg [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₂] [TopologicalAddGroup M₃]
(g : M₂ →SL[σ₂₃] M₃) (f : M →SL[σ₁₂] M₂) : g.comp (-f) = -g.comp f := by
@@ -1462,9 +1428,8 @@ theorem comp_neg [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddG
simp
#align continuous_linear_map.comp_neg ContinuousLinearMap.comp_neg
--- Porting note: cannot synth RingHomCompTriple
-set_option synthInstance.etaExperiment true in
-- Porting note: checked that lack of eta causes simp to fail, otherwise works
+-- This can probably be removed during lean4#2210 cleanup.
@[simp, nolint simpNF]
theorem neg_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₃] (g : M₂ →SL[σ₂₃] M₃)
(f : M →SL[σ₁₂] M₂) : (-g).comp f = -g.comp f := by
@@ -1472,9 +1437,8 @@ theorem neg_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddG
simp
#align continuous_linear_map.neg_comp ContinuousLinearMap.neg_comp
--- Porting note: cannot synth RingHomCompTriple
-set_option synthInstance.etaExperiment true in
-- Porting note: checked that lack of eta causes simp to fail, otherwise works
+-- This can probably be removed during lean4#2210 cleanup.
@[simp, nolint simpNF]
theorem comp_sub [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₂] [TopologicalAddGroup M₃]
(g : M₂ →SL[σ₂₃] M₃) (f₁ f₂ : M →SL[σ₁₂] M₂) : g.comp (f₁ - f₂) = g.comp f₁ - g.comp f₂ := by
@@ -1482,9 +1446,8 @@ theorem comp_sub [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddG
simp
#align continuous_linear_map.comp_sub ContinuousLinearMap.comp_sub
--- Porting note: cannot synth RingHomCompTriple
-set_option synthInstance.etaExperiment true in
-- Porting note: checked that lack of eta causes simp to fail, otherwise works
+-- This can probably be removed during lean4#2210 cleanup.
@[simp, nolint simpNF]
theorem sub_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddGroup M₃] (g₁ g₂ : M₂ →SL[σ₂₃] M₃)
(f : M →SL[σ₁₂] M₂) : (g₁ - g₂).comp f = g₁.comp f - g₂.comp f := by
@@ -1492,8 +1455,6 @@ theorem sub_comp [RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [TopologicalAddG
simp
#align continuous_linear_map.sub_comp ContinuousLinearMap.sub_comp
--- Porting note: cannot synth Mul
-set_option synthInstance.etaExperiment true in
instance ring [TopologicalAddGroup M] : Ring (M →L[R] M) :=
{ ContinuousLinearMap.semiring,
ContinuousLinearMap.addCommGroup with
@@ -1501,8 +1462,6 @@ instance ring [TopologicalAddGroup M] : Ring (M →L[R] M) :=
one := 1 }
#align continuous_linear_map.ring ContinuousLinearMap.ring
--- Porting note: cannot synth Module R R
-set_option synthInstance.etaExperiment true in
theorem smulRight_one_pow [TopologicalSpace R] [TopologicalRing R] (c : R) (n : ℕ) :
smulRight (1 : R →L[R] R) c ^ n = smulRight (1 : R →L[R] R) (c ^ n) := by
induction' n with n ihn
@@ -1516,8 +1475,6 @@ section
variable {σ₂₁ : R₂ →+* R} [RingHomInvPair σ₁₂ σ₂₁]
--- Porting note: cannot synth Semilinar Map Class
-set_option synthInstance.etaExperiment true in
/-- Given a right inverse `f₂ : M₂ →L[R] M` to `f₁ : M →L[R] M₂`,
`projKerOfRightInverse f₁ f₂ h` is the projection `M →L[R] LinearMap.ker f₁` along
`LinearMap.range f₂`. -/
@@ -1526,8 +1483,6 @@ def projKerOfRightInverse [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂
(id R M - f₂.comp f₁).codRestrict (LinearMap.ker f₁) fun x => by simp [h (f₁ x)]
#align continuous_linear_map.proj_ker_of_right_inverse ContinuousLinearMap.projKerOfRightInverse
--- Porting note: cannot synth →L
-set_option synthInstance.etaExperiment true in
@[simp]
theorem coe_projKerOfRightInverse_apply [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂)
(f₂ : M₂ →SL[σ₂₁] M) (h : Function.RightInverse f₂ f₁) (x : M) :
@@ -1535,22 +1490,18 @@ theorem coe_projKerOfRightInverse_apply [TopologicalAddGroup M] (f₁ : M →SL[
rfl
#align continuous_linear_map.coe_proj_ker_of_right_inverse_apply ContinuousLinearMap.coe_projKerOfRightInverse_apply
--- Porting note: cannot synth Semilinar Map Class
-set_option synthInstance.etaExperiment true in
--- Porting note: `nolint simpNF` is required because we don't have η for classes. (lean4#2074)
-@[simp] --, nolint simpNF]
+@[simp]
theorem projKerOfRightInverse_apply_idem [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂)
(f₂ : M₂ →SL[σ₂₁] M) (h : Function.RightInverse f₂ f₁) (x : LinearMap.ker f₁) :
f₁.projKerOfRightInverse f₂ h x = x := by
-- porting note: should be `ext1; simp` but TC search fails
+ -- check this during post lean4#2210 cleanup
ext1
refine sub_eq_self.2 ?_
calc f₂ (f₁ x) = f₂ 0 := by rw [x.2.out]
_ = 0 := f₂.map_zero
#align continuous_linear_map.proj_ker_of_right_inverse_apply_idem ContinuousLinearMap.projKerOfRightInverse_apply_idem
--- Porting note: cannot synth →L
-set_option synthInstance.etaExperiment true in
@[simp]
theorem projKerOfRightInverse_comp_inv [TopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂)
(f₂ : M₂ →SL[σ₂₁] M) (h : Function.RightInverse f₂ f₁) (y : M₂) :
@@ -1566,8 +1517,6 @@ section DivisionMonoid
variable {R M : Type _}
--- Porting note: cannot synth Module R R
-set_option synthInstance.etaExperiment true in
/-- A nonzero continuous linear functional is open. -/
protected theorem isOpenMap_of_ne_zero [TopologicalSpace R] [DivisionRing R] [ContinuousSub R]
[AddCommGroup M] [TopologicalSpace M] [ContinuousAdd M] [Module R M] [ContinuousSMul R M]
@@ -1583,6 +1532,7 @@ end DivisionMonoid
section SmulMonoid
-- Porting note: This is required to prevent timeouts.
+-- Check this again during lean4#2210 cleanup.
local infixr:73 " •SL " => @HSMul.hSMul _ _ _ (@instHSMul _ _ (@MulAction.toSMul _ _ _
(@ContinuousLinearMap.mulAction _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _)))
@@ -1672,6 +1622,7 @@ instance module : Module S₃ (M →SL[σ₁₃] M₃) where
#align continuous_linear_map.module ContinuousLinearMap.module
-- Porting note: Instances should be specified, or timeouts.
+-- Check this again during lean4#2210 cleanup.
instance isCentralScalar [Module S₃ᵐᵒᵖ M₃] [IsCentralScalar S₃ M₃] :
@IsCentralScalar S₃ (M →SL[σ₁₃] M₃)
(@SMulZeroClass.toSMul _ _ _ (@SMulWithZero.toSMulZeroClass _ _ _ _
@@ -1763,9 +1714,8 @@ variable {R : Type _} [CommRing R] {M : Type _} [TopologicalSpace M] [AddCommGro
variable [TopologicalAddGroup M₂] [ContinuousConstSMul R M₂]
--- Porting note: mismatched types
-set_option synthInstance.etaExperiment true in
-- Porting note: Instances should be specified, or timeouts.
+-- Check this again during lean4#2210 cleanup.
instance algebra : Algebra R (M₂ →L[R] M₂) :=
@Algebra.ofModule _ _ _ _ ContinuousLinearMap.module smul_comp fun _ _ _ => comp_smul _ _ _
#align continuous_linear_map.algebra ContinuousLinearMap.algebra
@@ -1781,8 +1731,6 @@ variable {A M M₂ : Type _} [Ring A] [AddCommGroup M] [AddCommGroup M₂] [Modu
[TopologicalSpace M] [TopologicalSpace M₂] (R : Type _) [Ring R] [Module R M] [Module R M₂]
[LinearMap.CompatibleSMul M M₂ R A]
--- Porting note: mismatched types
-set_option synthInstance.etaExperiment true in
/-- If `A` is an `R`-algebra, then a continuous `A`-linear map can be interpreted as a continuous
`R`-linear map. We assume `LinearMap.CompatibleSMul M M₂ R A` to match assumptions of
`LinearMap.map_smul_of_tower`. -/
@@ -1792,23 +1740,17 @@ def restrictScalars (f : M →L[A] M₂) : M →L[R] M₂ :=
variable {R}
--- Porting note: mismatched types
-set_option synthInstance.etaExperiment true in
@[simp] -- @[norm_cast] -- Porting note: This theorem can't be an `norm_cast` theorem.
theorem coe_restrictScalars (f : M →L[A] M₂) :
(f.restrictScalars R : M →ₗ[R] M₂) = (f : M →ₗ[A] M₂).restrictScalars R :=
rfl
#align continuous_linear_map.coe_restrict_scalars ContinuousLinearMap.coe_restrictScalars
--- Porting note: cannot coerce to function
-set_option synthInstance.etaExperiment true in
@[simp]
theorem coe_restrictScalars' (f : M →L[A] M₂) : ⇑(f.restrictScalars R) = f :=
rfl
#align continuous_linear_map.coe_restrict_scalars' ContinuousLinearMap.coe_restrictScalars'
--- Porting note: cannot synth OfNat
-set_option synthInstance.etaExperiment true in
@[simp]
theorem restrictScalars_zero : (0 : M →L[A] M₂).restrictScalars R = 0 :=
rfl
@@ -1818,8 +1760,6 @@ section
variable [TopologicalAddGroup M₂]
--- Porting note: mismatched types
-set_option synthInstance.etaExperiment true in
@[simp]
theorem restrictScalars_add (f g : M →L[A] M₂) :
(f + g).restrictScalars R = f.restrictScalars R + g.restrictScalars R :=
@@ -1846,8 +1786,6 @@ theorem restrictScalars_smul (c : S) (f : M →L[A] M₂) :
variable (A M M₂ R S)
variable [TopologicalAddGroup M₂]
--- Porting note: mismatched types
-set_option synthInstance.etaExperiment true in
/-- `ContinuousLinearMap.restrictScalars` as a `LinearMap`. See also
`ContinuousLinearMap.restrictScalarsL`. -/
def restrictScalarsₗ : (M →L[A] M₂) →ₗ[S] M →L[R] M₂ where
@@ -1858,8 +1796,6 @@ def restrictScalarsₗ : (M →L[A] M₂) →ₗ[S] M →L[R] M₂ where
variable {A M M₂ R S}
--- Porting note: cannot coerce to function
-set_option synthInstance.etaExperiment true in
@[simp]
theorem coe_restrictScalarsₗ : ⇑(restrictScalarsₗ A M M₂ R S) = restrictScalars R :=
rfl
@@ -2405,15 +2341,11 @@ variable {R : Type _} [Ring R] {R₂ : Type _} [Ring R₂] {M : Type _} [Topolog
variable {σ₁₂ : R →+* R₂} {σ₂₁ : R₂ →+* R} [RingHomInvPair σ₁₂ σ₂₁] [RingHomInvPair σ₂₁ σ₁₂]
--- Porting note: cannot synth RingHomInvPair
-set_option synthInstance.etaExperiment true in
-- @[simp] -- Porting note: simp can prove this
theorem map_sub (e : M ≃SL[σ₁₂] M₂) (x y : M) : e (x - y) = e x - e y :=
(e : M →SL[σ₁₂] M₂).map_sub x y
#align continuous_linear_equiv.map_sub ContinuousLinearEquiv.map_sub
--- Porting note: cannot synth RingHomInvPair
-set_option synthInstance.etaExperiment true in
-- @[simp] -- Porting note: simp can prove this
theorem map_neg (e : M ≃SL[σ₁₂] M₂) (x : M) : e (-x) = -e x :=
(e : M →SL[σ₁₂] M₂).map_neg x
@@ -2427,8 +2359,6 @@ section
variable [TopologicalAddGroup M]
--- Porting note: cannot synth RingHomInvPair
-set_option synthInstance.etaExperiment true in
/-- An invertible continuous linear map `f` determines a continuous equivalence from `M` to itself.
-/
def ofUnit (f : (M →L[R] M)ˣ) : M ≃L[R] M where
@@ -2449,8 +2379,6 @@ def ofUnit (f : (M →L[R] M)ˣ) : M ≃L[R] M where
continuous_invFun := f.inv.continuous
#align continuous_linear_equiv.of_unit ContinuousLinearEquiv.ofUnit
--- Porting note: cannot synth RingHomInvPair and mismatched types
-set_option synthInstance.etaExperiment true in
/-- A continuous equivalence from `M` to itself determines an invertible continuous linear map. -/
def toUnit (f : M ≃L[R] M) : (M →L[R] M)ˣ where
val := f
@@ -2465,8 +2393,6 @@ def toUnit (f : M ≃L[R] M) : (M →L[R] M)ˣ where
variable (R M)
--- Porting note: cannot synth RingHomInvPair
-set_option synthInstance.etaExperiment true in
/-- The units of the algebra of continuous `R`-linear endomorphisms of `M` is multiplicatively
equivalent to the type of continuous linear equivalences between `M` and itself. -/
def unitsEquiv : (M →L[R] M)ˣ ≃* M ≃L[R] M where
@@ -2483,8 +2409,6 @@ def unitsEquiv : (M →L[R] M)ˣ ≃* M ≃L[R] M where
rfl
#align continuous_linear_equiv.units_equiv ContinuousLinearEquiv.unitsEquiv
--- Porting note: mismatched types
-set_option synthInstance.etaExperiment true in
@[simp]
theorem unitsEquiv_apply (f : (M →L[R] M)ˣ) (x : M) : unitsEquiv R M f x = (f : M →L[R] M) x :=
rfl
@@ -2497,8 +2421,6 @@ section
variable (R) [TopologicalSpace R]
variable [ContinuousMul R]
--- Porting note: cannot synth RingHomInvPair
-set_option synthInstance.etaExperiment true in
/-- Continuous linear equivalences `R ≃L[R] R` are enumerated by `Rˣ`. -/
def unitsEquivAut : Rˣ ≃ R ≃L[R] R where
toFun u :=
@@ -2513,22 +2435,16 @@ def unitsEquivAut : Rˣ ≃ R ≃L[R] R where
variable {R}
--- Porting note: mismatched synthed arguments
-set_option synthInstance.etaExperiment true in
@[simp]
theorem unitsEquivAut_apply (u : Rˣ) (x : R) : unitsEquivAut R u x = x * u :=
rfl
#align continuous_linear_equiv.units_equiv_aut_apply ContinuousLinearEquiv.unitsEquivAut_apply
--- Porting note: mismatched synthed arguments
-set_option synthInstance.etaExperiment true in
@[simp]
theorem unitsEquivAut_apply_symm (u : Rˣ) (x : R) : (unitsEquivAut R u).symm x = x * ↑u⁻¹ :=
rfl
#align continuous_linear_equiv.units_equiv_aut_apply_symm ContinuousLinearEquiv.unitsEquivAut_apply_symm
--- Porting note: mismatched synthed arguments
-set_option synthInstance.etaExperiment true in
@[simp]
theorem unitsEquivAut_symm_apply (e : R ≃L[R] R) : ↑((unitsEquivAut R).symm e) = e 1 :=
rfl
@@ -2538,8 +2454,6 @@ end
variable [Module R M₂] [TopologicalAddGroup M]
--- Porting note: cannot synth RingHomInvPair
-set_option synthInstance.etaExperiment true in
/-- A pair of continuous linear maps such that `f₁ ∘ f₂ = id` generates a continuous
linear equivalence `e` between `M` and `M₂ × f₁.ker` such that `(e x).2 = x` for `x ∈ f₁.ker`,
`(e x).1 = f₁ x`, and `(e (f₂ y)).2 = 0`. The map is given by `e x = (f₁ x, x - f₂ (f₁ x))`. -/
@@ -2555,16 +2469,12 @@ def equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M) (h : Fun
ContinuousLinearMap.projKerOfRightInverse_apply_idem, Prod.mk_add_mk, add_zero, zero_add]
#align continuous_linear_equiv.equiv_of_right_inverse ContinuousLinearEquiv.equivOfRightInverse
--- Porting note: mismatched synthed arguments
-set_option synthInstance.etaExperiment true in
@[simp]
theorem fst_equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
(h : Function.RightInverse f₂ f₁) (x : M) : (equivOfRightInverse f₁ f₂ h x).1 = f₁ x :=
rfl
#align continuous_linear_equiv.fst_equiv_of_right_inverse ContinuousLinearEquiv.fst_equivOfRightInverse
--- Porting note: mismatched synthed arguments
-set_option synthInstance.etaExperiment true in
@[simp]
theorem snd_equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
(h : Function.RightInverse f₂ f₁) (x : M) :
@@ -2572,8 +2482,6 @@ theorem snd_equivOfRightInverse (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
rfl
#align continuous_linear_equiv.snd_equiv_of_right_inverse ContinuousLinearEquiv.snd_equivOfRightInverse
--- Porting note: mismatched synthed arguments and cannot synth semilinearmapclass
-set_option synthInstance.etaExperiment true in
@[simp]
theorem equivOfRightInverse_symm_apply (f₁ : M →L[R] M₂) (f₂ : M₂ →L[R] M)
(h : Function.RightInverse f₂ f₁) (y : M₂ × ker f₁) :
@@ -2676,8 +2584,6 @@ variable [AddCommGroup M] [TopologicalAddGroup M] [Module R M]
variable [AddCommGroup M₂] [Module R M₂]
--- Porting note: cannot synth RingHomInvPair
-set_option synthInstance.etaExperiment true in
@[simp]
theorem ring_inverse_equiv (e : M ≃L[R] M) : Ring.inverse ↑e = inverse (e : M →L[R] M) := by
suffices Ring.inverse ((ContinuousLinearEquiv.unitsEquiv _ _).symm e : M →L[R] M) = inverse ↑e by
@@ -2686,8 +2592,6 @@ theorem ring_inverse_equiv (e : M ≃L[R] M) : Ring.inverse ↑e = inverse (e :
rfl
#align continuous_linear_map.ring_inverse_equiv ContinuousLinearMap.ring_inverse_equiv
--- Porting note: cannot synth RingHomInvPair
-set_option synthInstance.etaExperiment true in
/-- The function `ContinuousLinearEquiv.inverse` can be written in terms of `Ring.inverse` for the
ring of self-maps of the domain. -/
theorem to_ring_inverse (e : M ≃L[R] M₂) (f : M →L[R] M₂) :
@@ -2724,23 +2628,17 @@ variable {R : Type _} [Ring R] {M : Type _} [TopologicalSpace M] [AddCommGroup M
open ContinuousLinearMap
--- Porting note: cannot coerce to function
-set_option synthInstance.etaExperiment true in
/-- A submodule `p` is called *complemented* if there exists a continuous projection `M →ₗ[R] p`. -/
def ClosedComplemented (p : Submodule R M) : Prop :=
∃ f : M →L[R] p, ∀ x : p, f x = x
#align submodule.closed_complemented Submodule.ClosedComplemented
--- Porting note: cannot synth SemilinearClassMap
-set_option synthInstance.etaExperiment true in
theorem ClosedComplemented.has_closed_complement {p : Submodule R M} [T1Space p]
(h : ClosedComplemented p) :
∃ (q : Submodule R M) (_ : IsClosed (q : Set M)), IsCompl p q :=
Exists.elim h fun f hf => ⟨ker f, isClosed_ker f, LinearMap.isCompl_of_proj hf⟩
#align submodule.closed_complemented.has_closed_complement Submodule.ClosedComplemented.has_closed_complement
--- Porting note: cannot synth RingHomCompTriple
-set_option synthInstance.etaExperiment true in
protected theorem ClosedComplemented.isClosed [TopologicalAddGroup M] [T1Space M]
{p : Submodule R M} (h : ClosedComplemented p) : IsClosed (p : Set M) := by
rcases h with ⟨f, hf⟩
@@ -2748,8 +2646,6 @@ protected theorem ClosedComplemented.isClosed [TopologicalAddGroup M] [T1Space M
exact this ▸ isClosed_ker _
#align submodule.closed_complemented.is_closed Submodule.ClosedComplemented.isClosed
--- Porting note: cannot synth OfNat
-set_option synthInstance.etaExperiment true in
@[simp]
theorem closedComplemented_bot : ClosedComplemented (⊥ : Submodule R M) :=
⟨0, fun x => by simp only [zero_apply, eq_zero_of_bot_submodule x]⟩
@@ -2762,8 +2658,6 @@ theorem closedComplemented_top : ClosedComplemented (⊤ : Submodule R M) :=
end Submodule
--- Porting note: cannot synth SemilinearMapClass
-set_option synthInstance.etaExperiment true in
theorem ContinuousLinearMap.closedComplemented_ker_of_rightInverse {R : Type _} [Ring R]
{M : Type _} [TopologicalSpace M] [AddCommGroup M] {M₂ : Type _} [TopologicalSpace M₂]
[AddCommGroup M₂] [Module R M] [Module R M₂] [TopologicalAddGroup M] (f₁ : M →L[R] M₂)
sSup
/iSup
(#3938)
As discussed on Zulip
supₛ
→ sSup
infₛ
→ sInf
supᵢ
→ iSup
infᵢ
→ iInf
bsupₛ
→ bsSup
binfₛ
→ bsInf
bsupᵢ
→ biSup
binfᵢ
→ biInf
csupₛ
→ csSup
cinfₛ
→ csInf
csupᵢ
→ ciSup
cinfᵢ
→ ciInf
unionₛ
→ sUnion
interₛ
→ sInter
unionᵢ
→ iUnion
interᵢ
→ iInter
bunionₛ
→ bsUnion
binterₛ
→ bsInter
bunionᵢ
→ biUnion
binterᵢ
→ biInter
Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>
@@ -1259,19 +1259,19 @@ theorem proj_pi (f : ∀ i, M₂ →L[R] φ i) (i : ι) : (proj i).comp (pi f) =
ext fun _c => rfl
#align continuous_linear_map.proj_pi ContinuousLinearMap.proj_pi
-theorem infᵢ_ker_proj : (⨅ i, ker (proj i : (∀ i, φ i) →L[R] φ i) : Submodule R (∀ i, φ i)) = ⊥ :=
- LinearMap.infᵢ_ker_proj
-#align continuous_linear_map.infi_ker_proj ContinuousLinearMap.infᵢ_ker_proj
+theorem iInf_ker_proj : (⨅ i, ker (proj i : (∀ i, φ i) →L[R] φ i) : Submodule R (∀ i, φ i)) = ⊥ :=
+ LinearMap.iInf_ker_proj
+#align continuous_linear_map.infi_ker_proj ContinuousLinearMap.iInf_ker_proj
variable (R φ)
/-- If `I` and `J` are complementary index sets, the product of the kernels of the `J`th projections
of `φ` is linearly equivalent to the product over `I`. -/
-def infᵢKerProjEquiv {I J : Set ι} [DecidablePred fun i => i ∈ I] (hd : Disjoint I J)
+def iInfKerProjEquiv {I J : Set ι} [DecidablePred fun i => i ∈ I] (hd : Disjoint I J)
(hu : Set.univ ⊆ I ∪ J) :
(⨅ i ∈ J, ker (proj i : (∀ i, φ i) →L[R] φ i) : Submodule R (∀ i, φ i)) ≃L[R] ∀ i : I, φ i
where
- toLinearEquiv := LinearMap.infᵢKerProjEquiv R φ hd hu
+ toLinearEquiv := LinearMap.iInfKerProjEquiv R φ hd hu
continuous_toFun :=
continuous_pi fun i => by
have :=
@@ -1289,7 +1289,7 @@ def infᵢKerProjEquiv {I J : Set ι} [DecidablePred fun i => i ∈ I] (hd : Dis
(0 : ((i : I) → φ i) →ₗ[R] φ i)))
split_ifs <;> [apply continuous_apply, exact continuous_zero])
_
-#align continuous_linear_map.infi_ker_proj_equiv ContinuousLinearMap.infᵢKerProjEquiv
+#align continuous_linear_map.infi_ker_proj_equiv ContinuousLinearMap.iInfKerProjEquiv
end Pi
@@ -1134,10 +1134,10 @@ theorem coe_prodMap [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (f
#align continuous_linear_map.coe_prod_map ContinuousLinearMap.coe_prodMap
@[simp, norm_cast]
-theorem coe_prod_map [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (f₁ : M₁ →L[R₁] M₂)
+theorem coe_prodMap' [Module R₁ M₂] [Module R₁ M₃] [Module R₁ M₄] (f₁ : M₁ →L[R₁] M₂)
(f₂ : M₃ →L[R₁] M₄) : ⇑(f₁.prodMap f₂) = Prod.map f₁ f₂ :=
rfl
-#align continuous_linear_map.coe_prod_map' ContinuousLinearMap.coe_prod_map
+#align continuous_linear_map.coe_prod_map' ContinuousLinearMap.coe_prodMap'
/-- The continuous linear map given by `(x, y) ↦ f₁ x + f₂ y`. -/
def coprod [Module R₁ M₂] [Module R₁ M₃] [ContinuousAdd M₃] (f₁ : M₁ →L[R₁] M₃)
by
s! (#3825)
This PR puts, with one exception, every single remaining by
that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh
. The exception is when the by
begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.
Essentially this is s/\n *by$/ by/g
, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated by
s".
@@ -1273,8 +1273,7 @@ def infᵢKerProjEquiv {I J : Set ι} [DecidablePred fun i => i ∈ I] (hd : Dis
where
toLinearEquiv := LinearMap.infᵢKerProjEquiv R φ hd hu
continuous_toFun :=
- continuous_pi fun i =>
- by
+ continuous_pi fun i => by
have :=
@continuous_subtype_val _ _ fun x =>
x ∈ (⨅ i ∈ J, ker (proj i : (∀ i, φ i) →L[R] φ i) : Submodule R (∀ i, φ i))
@@ -2811,4 +2810,3 @@ instance t3_quotient_of_isClosed [TopologicalAddGroup M] [IsClosed (S : Set M)]
end Submodule
end Quotient
-
@@ -326,11 +326,11 @@ abbrev ContinuousLinearEquivClass (F : Type _) (R : outParam (Type _)) [Semiring
namespace ContinuousSemilinearEquivClass
-variable (F : Type _) {R : Type _} {S : Type _} {_ : Semiring R} {_ : Semiring S} (σ : R →+* S)
- {σ' : S →+* R} {_ : RingHomInvPair σ σ'} {_ : RingHomInvPair σ' σ}
- (M : Type _) {_ : TopologicalSpace M} {_ : AddCommMonoid M}
- (M₂ : Type _) {_ : TopologicalSpace M₂} {_ : AddCommMonoid M₂}
- {_ : Module R M} {_ : Module S M₂}
+variable (F : Type _) {R : Type _} {S : Type _} [Semiring R] [Semiring S] (σ : R →+* S)
+ {σ' : S →+* R} [RingHomInvPair σ σ'] [RingHomInvPair σ' σ]
+ (M : Type _) [TopologicalSpace M] [AddCommMonoid M]
+ (M₂ : Type _) [TopologicalSpace M₂] [AddCommMonoid M₂]
+ [Module R M] [Module S M₂]
-- `σ'` becomes a metavariable, but it's OK since it's an outparam
instance (priority := 100) continuousSemilinearMapClass
Co-authored-by: Moritz Doll <moritz.doll@googlemail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Yury Kudryashov <urkud@urkud.name> Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>
The unported dependencies are